tag:blogger.com,1999:blog-82859292024-03-13T23:20:06.349-05:00Conway's Life: Work in ProgressMiscellaneous topics in Conway's Game of Life
-- unfinished projects of all kinds and conditionsDave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.comBlogger42125tag:blogger.com,1999:blog-8285929.post-65681968325322225572022-11-18T00:45:00.006-05:002022-11-18T11:25:32.600-05:00In Conway's Life, Fifteen Gliders Can Build Anything* !<p>A huge milestone in Conway's Game of Life history was finally reached on November 9, 2022. Pavel Grankovskiy completed the final subtask needed to build a complete <a href="https://conwaylife.com/wiki/Reverse_caber-tosser#MathAndCode%27s_RCT" target="_blank">RCT16</a> ("Reverse Caber Tosser", 16 gliders) <a href="https://conwaylife.com/forums/viewtopic.php?p=153348#p153348" target="_blank">demonstration pattern</a>.
<p>Some experimentation with variations on the theme proved that it was possible to perform the same trick without the sixteenth glider in the far northeast corner. Less than a week later, a revised <a href="https://conwaylife.com/forums/viewtopic.php?p=153609#p153609" target="_blank">"RCT15" demo pattern</a> was made available, with scripts to make it easier to watch the action. This was followed soon after by an actual full RCT15 macrocell pattern containing just 15 gliders, which would build the same sample object as the demo pattern eventually -- if any existing software were capable of running the pattern for long enough!
<p>Both of these RCT variants use an extraordinarily small number of gliders to construct a large and complex Life pattern. The 15- and 16-glider "demo" and "full" RCT patterns all produce exactly the same <a href="https://conwaylife.com/wiki/Seed" target="_blank">seed pattern</a> for <a href="https://conwaylife.com/ref/DRH/dec.counter.html target="_blank"">Alan Hensel's decimal counter</a> -- a pattern over 1200 cells wide and 600 cells high. In the final stages, the patterns evolve into this:
<p><div class="rle">
<div class="codebox">
<div class="selall">Code:
<a href="#" onclick="selectCode(this); return false;">Select all</a>
</div>
<div><code>x = 1383, y = 627, rule = B3/S23<br />
388b2o169b2o$389bo169bo$389bobo165bobo$390b2o165b2o8$386b2o173b2o$385b<br />
obo173bobo$385b2o175b2o5$384b2o177b2o$383bo2bo175bo2bo$384bobo175bobo$<br />
385bo177bo6$364bo219bo$363bobo217bobo$363b2o219b2o4$370b2o205b2o$369bo<br />
bo205bobo$369b2o207b2o6$403b3o137b3o2$417bo113bo$416bobo111bobo$366b2o<br />
48b2o113b2o48b2o$366b2o42b2o125b2o42b2o$409bobo125bobo$383b2o24b2o127b<br />
2o24b2o$382bo2bo177bo2bo$352bo30b2o179b2o30bo$276bo74bobo241bobo$275bo<br />
bo74b2o241b2o$276b2o100b2o38b2o109b2o38b2o$378b2o38b2o109b2o38b2o2$<br />
385bo15b2o143b2o15bo$384bobo13bo2bo42bo55bo42bo2bo13bobo$385bobo13b2o<br />
42bobo53bobo42b2o13bobo$386b2o40bo16b2o55b2o16bo40b2o$428bo91bo$428bo<br />
91bo2$381b2o183b2o$381b2o23b2o133b2o23b2o$405bo2bo25b2o77b2o25bo2bo$<br />
405bo2bo24bobo77bobo24bo2bo$406b2o25b2o79b2o25b2o$377b2o191b2o$376bobo<br />
191bobo$377bo193bo$403b2o139b2o$403b2o37b2o61b2o37b2o$442b2o61b2o2$<br />
413b2o10b2o95b2o10b2o$244b2o167b2o9bo2bo93bo2bo9b2o$243bobo179b2o95b2o<br />
$244bo5$430b2o85b2o$429bo2bo83bo2bo$429bo2bo83bo2bo$430b2o85b2o4$427b<br />
2o91b2o$427b2o91b2o$293b2o$292bobo$293bo4$153b2o$152bobo$151bobo$152bo<br />
131b2o$149bo135bo$148bobo131b3o$149b2o131bo16bo$200b2o96bobo$199bobo<br />
96b2o$132bo57b2o6bobo$131bobo55bobo7bo83b2o$127b2o3bo55bobo11b2o78bo2b<br />
o20bo$127bobo42bo16bo12bobo77bo2bo19bobo$128bo42bobo12bo16bo16bo62b2o<br />
21bo$144bo25bobo12bobo31bobo$143bobo24b2o14b2o27b2o3bo$142bobo29b2o39b<br />
obo82b2o$121bo20b2o30bobo39bo82bobo104b2o$120bobo52bo124bo106bo$119bob<br />
o285bobo$119b2o287b2o$2b2o119b2o$2bobo42b2o74bobo$3bo42bobo75bo$37b2o<br />
6bobo$bo34bobo7bo43b2o249bo380bo$obo32bobo11b2o39bobo247bobo80b2o99b2o<br />
195bobo$bo17bo16bo12bobo39bo248b2o81b2o99b2o161b2o33b2o$18bobo12bo16bo<br />
74b2o158b2o117b2o281bobo$17bobo12bobo54bo34bobo157bobo116bobo34b2o65b<br />
2o179bo$17b2o14b2o53bobo32bobo157bobo117b2o34bo2bo63bo2bo$21b2o61b2o3b<br />
o17bo16bo159bo155b2o65b2o$21bobo59bobo20bobo12bo$22bo51b2o6bobo20bobo<br />
12bobo$73bobo7bo21b2o14b2o312b2o75b2o$72bobo11b2o21b2o291b2o31b2o75b2o<br />
$73bo12bobo20bobo289bo2bo47b2o41b2o511bo$70bo16bo22bo291bobo37bo9b2o<br />
41b2o9bo500bobo$69bobo331bo37bobo61bobo470b2o27b2o$70b2o208bo161bobo<br />
59bobo222bo247bobo31bo$279bobo161b2o59b2o222bobo247bo31bobo$275b2o3bo<br />
260b2o185b2o281bobo$275bobo263bo438bo31b2o$276bo22bo123b2o114bobo437bo<br />
bo$298bobo81bo39bobo13b2o69b2o28b2o439bo$297bobo81bobo39bo14b2o69b2o$<br />
297b2o82b2o144b2o461bo$527bobo411b2o46bobo$528bo367b2o24b2o16bobo47bob<br />
o$291bo12bo591bobo23bobo16bo49b2o$290bobo10bobo82b2o507bobo6b2o15bobo<br />
84b2o$269bo19bobo11b2o82bobo508bo7bobo15bo18bo66bobo$268bobo18b2o96b2o<br />
154b2o349b2o11bobo32bobo66bobo$267bobo273bobo347bobo12bo34bo3b2o63bo$<br />
267b2o275b2o331bo16bo16bo35bobo$271b2o23bo579bobo31bobo35bobo$271bobo<br />
21bobo579bo3b2o27b2o37bo$272bo8bo13b2o583bobo62b2o$280bobo25b2o111b3o<br />
457bo62bobo$279bobo25bobo235b2o318bo79bo$279b2o27bo126bo108bo2bo316bob<br />
o$434bobo107bobo318bobo$384b2o48b2o109bo320b2o$286bo97b2o42b2o$272bo<br />
12bobo139bobo$271bobo11b2o14b2o98b2o24b2o$270bobo27bobo97bo2bo418b2o$<br />
270b2o29bo68bo30b2o419bobo$369bobo194bo256bobo$370b2o193bobo256bo$264b<br />
o12bo118b2o38b2o128b2o252b2o$263bobo10bobo117b2o38b2o381bobo$262bobo<br />
11b2o87b2o436bo16bo$262b2o100bobo36bo15b2o381bobo$292b2o71bo36bobo13bo<br />
2bo42bo94b2o242bo3b2o21b2o$291bobo109bobo13b2o42bobo93bobo244bobo20bob<br />
o$256bo12bo22bo111b2o40bo16b2o95b2o210bo34bo22bo$255bobo10bobo175bo<br />
324bobo17bo$254bobo11b2o176bo324b2o17bobo39bo$254b2o467b2o50bo15bobo<br />
37bobo$399b2o322bobo48bobo15b2o38bo$399b2o23b2o298bobo48bobo$248bo12bo<br />
22b2o137bo2bo25b2o71b3o197bo50b2o$247bobo10bobo20bobo137bo2bo24bobo<br />
230bo$246bobo11b2o22bo139b2o25b2o60bo169bobo$246b2o147b2o115bobo169b2o<br />
$394bobo116b2o48b2o$395bo123b2o42b2o$240bo12bo167b2o54b2o40bobo$239bob<br />
o10bobo22b2o142b2o37b2o15bobo40b2o24b2o$238bobo11b2o22bobo181b2o16bo<br />
66bo2bo180bo$238b2o37bo268b2o30bo149bobo$431b2o10b2o132bobo149bo3b2o$<br />
431b2o9bo2bo131b2o153bobo$232bo12bo197b2o66b2o38b2o180bo$231bobo10bobo<br />
264b2o38b2o$230bobo11b2o24b2o$230b2o37bobo256b2o15bo$270bo213bo42bo2bo<br />
13bobo159bo33bo$483bobo42b2o13bobo159bobo31bobo$224bo12bo210b2o34b2o<br />
16bo40b2o161bobo31bobo$223bobo10bobo208bo2bo51bo101b2o101b2o32b2o$222b<br />
obo11b2o209bo2bo51bo101bobo130b2o$222b2o39b2o183b2o155bo130bobo$262bob<br />
o283b2o151bo12bo22bo$263bo196b2o61b2o23b2o150bobo10bobo$216bo12bo229bo<br />
2bo32b2o25bo2bo175b2o11bobo$215bobo10bobo214b2o13b2o33bobo24bo2bo189b<br />
2o$214bobo11b2o215b2o49b2o25b2o$214b2o336b2o$256b2o294bobo154bo12bo$<br />
255bobo295bo154bobo10bobo$208bo12bo34bo200b2o67b2o181b2o11bobo$207bobo<br />
10bobo233bo2bo27b2o37b2o195b2o$206bobo11b2o234bobo28b2o206b2o$206b2o<br />
249bo237bobo$445b2o57b2o10b2o178bo20bo12bo$249b2o194bobo55bo2bo9b2o<br />
198bobo10bobo$200bo12bo34bobo195b2o56b2o211b2o11bobo$199bobo10bobo34bo<br />
481b2o$198bobo11b2o235bo$198b2o248bobo251b2o$449b2o251bobo20bo12bo$<br />
703bo20bobo10bobo$192bo12bo36b2o255b2o93b2o4b2o123b2o11bobo$191bobo10b<br />
obo34bobo254bo2bo91bo2bo4bo137b2o$190bobo11b2o36bo255bo2bo91bo2bo4bobo<br />
$190b2o307b2o93b2o6b2o$709b2o22bo12bo$709bobo20bobo10bobo$184bo12bo<br />
512bo22b2o11bobo$183bobo10bobo36b2o265b2o243b2o$182bobo11b2o36bobo265b<br />
2o$182b2o51bo$741bo12bo$716b2o22bobo10bobo$176bo12bo526bobo22b2o11bobo<br />
$175bobo10bobo526bo37b2o$174bobo11b2o38b2o$174b2o51bobo$228bo520bo12bo<br />
$472b2o274bobo10bobo$168bo12bo290b2o249b2o24b2o11bobo$167bobo10bobo<br />
540bobo37b2o$166bobo11b2o273b2o267bo$166b2o53b2o231bo2bo$220bobo232b2o<br />
300bo12bo$221bo534bobo10bobo$160bo12bo583b2o11bobo$159bobo10bobo285b2o<br />
268b2o39b2o$158bobo11b2o286b2o268bobo$158b2o283b2o286bo$214b2o227b2o9b<br />
o310bo12bo$213bobo237bobo308bobo10bobo$152bo12bo48bo237bobo310b2o11bob<br />
o$151bobo10bobo285b2o325b2o$150bobo11b2o304b2o265b2o$150b2o318bobo264b<br />
obo$471bo266bo34bo12bo$207b2o248b2o313bobo10bobo$144bo12bo48bobo248b2o<br />
314b2o11bobo$143bobo10bobo48bo579b2o$142bobo11b2o$142b2o600b2o$453b2o<br />
68b2o219bobo34bo12bo$452bobo20b2o46bobo219bo34bobo10bobo$149bo50b2o<br />
251bo21b2o47bo256b2o11bobo$148bobo48bobo593b2o$148b2o50bo291b2o$491bo<br />
2bo$492b2o257b2o36bo12bo$454b2o295bobo34bobo10bobo$454bobo295bo36b2o<br />
11bobo$193b2o260bo31b2o314b2o$192bobo292b2o42b2o$193bo310b2o24bo2bo$<br />
494bo9b2o25b2o264bo12bo$141b2o350bobo262b2o36bobo10bobo$141b2o351bobo<br />
261bobo36b2o11bobo$495b2o262bo51b2o$186b2o$185bobo340b2o$186bo340bo2bo<br />
274bo12bo$473b2o15b2o35bobo274bobo10bobo$466bo5bo2bo14b2o36bo236b2o38b<br />
2o11bobo$465bobo5b2o290bobo51b2o$465bo2bo297bo$179b2o285b2o$178bobo<br />
279b2o351bo12bo$179bo279bobo35b2o313bobo10bobo$460bo36bo315b2o11bobo$<br />
498b3o271b2o53b2o$482b2o16bo95bo175bobo$481bobo111bobo175bo$172b2o308b<br />
o55b2o56b2o223bo12bo$171bobo256bo107bobo279bobo10bobo$172bo256bobo107b<br />
o281b2o11bobo$429b2o67b2o335b2o$497bo2bo278b2o$497bobo279bobo$320bo73b<br />
o103bo281bo48bo12bo$319bobo71bobo46b2o161bo222bobo10bobo$319b2o72b2o<br />
47bobo159bobo222b2o11bobo$443bo57b2o102b2o236b2o$501bobo$502bo283b2o$<br />
786bobo48bo$313bo473bo48bobo$312bobo297bo224b2o$312b2o297bobo239bo$<br />
612b2o238bobo$853bobo$793b2o59b2o$477b2o314bobo$306bo170bobo314bo$305b<br />
obo170bo140bo228bo$305b2o311bobo226bobo$619b2o227b2o2$800b2o$800bobo$<br />
801bo$298bo55b2o270bo$297bobo54b2o198b2o69bobo$297b2o255b2o70b2o2$807b<br />
2o46b2o$807bobo45b2o$808bo$633bo$290bo341bobo$289bobo341b2o$289b2o56b<br />
2o211b2o$346bobo211bobo251b2o$347bo213bo252bobo$815bo$640bo$283bo69b2o<br />
199b2o83bobo$282bobo54b2o11bobo199bobo83b2o$282b2o54bobo10bobo201bobo$<br />
339bo12bo203bo13b2o$472b2o96bobo$471bobo97bo$345b2o125bo174bo176b2o$<br />
276bo54b2o11bobo299bobo175bobo$275bobo52bobo10bobo218b2o81b2o176bo$<br />
275b2o54bo12bo219bobo11b2o$565bobo10bobo$566bo12bo$337b2o$336bobo315bo<br />
$269bo52b2o11bobo234b2o79bobo$268bobo50bobo12bo235bobo11b2o66b2o$268b<br />
2o52bo250bobo10bobo$574bo12bo2$328b2o$327bobo250b2o79bo$313b2o11bobo<br />
251bobo11b2o64bobo$261bo50bobo12bo253bobo10bobo64b2o$260bobo50bo268bo<br />
12bo$260b2o2$319b2o267b2o$305b2o11bobo159bo107bobo11b2o$304bobo10bobo<br />
159bobo107bobo10bobo64bo$254bo50bo12bo161bobo107bo12bo64bobo$253bobo<br />
225b2o186b2o$253b2o263bo$311b2o204bobo76b2o$297b2o11bobo162bo42bo77bob<br />
o11b2o$296bobo10bobo162bobo120bobo10bobo$297bo12bo164b2o43bo77bo12bo$<br />
247bo271bobo$246bobo270b2o157bo$246b2o55b2o299b2o71bobo$289b2o11bobo<br />
299bobo11b2o58b2o$288bobo10bobo301bobo10bobo$289bo12bo303bo12bo$382bo$<br />
240bo140bobo$239bobo53b2o85b2o136b2o90b2o71bo$239b2o53bobo223bobo89bob<br />
o11b2o56bobo$280b2o11bobo225bobo89bobo10bobo56b2o$279bobo12bo227bo91bo<br />
12bo$42bo237bo625bo$41bobo488bo372bobo$42b2o16b2o171bo297bobo86b2o265b<br />
2o16b2o$60b2o170bobo51b2o244bo87bobo11b2o251b2o$232b2o38b2o11bobo57b2o<br />
274bobo10bobo$271bobo10bobo57bobo187bo87bo12bo$272bo12bo59bo187bobo47b<br />
o$533b2o47bobo111bo$583bo44b2o65bobo$226bo51b2o264bo83bobo65b2o$225bob<br />
o36b2o11bobo263bobo6bo32bo43bobo11b2o$225b2o36bobo10bobo264b2o7b3o29bo<br />
bo43bo12bobo$23b2o239bo12bo262bo14bo28b2o58bo279b2o$22bobo514bobo12b2o<br />
368bobo$23bo28b2o486bobo7b2o43bo107bo191b2o28bo$52b2o216b2o269b2o7bobo<br />
41bobo6bo33b2o63bobo190b2o$219bo36b2o11bobo280bo41b2o7b3o31bobo63b2o$<br />
42b2o174bobo34bobo10bobo281b2o11bo25bo14bo31bobo264b2o$42b2o13bo160b2o<br />
36bo12bo294bobo23bobo12b2o32bo13b2o236bo13b2o$56bobo506bobo23bobo7b2o<br />
50bobo234bobo$49bo6bobo507b2o24b2o7bobo50bo235bobo6bo$48bobo6bo204b2o<br />
339bo287bo6bobo$47bobo198b2o11bobo339b2o11bo282bobo$47b2o163bo34bobo<br />
10bobo352bobo29b2o63bo187b2o$211bobo34bo12bo354bobo28bobo11b2o48bobo$<br />
211b2o404b2o29bobo10bobo48b2o$622bo26bo12bo$254b2o261b2o102bobo$240b2o<br />
11bobo260bo2bo101b2o3bo$239bobo10bobo261bo2bo105bobo27b2o$205bo34bo12b<br />
o263b2o107bo28bobo61bo$50b2o8b2o142bobo449bobo59bobo166b2o8b2o$50b2o8b<br />
2o142b2o451bo61b2o166b2o8b2o$246b2o$77b2o10b2o141b2o11bobo271bo112bo<br />
40b2o183b2o10b2o$76bo2bo9b2o140bobo10bobo270b3o111bobo39bobo182b2o9bo<br />
2bo$77b2o153bo12bo164bo105bo114b2o41bo195b2o$198bo210bobo104b2o109b2o<br />
97bo$197bobo208bo2bo215bobo13b2o80bobo$72b2o123b2o39b2o169b2o217bobo<br />
12bobo21b2o57b2o147b2o$72b2o150b2o11bobo389bo9bo5bo21bobo11b2o192b2o$<br />
223bobo10bobo193bo206b3o3b2o21bobo10bobo$79bo144bo12bo179b2o12bobo208b<br />
o26bo12bo186bo$78bobo336b2o13b2o207b2o225bobo$71b2o6bobo651bo133bobo6b<br />
2o$70bobo7b2o148b2o443b2o55bobo132b2o7bobo$70b2o144b2o11bobo443bobo55b<br />
2o142b2o$215bobo10bobo214b2o229bobo$187bo28bo12bo214bobo203b2o25bo13b<br />
2o$75b2o109bobo256bo204bobo38bobo178b2o$75b2o109b2o463bobo38bo179b2o$<br />
65b2o155b2o428bo229b2o$64bobo141b2o11bobo517bo140bobo$64b2o141bobo10bo<br />
bo439bo22b2o53bobo140b2o$208bo12bo439bobo21bobo11b2o40b2o$180bo481bo<br />
23bobo10bobo$179bobo505bo12bo$179b2o33b2o448bo$213bobo447bobo$212bobo<br />
245bo202b2o28b2o53bo$213bo179b2o57bo6bobo231bobo11b2o38bobo$393bobo54b<br />
3o7b2o232bobo10bobo38b2o$173bo22b2o196bo54bo14bo230bo12bo$172bobo20bob<br />
o251b2o12bobo$172b2o22bo256b2o7bobo$452bobo7b2o237b2o$452bo211b2o35bob<br />
o11b2o$202b2o235bo11b2o211bobo35bobo10bobo$188b2o11bobo234bobo224bobo<br />
35bo12bo$166bo20bobo10bobo234bobo226bo$165bobo20bo12bo235b2o320bo$165b<br />
2o266bo275b2o47bobo$432bobo274bobo47b2o$194b2o233bo3b2o275bobo11b2o$<br />
180b2o11bobo232bobo280bo12bobo$179bobo10bobo234bo295bo$159bo20bo12bo$<br />
158bobo262bo342bo$158b2o222bo39bobo246b2o45b2o45bobo80b2o$186b2o193bob<br />
o39b2o246bobo44bobo11b2o32b2o81bo$172b2o11bobo190bo3b2o43b2o238bo5bo<br />
45bobo10bobo111b3o$171bobo10bobo190bobo31b2o13bobo238b3o3b2o45bo12bo<br />
112bo$172bo12bo192bo16bo14bobo12bobo242bo$152bo241bobo13bo5bo9bo242b2o<br />
$151bobo218bo22b2o12b2o3b3o309b2o45bo$151b2o25b2o191bobo25bo13bo312bob<br />
o43bobo$164b2o11bobo192b2o24bobo12b2o312bobo43b2o$163bobo10bobo197b2o<br />
19bobo328bo$164bo12bo182b2o13bobo19b2o275bo$359bobo12bobo296bobo68b2o$<br />
145bo213bo5bo9bo297b2o69bobo$144bobo23b2o186b2o3b3o303b2o74bo34bo$144b<br />
2o10b2o11bobo190bo306bobo107bobo$155bobo10bobo191b2o306bobo107b2o$156b<br />
o12bo501bo66b2o$342bo395bobo11b2o$341bobo395bobo10bobo$162b2o178bo397b<br />
o12bo$148b2o11bobo69b2o23b2o98bo319bo108bo$147bobo10bobo69bobo22bobo<br />
80bo16bobo317bobo106bobo$148bo12bo71bo23bo5bo75bobo16b2o317b2o3bo63b2o<br />
39b2o$256b2o3b3o76b2o20b2o317bobo62bobo11b2o$260bo100bobo318bo64bobo<br />
10bobo$154b2o104b2o45bo22bo29bobo385bo12bo$153bobo150bobo13bo6bobo29bo<br />
326bo$152bobo152b2o11b3o7b2o355bobo$153bo157b2o6bo14bo352b2o65b2o$295b<br />
2o13bobo6b2o12bobo347b2o69bobo11b2o26bo$125b2o124b2o26bo14bobo12bobo<br />
11b2o7bobo348bobo13b2o54bobo10bobo24bobo$124bobo123bobo25bobo13bo5bo9b<br />
o11bobo7b2o350bobo12bobo54bo12bo26b2o$125bo123bobo27b2o12b2o3b3o21bo<br />
362bo9bo5bo$238b2o10bo32bo13bo23b2o372b3o3b2o$168bo69bobo41bobo12b2o<br />
399bo63b2o$167bobo69bo41bobo413b2o63bobo11b2o$168b2o111b2o480bobo10bob<br />
o24bo87b2o$60bo111b2o590bo12bo24bobo86bo$59bobo109bobo629b2o87b3o$60b<br />
2o16b2o90bobo721bo$78b2o91bo17bo468bo47b2o62b2o$188bobo466bobo46bobo<br />
61bobo$189bo54b2o411b2o48bobo61bobo$149b2o54bo22bo14bobo462bo63bo13b2o<br />
22bo$149bobo35bo16bobo13bo6bobo13bo5bo536bobo20bobo$150bo35bobo16b2o<br />
11b3o7b2o12b2o3b3o468bo68bo22b2o$187b2o20b2o6bo14bo13bo470bobo$208bobo<br />
6b2o12bobo12b2o470bo$207bobo11b2o7bobo547b2o$41b2o165bo11bobo7b2o488bo<br />
59bobo11b2o$40bobo177bo498bobo59bobo10bobo$41bo28b2o147b2o498b2o61bo<br />
12bo$70b2o84b2o661bo$156bobo571bo87bobo$60b2o95bo493bo77bobo6bo49b2o<br />
29b2o$60b2o13bo574bobo76b2o7b3o47bobo11b2o$74bobo574b2o73bo14bo47bobo<br />
10bobo$67bo6bobo648bobo12b2o48bo12bo$66bobo6bo650bobo7b2o$65bobo659b2o<br />
7bobo87bo$65b2o671bo57b2o27bobo$738b2o11bo44bobo27b2o60bo$750bobo44bob<br />
o87bobo$751bobo44bo13b2o55b2o16b2o$752b2o58bobo54b2o$673b2o138bo$672bo<br />
2bo157bo$672bo2bo156bobo$68b2o8b2o593b2o131b2o25b2o$68b2o8b2o726bobo<br />
11b2o$121bo15bo669bobo10bobo$95b2o10b2o11bobo13bobo669bo12bo$94bo2bo9b<br />
2o12bo15bo537bo76bo$95b2o576b3o76b3o151b2o$672bo82bo58b2o90bobo$672b2o<br />
80b2o44bo13bobo11b2o47b2o28bo$90b2o658b2o47bobo13bobo10bobo46b2o$90b2o<br />
24bo15bo617bobo47b2o14bo12bo$115bobo13bobo566b2o50bo134b2o$97bo18b2o<br />
14b2o566b2o50b2o119bo13b2o$96bobo723b2o48bobo$89b2o6bobo722bobo22b2o<br />
23bobo6bo$88bobo7b2o592b2o129bobo21bobo23bo6bobo$88b2o601bo2bo129bo23b<br />
o32bobo$692bobo187b2o$117b2o574bo64bo$93b2o22bobo637bobo$93b2o23bo638b<br />
2o$83b2o669bo$82bobo668bobo$82b2o670bobo$755b2o3bo$759bobo107b2o8b2o$<br />
760bo108b2o8b2o$819b2o$762bo55bobo19b2o10b2o$144b2o615bobo55bo20b2o9bo<br />
2bo$89b2o53bobo614b2o89b2o$89bobo53bo$90bo$857b2o$857b2o2$795bo55bo$<br />
762b2o30bobo53bobo$762bobo29b2o53bobo6b2o$763bobo24b2o57b2o7bobo$764bo<br />
25bobo66b2o$791bobo$681b2o91bo17bo$680bobo90bobo78b2o$681bo92bo79b2o$<br />
864b2o$776bo50b2o6b2o27bobo$775bobo48bo2bo4bobo28b2o$775b2o49bo2bo4bo$<br />
827b2o4b2o17$752b2o$751bobo$752bo$843b2o$842bobo$843bo11$1380bo$1378bo<br />
3bo$142b2o1233bo$142b2o1233bo4bo$1377b5o2$141b2o$141b2o4$135b2o$135b2o<br />
$774b2o$773bobo$141b2o631bo$141b2o!<br />
#C [[ X -52 Y -143 ZOOM -2 STEP 5 AUTOSTART LOOP 12000 THUMBNAIL THUMBSIZE 2 ]]</code></div></div>
<canvas height="540" style="margin-left: 1px;" width="420"></canvas></div>
<h3>What Is This All About?</h3>
<p>A glance through the <a href="https://conwaylife.com/wiki" target="_blank">LifeWiki</a> will tell you that throughout the half-century-plus history of Conway's Life as a mathematical recreation, Lifenthusiasts have liked to build things. As the decades went by, they designed and constructed more and more complicated mechanisms.
<p>Relatively recently, these mechanisms have begun to include Life patterns that make copies of themselves. This kind of construction is generally done by crashing gliders together in just the right way. A big research topic has always been <i>what exactly can we build by crashing gliders together?</i> -- and an obvious corollary, for any given Life pattern, is <i>how few gliders can we use?</i>
<p>For the last few decades, glider synthesis problems have been for some dedicated Lifenthusiasts what daily Wordles, weekly Sudokus, or monthly cryptic crosswords might be for other types of puzzle-solvers.
<p>One big difference, though, is that glider synthesis puzzles generally don't have a solution you can look up in the back (with a few rare exceptions nowadays in the <a href="https://conwaylife.com/book/" target="_blank">Life textbook</a>). They're all puzzles that nobody has ever solved before, and there's an unbounded number of them. A <a href="https://conwaylife.com/forums/viewtopic.php?p=153366#p153366" target="_blank">recent set of extra-hard problems</a> was posted on November 10th, for example -- and they were all solved in <a href="https://conwaylife.com/forums/viewtopic.php?p=153564#p153564" target="_blank">well under a week</a>.
<p>Conversely, we can ask <i>what can we build with a fixed number of gliders</i>? And for a while, it's clear that the more gliders we have, the more different objects we can build, and the objects get gradually larger and more complex on average. We can ask
<p><i>how many gliders does it take to construct... </i><br />
<i>... a <a href="https://conwaylife.com/wiki/Block">block</a>?</i> (Two.)<br />
<i>... a <a href="https://conwaylife.com/wiki/Lightweight_spaceship">lightweight spaceship</a>?</i> (Three.)<br />
<i>... a <a href="https://conwaylife.com/wiki/Glider-producing_switch-engine">glider-producing switch engine?</a></i> (Four.)<br />
<i>... a <a href="https://conwaylife.com/wiki/Unix">unix oscillator?</a></i> (Five.)<br />
<i>... a <a href="https://conwaylife.com/wiki/Queen_bee_shuttle">queen bee shuttle?</a></i> (Six.)<br />
<i>... a <a href="https://conwaylife.com/wiki/Coe_ship">Coe ship</a>?</i> (Seven.)<br />
<i>... a <a href="https://conwaylife.com/wiki/Gosper_glider_gun">Gosper glider gun</a>?</i> (Eight.)<br />
<i>... a <a href="https://conwaylife.com/wiki/2-engine Cordership">2-engine Cordership</a>?</i> (Nine.)<br />
<i>... a <a href="https://conwaylife.com/wiki/Blinker_puffer_1">blinker puffer</a>?</i> (Ten.)<br />
<p><div class="rle">
<div class="codebox">
<div class="selall">Code:
<a href="#" onclick="selectCode(this); return false;">Select all</a>
</div>
<div><code>x = 998, y = 822, rule = B3/S23<br />
991bobo$991b2o$992bo5$195bo$178bo17b2o$176bobo16b2o$177b2o$992bo$991bo<br />
$991b3o9$997bo$995b2o$996b2o23$851bo$851bobo$851b2o34$183bo$184bo$182b<br />
3o26$221bo$222bo$220b3o5$202bo$200bobo$201b2o31$677bo$677bobo16bo$677b<br />
2o17bobo$161bobo10bo521b2o$162b2o11b2o$162bo11b2o32$145bo436bo$146b2o<br />
433bo$145b2o434b3o4$581bo$149bo431bobo$150bo430b2o$148b3o3bo$155bo$<br />
153b3o34$117bobo355bo$118b2o355bobo$118bo356b2o34$92bo$93bo$91b3o7$<br />
358bo$357bo$357b3o$107bo$108bo$106b3o2$350bo$349bo$349b3o17$237bo$237b<br />
obo$237b2o27$83bo$81bobo$82b2o$222bo$221bo$221b3o24$127bo$125b2o$41bo<br />
84b2o$39bobo$40b2o21$27bo$27bobo$27b2o$2bo$obo$b2o55$126b2o$126bobo$<br />
126bo31$225bo$224b2o$224bobo65$376b2o$375b2o$377bo29$121bo356b2o$108b<br />
2o11b2o355bobo$109b2o9bobo355bo$108bo$464b3o$464bo$465bo36$145b3o$147b<br />
o$146bo$142b2o$141bobo$143bo34$171b2o520b2o$172b2o519bobo9b3o$171bo<br />
521bo11bo$188bo517bo$188b2o$187bobo31$224b2o$223bobo$225bo$812b2o$811b<br />
2o$813bo15$204b3o$206bo$205bo600bo$805b2o$805bobo5$183b3o$185bo$184bo<br />
68$186b2o782b2o$187b2o781bobo$186bo783bo14$193b2o$194b2o$193bo4$995b3o<br />
$995bo$996bo$204b3o$206bo$205bo!<br />
#C [[ THUMBNAIL THUMBSIZE 2 LABELSIZE 50 COLOR LABEL Yellow LABELALPHA .8 ]]
#C [[ ZOOM 10 X -483 Y -10 AUTOSTART PAUSE 2 GPS 20 LOOP 1800 ]]<br />
#C [[ T 50 ]] # block<br />
#C [[ T 150 X -413 Y 0 ]]<br />
#C [[ T 200 ]] # LWSS<br />
#C [[ T 300 X -340 Y 0 ]]<br />
#C [[ T 360 ]] # GPSE<br />
#C [[ T 450 X -270 Y 0 ]]<br />
#C [[ T 575 ]] # unix<br />
#C [[ T 650 X -200 Y 0 ]]<br />
#C [[ T 700 ]] # queen bee shuttle<br />
#C [[ T 820 X -130 Y 0 ]]<br />
#C [[ T 880 ]] # Coe ship<br />
#C [[ T 950 X -60 Y 0 ]] <br />
#C [[ T 1100 ]] # 2-engine Cordership<br />
#C [[ T 1150 X 20 Y 0 Z 8 ]]<br />
#C [[ T 1250 ]] # blinker puffer<br />
#C [[ T 1550 X 96 Y 0 Z 10 ]]<br />
#C [[ T 1700 ]]<br />
#C [[ T 1775 X -483 Y -10 ]]<br />
#C [[ LABEL 13 413 10 "block\n(2 gliders)" ]]<br />
#C [[ LABEL 85 423 10 "LWSS\n(3 gliders)" ]]<br />
#C [[ LABEL 150 423 10 "GPSE\n(4 gliders)" ]]<br />
#C [[ LABEL 223 423 10 "unix\n(5 gliders)" ]]<br />
#C [[ LABEL 292 423 10 "queen bee shuttle\n(6 gliders)" ]]<br />
#C [[ LABEL 368 423 10 "Coe ship\n(7 gliders)" ]]<br />
#C [[ LABEL 435 423 10 "Gosper glider gun\n(8 gliders)" ]]<br />
#C [[ LABEL 512 428 10 "2-engine Cordership\n(9 gliders)" ]]<br />
#C [[ LABEL 595 423 10 "blinker puffer\n(10 gliders)" ]]<br />
</code></div></div>
<canvas height="540" style="margin-left: 1px;" width="420"></canvas></div>
<p>... and so on, with buildable structures getting just a little bigger and more complicated each time we add another glider. This all holds up very nicely, until suddenly we get to
<p><i> ... a pattern that can compute the digits of pi and print them out in the Life universe?</i> (Fifteen.)
<p>Substitute a description of any Life pattern that can be constructed -- a thousand gliders that collide and produce nothing but empty space, or a million blocks in the shape of the Flying Spaghetti Monster, or a <a href="https://conwaylife.com/wiki/Speed_Demonoid" target="_blank">spaceship that travels by making reflected copies of itself</a>, or whatever. No matter what pattern you ask about, if it can be constructed at all, the answer is always fifteen gliders -- or less, of course. But for big patterns, it's usually fifteen.
<p>That doesn't seem to make a lot of sense, to put it mildly. So... what exactly is going on here?
<h3>The Full-Sized RCT15</h3>
<p>The simple version of any RCT15 pattern starts with exactly fifteen gliders in an otherwise empty Life universe. Ordinarily you would have to collide two thousand gliders or more, to construct a pattern as large and complex as Hensel's decimal counter. The activated pattern contains almost a hundred gliders, after all, just in its various signal loops. But the entire pattern can be constructed with exactly fifteen gliders... provided that those gliders start very, very far apart.
<p>Completely counterintuitively, any pattern that can be constructed by colliding <b>any</b> number of gliders, can also be constructed by these exact same fifteen gliders, in three groups: 7 in the far southwest, and 4 each in the far northwest and far southeast. The RCT16 design had one more glider in the far northeast, as shown in the four-quadrant diagram below.
In either RCT15 or RCT16, the only thing that changes is the groups' relative positions. In general, to build a bigger and more complex object, the groups will have to move farther apart -- a <b>lot</b> farther apart.
<p>For example, moving those groups of gliders to exactly the correct distances from each other would build a complete <a href="https://conwaylife.com/wiki/Gemini" target="_blank">Gemini spaceship</a> -- eventually! -- even though a Gemini spaceship is an enormous pattern consisting of over 800,000 live cells. Constructing one of these spaceships would otherwise require <a href="https://conwaylife.com/wiki/Glider_synthesis#Spaceship_syntheses" target="_blank">173,449 colliding gliders</a> (at least that's the current known recipe).
<p>We can do this same construction in 15 gliders, but we'll have to expand the size of the RCT pattern, and also wait an inordinately long time. It will be, not just hundreds of thousands of times bigger and slower, but hundreds of thousands of <b>factors of two</b> bigger and slower than the RCT demo pattern that builds the decimal counter pattern shown above.
<h3>Storing Data in Empty Space: How Does It Work?</h3>
<p>The target Life pattern's "construction recipe" is encoded into the distances between glider groups, with a tricky "divide by two and take the remainder" mechanism. See <a href="%3Ch3%3EThe%20RCT%20Demo%20Pattern%3C/h3%3E" target="_blank">this LifeViewer animation</a> to get a closer look at the details. The mechanism is also described in detail in previous posts on this blog, and <a href="https://conwaylife.com/forums/viewtopic.php?p=152565#p152565" target="_blank">elsewhere</a>. Anyone interested in either the developmental history of the RCT idea, or the low-level mechanisms that make it all work, should definitely have a look at <a href="https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/" target="_blank">Brett Berger's November 16 blog post</a> on these subjects.
<p>Briefly, a glider bounces back and forth between the center of the pattern and a slowly moving object known as a GPSE, which is approaching from the southeast. The distance that the glider travels between successive bounces is always decreasing, and the glider is exactly three times as fast as the GPSE. The result is that the distances reduce by a factor of two after each round trip by the glider. We can adjust the initial separation between the 15 gliders, to get a free choice of <a href="https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html">ending up with a remainder of either 0 or 1</a> after each division.
<p>Another useful feature of GPSEs -- "glider-producing switch engines" -- is that they emit streams of gliders aimed in the direction they're traveling. The RCT's initial configuration produces four GPSEs in three corners of the pattern, all aimed toward the center. The collision of streams of gliders in the center is carefully arranged to perform a mechanical calculation where the total distance is repeatedly divided by 2, and the remainder (either 0 or 1) can be tested.
<p>Depending on this remainder, the central collision releases either a single glider or a pair of gliders, heading northeast. The sequence of single and double gliders corresponds to the sequence of bits in the binary representation of the original distance, reading from right to left.
<h3>Getting Something for (Almost) Nothing</h3>
<p>The very sparse sequence of single and double gliders is aimed at a target object, which originally is just some junk from an initial collision between gliders from tne northwest and southwest. Or, in the RC16 case, the initial target is the lone glider from the northeast.
<p>With just the right sequences of single and double gliders, it turns out that we can change the target object -- pull it southwest, push it northeast, emit perpendicular gliders, and so forth. By carefully stringing together these sequences, we can instruct the target object to construct simple objects in specified locations. An early demonstration was a <a href="https://conwaylife.com/forums/viewtopic.php?p=144315#p144315">2028-bit sequence</a> for building an 8-cell object called a shillelagh.
<p>The problem is that the GPSEs in the original pattern are very messy, producing long streams of ash as they move towards the center. The various collisions create even more clumps of mess along those trails, culminating in the final big collision at the centre. To qualify as a genuine glider synthesis, our 15-glider recipe has to be completely 'clean': it has to produce nothing other than the desired object, not even any escaping gliders. So a big part of the RCT project is to figure out how to reliably clean up all of the extra mess, including the incredibly long ash trails, each slightly different from the others, coming from each of three corners of the initial pattern.
<h3>Ours Not To Reason Why...</h3>
<p>A very reasonable question might be asked at this point! If this GPSE-based mechanism produces such a huge mess, why not use some other structure instead that doesn't create all these difficulties? In point of fact, an earlier design for universal construction with a fixed number of gliders had a cost of <a href="https://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html">329 gliders</a> instead of 15, with only relatively minor cleanup problems. Here again, see <a href="https://biggieblog.com/building-arbitrary-life-patterns-in-15-gliders/" target="_blank">Brett Berger's blog post</a> for more details.
<p>Long story short, the RCT project acquired a certain momentum after a while. It was clear several years ago that fixed-cost universal construction was possible, so the interesting question once again was: <i>what is the absolute smallest total number of gliders that we can do this with?</i> As of November 15th, the RCT15 patterns represent our collective best effort to answer this question: "Fifteen!"
<h3>Yet More Obsessive Optimizing</h3>
<p>After the total cost of a fixed-cost recipe was successfully boiled down to the current minimum of 15, reducing the size of the bounding box became a secondary goal. For the RCT design, this is equivalent to minimizing the number of bits in the recipe. Every time you find a way to reduce the recipe by a single bit, the pattern's diameter is cut in half (!). Compared to this, other possible optimizations really aren't going to amount to much of anything.
<p>The sequences of single and paired gliders coming from the central collision are capable of universal construction, but it's a very inefficient process -- you need a lot of bits to successfully fire even a single glider. It would be much cheaper to encode construction-arm operations in a much shorter bit sequences. So the first thing that the RCT project builds is a decoder for exactly those shorter bit sequences, or "codons". This structure is called a "<a href="https://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html">decoder and better construction arm</a>" (DBCA), and as soon as it is fully constructed, it immediately takes over the work of constructing and destroying things, much more efficiently: DBCA recipes are about twelve times cheaper.
<p>That isn't the end of the bootstrap process, though! The DBCA is efficient enough to build an even more complicated mechanism, the "<a href="https://conwaylife.com/forums/viewtopic.php?p=147056#p147056">extreme compression construction arm</a>" (ECCA), which takes over construction work from the DBCA. The ECCA is 30% more efficient than the DBCA, <b>and</b> it can fire gliders in multiple directions, <b>and</b> it contains integrated self-destruct circuitry: it is designed to disappear completely when it is struck by just one single glider in exactly the right place.
<p>Remember, the point of this whole exercise is not to build a DBCA or an ECCA. The point is to build <i>whatever pattern we want to build</i>, starting with just fifteen gliders. The DBCA and ECCA are just intermediate steps along the way. They're very useful intermediate steps, but in the end they're going to have to get cleaned up along with all the rest of the mess -- leaving behind nothing besides the Life pattern that we're really trying to construct.
<p>This three-stage bootstrap design turned out to be much more cost-effective than two stages, or just one stage. However, the improvements stop there: building a fourth bootstrap stage would just make everything more expensive. The ECCA can already do everything that we need it to do, including cleaning up itself, the DBCA, and all of the GPSE ash trails -- and constructing the final target pattern.
<h3>The RCT Demo Pattern</h3>
<p>The full RCT16 pattern from November 9 encodes a 1,650,504-bit recipe into the distances between the initial gliders -- which means that the pattern fits in a bounding box with each side somewhat longer than 2^1650504 cells. That's a number with almost half a million digits. RCT15's recipe contains a slightly larger number of bits -- 1,665,791 -- both because it hasn't been optimized as thoroughly as the RCT16 was, and because there's slightly more to clean up.
<p>Neither of the full patterns can be simulated effectively on any software that we currently have available. <a href="https://golly.sourceforge.net" target="_blank">Golly</a>, the software we use to work with these RCT patterns, is very good at handling big bounding boxes, but even it can't readily deal with such a ridiculously large size.
<p>Luckily there's a good workaround! Bits come in from the RCT retrieval mechanism very slowly at first, then faster and faster -- each one arriving in half the time of the one before. So we can build a <a href="https://conwaylife.com/forums/viewtopic.php?p=153348#p153348" target="_blank">smaller RCT pattern</a> that shows exactly how the mechanism works, and then "supercharge" it by inserting extra gliders to represent additional bits, during one of the very slow stages where the early-stage RCT is waiting around for a long time for the next bit to come in.
<p>These extra gliders are constructed with sparse streams of <a href="https://conwaylife.com/wiki/Middleweight_spaceship" target="_blank">MWSSes</a>, carefully placed out of the way of the rest of the pattern. The inserted gliders arrive at the mechanism that interprets incoming bits, in exactly the same way as any other gliders encoding incoming bits. But they arrive fast enough that we can actually watch the entire process of construction and destruction that the RCT needs to go through to accomplish its magic.
<h3>The RCT Viewer script</h3>
<p>It can be hard to zoom and pan around in Golly to find the locations where interesting things are happening, in a ridiculously large and long-running pattern like the RCT demo pattern. <a href="https://conwaylife.com/forums/viewtopic.php?p=153609#p153609" target="_blank">This Lua script</a> is currently the easiest way to get Golly to do most of the tricky zooming and panning work for you. The script can be stopped at any time by hitting the Escape key, to investigate a particular stage in more detail.
<p>To use the script, start by opening the <b>rct15.mc.gz</b> file in Golly. Then navigate to the <a href="https://conwaylife.com/forums/viewtopic.php?p=153609#p153609" target="_blank">forum page where the RCT viewer Lua script is published</a>, click "Select All" in the code box, hit Ctrl+C to copy, and then in Golly choose <b>File > Run Clipboard</b>. The script will do the rest. Lua is embedded in the Golly executable on all platforms that Golly supports, so there's no extra language download/install process.
<p>The above final stage of an RCT15 synthesis of a decimal counter appears at T=6,749,629,825,000 in the demo pattern. This may still seem like a very large number, but it's easily with reach of a Golly simulation -- as you'll see if you try running the pattern yourself, either with or without the viewer script.
<h3> ... Anything* ?</h3>
<p>In Conway's Life, the claim of universal construction -- the ability of a mechanism to build "anything" -- is inevitably limited by the existence of <a href="https://conwaylife.com/wiki/Garden_of_Eden">Gardens of Eden</a>, <a href="https://conwaylife.com/wiki/Grandfather_problem" target="_blank">grandparentless patterns</a>, and other patterns that provably can <b>not</b> be constructed by any number of colliding gliders -- including some recently discovered <a href="https://conwaylife.com/wiki/Unique_father_problem">still lifes</a> and <a href="https://conwaylife.com/wiki/Unsynthesizable_oscillator_1" target="_blank">oscillators</a>.
<p>To summarize: all Conway's Life universal constructors can construct anything <i>that can be constructed</i>, so they can all build any structure that any other universal constructor can build.
<p>The big surprise is that a structure consisting of just 15 gliders can now be officially added to the group of proven universal constructors. Other known universal constructor mechanisms (there are several known just in Conway's Life) encode their instructions in the positions of objects on a 1D or 2D "memory tape", or in the positions of long streams of gliders. It's very strange to find a way to encode the same information using just fifteen gliders and a whole lot of empty space.
<p>For the RCT there are some lower limits even smaller than the classic initial pattern with 15 gliders and 75 cells, if we're measuring in terms of total population and bounding box size.
The initial four quadrants of the RCT always look exactly like the following, except that they're initially a lot farther apart. The mechanism can't really store any information at this small scale, and the <a href="https://conwaylife.com/wiki/Glider-producing_switch_engine" target="_blank">glider-producing switch engines</a> crash in an uncontrolled way. However, these views of the four quadrants might make it easier to inspect what the corners of all RCT patterns look like:
<p><div class="rle" float: left>
<div class="codebox">
<div class="selall">Code:
<a href="#" onclick="selectCode(this); return false;">Select all</a>
</div>
<div><code>x = 2611, y = 1354, rule = LifeHistory<br />
542.14D114.7D1365.14D$456.29D53.22D15.56D37.11D32.38D1207.29D53.22D<br />
15.56D39.7D53.16D$455.33D47.28D12.57D34.13D31.40D1205.33D47.28D12.57D<br />
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455.40D34.40D6.57D28.19D31.40D1205.40D34.40D6.57D30.17D40.34D$455.42D<br />
31.42D5.57D27.20D31.40D1205.42D31.42D5.57D28.19D39.35D$455.42D30.44D<br />
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24.24D31.39D1206.43D28.45D4.56D26.22D37.37D$455.11D14.19D26.18D13.15D<br />
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6.11D31.11D1234.11D22.13D20.14D31.5D27.11D40.14D4.12D33.12D$455.11D<br />
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59.11D31.11D1234.11D24.11D17.12D68.11D58.12D29.11D$455.11D24.11D16.<br />
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58.12D28.10D5.25D$455.11D10.21D19.11D71.11D59.11D31.36D1209.11D10.21D<br />
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58.12D27.18D16.15D$455.36D25.11D71.11D59.11D59.15D1202.36D25.11D71.<br />
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11D62.13D1201.11D13.14D23.11D71.11D58.12D27.11D27.12D$455.11D15.13D<br />
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27.11D28.11D$455.11D17.12D21.12D70.11D59.11D63.13D1200.11D17.12D21.<br />
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20.12D19.12D69.11D58.12D28.11D28.11D$455.11D20.12D19.12D69.11D59.11D<br />
64.12D1200.11D20.12D19.12D69.11D58.12D28.11D28.11D$455.11D20.13D18.<br />
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36.D28.11D58.12D29.11D25.12D$455.11D23.12D19.14D33.4D27.11D59.11D62.<br />
12D1202.11D23.12D19.14D33.4D27.11D58.12D29.12D24.12D$455.11D24.12D19.<br />
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28.7D27.11D58.12D30.12D22.12D$455.11D25.12D19.16D24.9D27.11D59.11D28.<br />
3D28.14D1203.11D25.12D19.16D24.9D27.11D58.12D30.12D21.12D$455.11D25.<br />
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1207.11D26.13D21.45D27.11D41.44D18.39D$455.11D27.12D22.43D28.11D41.<br />
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<p>After fifteen ticks, the RCT16 pattern drops to a population of only 66 cells, in a slightly smaller bounding box, and the RCT15 pattern drops to 61 cells at the same point (not too surprisingly). Some nontrivial re-working of the RCT design might possibly drop the minimum population by another ten cells or more.
<p>It has not been proven that 15 gliders is the minimal number that supports RCT-type universal construction. However, we can be confident that there are less than a dozen new smaller RCT{n} pattern records remaining to be set! (Collisions between three gliders have been enumerated fairly thoroughly at this point.)Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-77111676629648345182022-07-05T12:43:00.017-05:002022-11-11T12:40:25.052-05:00Current RCT Technology, Part 3: The Extreme Compression Construction Arm (ECCA)<h1>Quick Recap</h1>
<p>There's been a lot of detail in the last couple of posts, and there's probably some danger of getting lost in the weeds here. Time for a short summary of what pieces of the RCT project have been completed so far, and which pieces are still left to do.
<p><span style="font-size:1.5em">1.</span> <span style="color:green;">COMPLETE:</span> Fifteen gliders crash to create four glider-producing switch engines, which send long streams of gliders to collide at the RCT <b>epicentre</b>.
<p><span style="font-size:1.5em">2.</span> <span style="color:green;">COMPLETE:</span> A sixteenth glider hits the initial output gliders from that glider-stream collision, to provide a target elbow for the RCT's initial construction arm.
<p><span style="font-size:1.5em">3.</span> <span style="color:green;">COMPLETE:</span> Using a "divide by two and take the remainder" mechanism, the RCT repeatedly measures the parity of the distance between the epicentre and the southeastern GPSE, and emits either a single glider or a pair of gliders toward the target elbow.
<p><span style="font-size:1.5em">4.</span> <span style="color:green;">COMPLETE:</span> Recipes are known that create a target a safe distance off to the side, move the elbow forward and back as needed, and emit gliders on any chosen lane. The RCT's initial construction arm is therefore provably universal.
<p><span style="font-size:1.5em">5.</span> <span style="color:green;">COMPLETE:</span> The RCT's initial construction arm builds a DBCA (see previous post) and routes data from the RCT into these, for a ~12x improvement in construction efficiency.
<p><span style="font-size:1.5em">6.</span> <span style="color:orange;">PARTLY COMPLETE:</span> The DBCA builds an ECCA -- Extreme Compression Construction Arm, see below -- and routes input RCT data into it, for an additional ~30% efficiency improvement. The ECCA has been <a href="https://conwaylife.com/forums/viewtopic.php?p=147582#p147582">completely designed</a> (implementation details <a href="https://conwaylife.com/forums/viewtopic.php?p=147056#p147056">here</a>) but as of 5 July 2022, integrated self-destruct circuitry still needs to be added.
<p><span style="font-size:1.5em">7.</span> <span style="color:orange;">PARTLY COMPLETE:</span> The DBCA builds a "catcher" for incoming GPSEs, then builds a <a href="https://conwaylife.com/forums/viewtopic.php?p=146237#p146237">pseudo-BSRD</a> (more details <a href="https://conwaylife.com/forums/viewtopic.php?p=147048#p147048">here</a>) and routes all remaining RCT construction data into it. The pseudo-BSRD delays the final construction and cleanup stages until after the GPSEs have crashed at the epicentre and all debris can be safely cleaned up.
<p><span style="font-size:1.5em">8.</span> <span style="color:red;">TBD:</span> The ECCA, working with data emitted by the pseudo-BSRD, cleans up all of the DBCA's circuitry, and all of the non-periodic ash from the GPSE crashes.
<p><span style="font-size:1.5em">9.</span> <span style="color:green;">COMPLETE:</span> The ECCA builds a seed for the ATBC -- the <b>Actual Thing Being Constructed</b>, which is the real end goal of one of these RCT construction/deconstruction projects. A sample ATBC seed for a large object not ordinarily constructible with 16 gliders can be found <a href="https://conwaylife.com/forums/viewtopic.php?p=147825#p147825">here</a>. When triggered, the seed will build <a href="https://conwaylife.com/ref/DRH/dec.counter.html">Alan Hensel's decimal counter</a>. To construct the seed, the ECCA will fire 7284 slow gliders, which will be encoded by about 52,000 bits coming from the RCT mechanism.
<p><span style="font-size:1.5em">10.</span> <span style="color:orange;">MOSTLY COMPLETE:</span> The ECCA builds and triggers 106 Cordership seeds. These Corderships fly past the periodic GPSE ash and clean it all up. The required fleet of Corderships has been designed and tested; a recipe to build and launch them one at a time has not been compiled yet, but this is a fairly straightforward task.
<p><span style="font-size:1.5em">11.</span> <span style="color:orange;">PARTLY COMPLETE:</span> The Corderships are caught and cleanly removed by "Corderabsorbers" which will have been constructed at the sites of the "ash blobs" left behind by the GPSE launches. All Corderabsorbers have been designed and tested, but recipes to build them have not been compiled yet. For the southwest Corderabsorbers, this will require using <b>slow^2 salvos</b>. No generalized compiler for slow^2 salvos exists at the moment, but one can easily be written.
<p><span style="font-size:1.5em">12.</span> <span style="color:green;">COMPLETE:</span> The final Corderabsorber in the southeast releases an output glider, which triggers the ATBC seed. All cleanup is complete, so the only thing left in the Life universe is the ATBC.
<h1>The ECCA</h1>
<p>A detailed description of the Extreme Compression Construction Arm can be found <a href="https://conwaylife.com/forums/viewtopic.php?p=147056#p147056">here</a>.
<p><b>EDIT 11/11/2022</b>: I'll leave this post as a snapshot of the RCT blueprint as it was at this stage of development. The final design (see links in the <a href="https://b3s23life.blogspot.com/2022/11/in-conways-life-sixteen-gliders-can.html">November 10 post</a>) still works very much along these same lines, but several changes have been made to the build order and other details. For example, to improve Golly's ability to explore the final stages of the pattern, the Actual Thing Being Constructed has been moved to the epicentre instead of the far southwest corner.
Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-10791085381355355172022-05-29T04:37:00.038-05:002022-06-15T13:45:31.600-05:00Current RCT Technology, Part 2: the DBCA (Decoder and Better Construction Arm)<p><a href="https://b3s23life.blogspot.com/2022/04/current-rct-technology-part-1-build.html">Part 1</a> of this series of posts on RCT (<a href="https://conwaylife.com/wiki/Reverse_caber-tosser">reverse caber tosser</a>) patterns described the basic mechanism of storing construction information in very large distances, and extracting it with a mechanism that amounts to repeatedly dividing the distance by two and taking the remainder. The minimum number of gliders needed to produce a working <a href="https://conwaylife.com/wiki/Universal_constructor">universal construction</a> arm turns out to be ridiculously small -- only 16 gliders as of this writing, and there's no guarantee that this is the cheapest possible mechanism.
<p>However, a construction-arm mechanism can make it possible to build any desired constructible object, without necessarily being very <i>efficient</i> about it. In this case, the RCT's native construction arm needs a very long string of bits to produce an output glider -- over an order of magnitude more bits than we would need with a more efficient encoding mechanism.
<h1>The DBCA...</h1>
<p>This means that, in our continuing quest to build any possible glider-constructible object using only sixteen gliders, it's now time for an apparently insane diversion. Rather than going ahead and building what we want to build -- the ATBC, or Actual Thing Being Constructed, which is the real goal of any RCT construction -- we instead go through a "bootstrap" stage, where we build a whole new construction arm mechanism that's much more efficient than the original, and then use that new construction arm to do a lot of cleanup ... plus building the ATBC, almost as an afterthought, at the very end.
<p>This extra "bootstrap" mechanism is called the <b>DBCA</b> -- Decoder and Better Construction Arm.
<p>Somewhat counterintuitively, if an RCT pattern takes the time to build a DBCA before doing anything else, it will end up completing its final construction much faster than it would have otherwise. Any given construction -- even if it's only something very small and simple, like the single <a href="https://conwaylife.com/wiki/Shillelagh">shillelagh</a> from the example -- will need only a fraction of the number of bits that would have to be stored in the RCT mechanism if it used only the native RCT construction arm.
<p>This first bootstrap stage will also help to enable a second bootstrap stage, which will be even more useful than the first. The DBCA allows for roughly a twelvefold efficiency improvement, but the actual construction and cleanup problem is still painfully difficult: new bits will only keep getting fed into the DBCA while the switch-engines are still producing incoming gliders. We can't do any cleanup until after the four GPSEs have arrived at the epicenter and have been safely stabilized -- but at that point, we won't have any more recipe information coming in to tell the DBCA how to do the cleanup!
<h1>... And The BSRD</h1>
<p>The idea behind the next bootstrap stage -- called the BSRD, for "Binary Storage and Retrieval Device" -- is to find a way to store incoming information, so that we can delay the last stage of the RCT's complicated construction and cleanup process. We'll still complete the repeated process of dividing the RCT distance by two and taking the remainder, but now we'll store all that information somewhere instead of building anything immediately. Then, after the incoming glider streams have all been absorbed, and the incoming switch engines have all stabilized into very long trails of safe stable ash, we'll make use of the stored information to run the DBCA to do any final construction and cleanup tasks.
<p>The original plan was to construct a BSRD with a static data tape -- a long line of blocks and blanks representing 1s and 0s, let's say, that can be read by an "index elbow" moved by a <a href="https://conwaylife.com/wiki/Slide_gun">slide gun</a> type device, similar to the binary tapes in the pi and phi calculators, but rebuilt to make them more easily constructible by slow salvos.
<p>However, it turns out that a storage unit can probably be built that's at least a couple of orders of magnitude cheaper than that. See the "pseudo-BSRD" discussion below.
<h1>A complete DBCA recipe</h1>
<p>On 27 May 2022, Pavel Grankovskiy completed an RCT recipe for a <a href="https://conwaylife.com/forums/viewtopic.php?p=146111#p146111">working DBCA mechanism</a>, including quite a bit of periodic circuitry, based in part on an <a href="https://conwaylife.com/forums/viewtopic.php?p=145213#p145213">earlier design by Adam P. Goucher</a>. Periods that are multiples of 8 happen to work well with incoming GPSE glider streams, and it's somewhat cheaper to build a period-8 <a href="https://conwaylife.com/wiki/Bumper">bumper</a> or <a href="https://conwaylife.com/wiki/Bouncer">bouncer</a> than a stable <a href="https://conwaylife.com/wiki/Snark">Snark</a> reflector. It's also cheaper to build a suppressed period-256 <a href="https://conwaylife.com/wiki/Shotgun">shotgun</a> for the common parts of the various salvos for a construction arm, than to build an all-stable synchronized shotgun.
<p>The combined improvements to the original design allow the entire DBCA structure to be constructed at about 60% of the original estimated cost.
<h1>... and a complete BSRD, too!</h1>
<p>In regards to completing a proof-of-concept RCT design, a further pleasant surprise showed up on May 27th, when Grankovskiy pointed out that <a href="https://discord.com/channels/357922255553953794/370571014654001154/979838579754823710">only a few small circuits needed to be added</a> to produce a completely functional BSRD -- or rather, a "pseudo-BSRD", since the structure is not really a binary storage device. Instead of writing data to a static binary tape near the epicentre, the pseudo-BSRD will simply deflect the gliders coming in from the RCT mechanism, sending them out to faraway reflectors near the southeast GPSE launch point.
<p>By the time the first gliders get back to the epicentre, the incoming GPSEs have safely finished their work and have been caught by carefully placed absorbers, all the stored bits have been sent to the pseudo-BSRD, and the DBCA can begin the incredibly long process of cleaning up the GPSEs' ash trails.
The original pseudo-BSRD design used p8 reflectors and Snarks, which was more expensive than strictly necessary. A <a href="https://conwaylife.com/forums/viewtopic.php?p=146237#p146237">stable rebuild</a> was completed a few days later, and for the time being there seems to be a consensus that that's a good enough option to implement. The pseudo-BSRD is probably somewhere between two and three orders of magnitude simpler than the original projected BSRD design, so this was a massive reduction in the complexity of the full RCT prototype.
<h1>Highlights of the DBCA</h1>
<p>Some of the key details of the new Goucher-Grankovskiy construction arm are summarized in an <a href="https://conwaylife.com/forums/viewtopic.php?p=146121#p146121">earlier forum post</a> in the same thread. The DBCA recipe pattern is too big to be readily animated with LifeViewer, but several key moments are highlighted in that post. The full pattern can very easily be run to completion using Golly.
<p>Here are a few items that weren't called out in detail in the forum post. <b>Zoom in toward the upper left corner below</b>, and you'll see labels appear for the nine possible output signals from the unary counter there. The following LifeViewer pattern places nine single-glider signals that produce each of those nine outputs (one right after the other, instead of separated by vast amounts of time as in a real RCT pattern). There are four types of glider output (even and odd color-changing and color-preserving 90-degree gliders), followed by INC16, DEC8, INC4, DEC2, and INC1.
<p><div class="rle">
<div class="codebox">
<div class="selall">Code:
<a href="#" onclick="selectCode(this); return false;">Select all</a>
</div>
<div><code>x = 1319, y = 2156, rule = B3/S23<br />
583b2o$583b2o$569bo$569b3o$572bo9bob2o$571b2o9bobo$583bo$576bo6b2o$<br />
575bobo5b2o$575bo2bo4b2o$576b2o11$550b2o81bo$546b2obo2bob2o8b2o66b3o$<br />
546b2o2bo4bo7bobo65bob3o$551bo13bo55bo8bo3bo$552bobo66b3o5bo3bo$624bo<br />
3b3obo$623b2o4b3o$555bo74bo$554bobo69bo$553bo2bo68bobo$554b2o65b2o2b2o<br />
$621b2o2$550b2o$549bobo$549bo$548b2o5$598b2o$591b2o5b2o$591b2o3$593b2o<br />
27b2o$593b2o27b2o$587b2o$587b2o$628b2o$628b2o$624b2o$624b2o$550b2o51bo<br />
$550b2o51b2o$536bo65bobo$536b3o90b2o$539bo11b2o76b2o$538b2o9bob2o105b<br />
2o5b2o$549bo75bobo30b2o5bo$543bo5bo76b2o35bobo$542bobo4bo2bo73bo36b2o$<br />
542bo2bo4b2o107b2o$543b2o114bobo$588b2o70bo$587bo2bo$586b6o71b2o$586b<br />
6o71b2obo$586b2o79bo$585b3o76bo$585b2o78bob2o$582b2ob2o80b2o$582bobobo<br />
11b2o46bo$583b4o6b2o2b3o2b2o40b2o$584b2o7bo2bobo4b2o40b2o$589b2o3bo3bo<br />
b2obo$588bo2bo5bo3b2o28bo$587bo3bo40b2o$583b2o2bo2bo40b2o$583b2o2bo2bo<br />
$624b2o$624b2o$588bo2bo26b2o$589b2o27b2o3$620b2o$519b2o92b2o5b2o$520b<br />
2o91b2o$519bo6$636b2o3b2o$635bo2bobo2bo$630bo5b2o3b2o5bo$629bobo15bobo<br />
$630bo17bo2$600b2o$601bo$601bobo$602b2o3$606b2o18bo$605bo2bo16b3o$606b<br />
obo15b3obo$607bo17bo3bo8bo$626bo3bo5b3o20b3o$533b2o92bob3o3bo26bo$533b<br />
o70b2o22b3o4b2o21bo3bo$531bobo70b3o22bo18bo8bobo2bo$516b2o13b2o65b2o2b<br />
o2bobo25bo14b3o4bo2bobo$516b2o80b2o2b2o2b2o24bobo16bo3bo3bo$602b2o29b<br />
2o2b2o11b2o3bo$637b2o17b3o$496b2o155bo$496b2o154bobo$648b2o2b2o$648b2o<br />
$495bo193bobo$494bobo193b2o$495bo194bo$492b3o$492bo$629bobo$630b2o$<br />
630bo61bo$535b2o153bobo$535b2o154b2o7$532b2o$532bo$533b3o$535bo6$503b<br />
2o$503b2o2$455b2o23b2o$456b2o22b2o$455bo46b2o$502bo186b2o5b2o$460b2o<br />
38bobo186b2o5bo$460b2o38b2o192bobo$694b2o$690b2o$459bo230bobo$458bobo<br />
230bo$459bo$456b3o235b3o$456bo237b3o$694b3o$697b3o$697b3o$499b2o196b3o<br />
$499b2o7$496b2o$496bo$497b3o$499bo6$467b2o$467b2o2$444b2o307bobo$444b<br />
2o308b2o$466b2o286bo$466bo$424b2o38bobo$424b2o38b2o227bobo$694b2o$694b<br />
o61bo$423bo330bobo$422bobo330b2o$423bo$420b3o$420bo4$463b2o$463b2o6$<br />
744bo$460b2o281bobo$460bo281bo3bo$461b3o277bo3bo$463bo276bo3bo$391b2o<br />
346bo3bo$392b2o346bobo$391bo349bo$737bo$736bobo$431b2o303b2o$431b2o<br />
307b2o$740bobo$408b2o325b2o5bo$408b2o325b2o5b2o$430b2o$430bo$388b2o38b<br />
obo$388b2o38b2o3$387bo$386bobo$387bo$384b3o$384bo124bo$507b3o$506bo$<br />
505bobo$427b2o76bobo$427b2o77bo42bo$547b3o$546bo$546b2o2$490b2o99bo$<br />
490b2o97b3o$424b2o162bo$424bo100b2o60bobo$425b3o96bobo60bobo$427bo82b<br />
2o12bo63bo$510bobo10b2o292bobo$512bo305b2o$503b2o7b2o304bo$503b2o23b2o<br />
$527bobo42b2o$395b2o96bob2o30bo44b2o183bobo$395b2o94b3ob2o29b2o230b2o$<br />
490bo267bo61bo$372b2o117b3ob2o254b3o64bobo$372b2o119bobo96b2o160bo64b<br />
2o$394b2o97bobo96bobo155bo3bo$394bo99bo99bo145bo8bobo2bo$352b2o38bobo<br />
142b2o46b2o7b2o144b3o4bo2bobo$352b2o38b2o143b2o46b2o156bo3bo3bo$545b2o<br />
195b2o3bo$545bo29bob2o169b3o$351bo194b3o24b3ob2o166bo$350bobo150b2o43b<br />
o23bo171bobo$351bo151b2o68b3ob2o161b2o2b2o$348b3o196bo27bobo162b2o$<br />
348bo197bobo26bobo$546bobo27bo$490bo54b2ob3o$489bobo59bo$391b2o96bobo<br />
53b2ob3o$391b2o94b3ob2o52b2obo$486bo$487b3ob2o44b2o46b2o$327b2o160bob<br />
2o35b2o7b2o46b2o$328b2o199bo$327bo201bobo$530b2o$388b2o182bo$388bo182b<br />
obo$389b3o96b2o81bobo$391bo95bobo60b2o17b3ob2o$487bo62b2o16bo$486b2o7b<br />
o73b3ob2o$494bobo74bob2o$495bo$502b2o$359b2o141b2o31bo$359b2o173bobo$<br />
534bobo$336b2o197bo34b2o$336b2o194b3o34bobo$358b2o172bo36bo$358bo209b<br />
2o7bo$316b2o38bobo217bobo$316b2o38b2o219bo$554b2o28b2o$554b2o28b2o195b<br />
2o5b2o$315bo253bo211b2o5bo$314bobo237bo12b3o216bobo$315bo237bobo10bo<br />
49b2o168b2o$312b3o238bo2bo9b2o48b2o164b2o$312bo241bo2bo73bo150bobo$<br />
562bo53bo12b3o151bo$554bo2bo3bobo51bobo10bo$554b2o4bo2bo51bo2bo9b2o<br />
156b3o$355b2o204b2o53bo2bo166b3o$355b2o267bo161b3o$616bo2bo3bobo163b3o<br />
$616b2o4bo2bo163b3o$623b2o164b3o89bobo$882b2o$588b2o292bo2$352b2o233bo<br />
3bo$352bo233bo4bo229bobo$353b3o229bobobo232b2o$355bo228bobobo233bo61bo<br />
$582bo4bo294bobo$517b2o63bo3bo118bo177b2o$517bo15bo9bo159b3o$515bobo<br />
15b3o5b3o37bo2b2o116bo$515b2o19bo3bo39bobo119b2o$323b2o210b2o3b2o38b2o<br />
$323b2o259b2o161bo$584bobo158b3o163bo$300b2o192b2o83b2o5bo157bo164b3o$<br />
300b2o192b2o83b2o5b2o93b2o60bobo162bo$322b2o356bobo60bobo162b2o$322bo<br />
357bo63bo$280b2o38bobo356b2o$280b2o38b2o204b2o$526b2o$538b2o144b2o$<br />
279bo257bo2bo142bobo42b2o$278bobo257b2o4b2o137bo44b2o$279bo264bobo135b<br />
2o$276b3o267bo$263b2o11bo269b2o$264b2o270b2o210b2o$263bo242b2o29bo210b<br />
obo$506bo27b3o213bo$319b2o186b3o11b2o11bo140bo17b2o46b2o7b2o120b2o$<br />
319b2o188bo11b2o2b2o147bobo16b2o46b2o129b3o$525bobo145bo3bo23b2o163b2o<br />
2bo2bobo$526bo145bo3bo24bo29bob2o131b2o2b2o2b2o$530bo140bo3bo26b3o24b<br />
3ob2o135b2o$523b2o4bobo138bo3bo29bo23bo$524bo3bo3bo138bobo55b3ob2o$<br />
521b3o5bo3bo138bo30bo27bobo$316b2o203bo8bo3bo133bo33bobo26bobo132bo$<br />
316bo214bo3bo131bobo32bobo27bo132bobo$317b3o212bobo132b2o32b2ob3o135b<br />
2o21bo2bo$319bo213bo137b2o34bo134b2o22b2o$671bobo27b2ob3o$666b2o5bo27b<br />
2obo$666b2o5b2o195b2o$693b2o46b2o127bobo$684b2o7b2o46b2o129bo$287b2o<br />
312bo83bo186b2o$287b2o310b3o83bobo$598bo87b2o$264b2o332b2o128bo58b3o$<br />
264b2o461bobo56bo$286b2o439bobo56bo3bo$286bo419b2o17b3ob2o55bo2bobo91b<br />
3o$244b2o38bobo139b2o278b2o16bo63bobo2bo91bo$244b2o38b2o291b2o146b3ob<br />
2o58bo3bo90bo$424bo3bo147bobo148bob2o62bo$424bo4bo146bo213b3o$243bo<br />
182bobobo144b2o218bo$242bobo182bobobo259bo102bobo$243bo184bo4bo256bobo<br />
102b2o$240b3o186bo3bo94b2o50b2o108bobo98b2o85b2o$240bo286bo2bo4b2o42bo<br />
bo109bo34b2o62bobo84bo2bo4b2o$430b2o2bo92bobo5b2o42bo108b3o34bobo62bo<br />
5b2o79bobo5b2o$433bobo92bo49b2o108bo36bo63b2o5b2o80bo$434b2o288b2o7bo<br />
151bo$283b2o145b2o91b2o9b2o196bobo138b2o9bobo$283b2o144bobo92bo9b2obo<br />
195bo140bo9bo2bo$429bo5b2o84b3o13bo172b2o28b2o129b3o11bo2bo$428b2o5b2o<br />
84bo15bo172b2o28b2o129bo$534bo2bo51b2o134bo159bo2bo$535b2o52b2o119bo<br />
12b3o159b2o$597b2o110bobo10bo198b2o20b2o$597bo111bo2bo9b2o193b2o2b2o2b<br />
2o16b2o$280b2o316b3o109bo2bo203bobo2bo2b2o$280bo319bo117bo199b3o$281b<br />
3o426bo2bo3bobo199b2o$283bo315bo110b2o4bo2bo$598bobo116b2o$454b2o142bo<br />
bo316bo$450b2o2b2o141b2ob3o313bobo$449bobo75bo75bo312bo2bo$450bo76b3o<br />
67b2ob3o314b2o9b2o$251b2o277bo66b2obo327b2o$251b2o192b3o4b2o75b2o213b<br />
2o$445b3o4bo91b2o43b2o330b2o$228b2o215b3o5b3o88bo35b2o7b2o152bo3bo173b<br />
obo$228b2o212b3o10bo86bobo36bo160bo4bo175bo$250b2o190b3o86bo10b2o37bob<br />
o157bobobo177b2o$250bo191b3o85bobo49b2o156bobobo$199b2o7b2o38bobo279bo<br />
bo205bo4bo$200b2o6b2o38b2o275b2o4bo141b2o63bo3bo$199bo324bobo15b2o129b<br />
o15bo9bo$524bo17bobo57b2o67bobo15b3o5b3o37bo2b2o206b2o$207bo305b2o8b2o<br />
19bo57b2o67b2o19bo3bo39bobo209bo$206bobo304b2obo27b2o145b2o3b2o38b2o<br />
211b3o$207bo309bo222b2o209bo$204b3o307bo225bobo$204bo310bob2o131b2o83b<br />
2o5bo$517b2o68bo62b2o83b2o5b2o176b2o5b2o$586bobo332bo5b2o$521bo11b2o<br />
51bobo332bobo$247b2o271bobo10b2o52bo334b2o$247b2o272b2o61b3o95b2o242b<br />
2o$517b2o65bo97b2o241bobo10b2o$516bobo175b2o230bo11b2o$516bo5b2o90b2o<br />
77bo2bo$515b2o5b2o170b2o4b2o220b2o$612bo3bo83bobo217bob2o$612bo4bo84bo<br />
216bo$244b2o300bo67bobobo83b2o218bo$244bo299b3o68bobobo72b2o134b2o88b<br />
2obo27b2o$245b3o295bo72bo4bo40b2o29bo109bo9bo15bo88b2o8b2o19bo$247bo<br />
295b2o72bo3bo40bo27b3o110b3o5b3o15bobo97bo17bobo$663b3o11b2o11bo115bo<br />
3bo19b2o97bobo15b2o$618b2o2bo42bo11b2o2b2o122b2o3b2o118b2o4bo$621bobo<br />
57bobo251bobo$622b2o58bo252bobo$618b2o66bo164b2o83bo10b2o$215b2o305b2o<br />
93bobo59b2o4bobo163b2o94bobo$215b2o306bo93bo5b2o55bo3bo3bo260bo$191b2o<br />
330bobo90b2o5b2o52b3o5bo3bo259b2o$187b4o4b2o327b2o151bo8bo3bo243b2o$<br />
187b3ob2o2b2o490bo3bo127b2o114bo$192bo495bobo128b2o111b3o$146b2o541bo<br />
117b2o123bo$139b2o5b2o658bo2bo$79b2o58b2o660b2o4b2o$79b2o58b2o55bo603b<br />
obo$65bo74b2o3b2o48bobo602bo$65b3o71bo2bo2b2o23b2o22bo2bo601b2o$68bo9b<br />
ob2o58bo2bo26b2o23b2o445b2o165b2o$67b2o9bobo54b2o6bo494b2o2b2o165bo29b<br />
2o$79bo55b2o3bo2bo6b2o386b2o97bobo170b3o27bo$72bo6b2o59bobo33b2o13b2o<br />
345b2o98bo173bo11b2o11b3o$71bobo5b2o60bo34b2o12bobo520b3o104b2o2b2o11b<br />
o$71bo2bo4b2o63b2o26b2o16bo442b3o4b2o71b3o103bobo$72b2o71bo26b2o15b2o<br />
442b3o4bo72b3o100bo3bo$633b3o5b3o72b3o97b2o$630b3o10bo72b3o96b2obo3b2o<br />
$630b3o83b3o95bo2b3o2bo$177b2o451b3o180bobobo5b3o$134b2o41b2o542bo90bo<br />
bobo8bo$135bo9bo574bobo87b3o2bo$135bobo3bo3bo575b2o88bob2o$136b2o4bo2b<br />
o538b2o31b2o93b2o$142b2ob2o16bobo517bo2bo4b2o23bobo55b2o37bo$143bobo<br />
18b2o517bobo5b2o23bo5b2o50bo238b2o$144bo19bo519bo30b2o5b2o48bobo212b4o<br />
22b2o$772b2o208b2o7bo$216b2o461b2o9b2o290b2o2b2o3bo$209b2o4bo2bo461bo<br />
9b2obo292b2o2bo$209b2o5bobo458b3o13bo74b2o$217bo459bo15bo73bo2bo$171b<br />
2o37bo479bo2bo73bobo$171bo37bobo9b2o327b2o139b2o75bo213bo$130b2o40b3o<br />
33bo2bo9bo327bo2bo4b2o422bobo$130b2o42bo32bo2bo11b3o324bobo5b2o422bo2b<br />
o13b2o$224bo325bo431b2o14b2o$207bo2bo561b2o$209b2o334b2o9b2o210b2obo2b<br />
ob2o$135b2o409bo9b2obo208b2o2bo4bo208b2o$135b2o406b3o13bo213bo212bobo$<br />
131b2o410bo15bo214bobo211bo$131b2o423bo2bo428b2o$172b2o383b2o$172b2o$<br />
137b2o27b2o$137b2o27b2o850b2o$1018bo$749b2o268b3o$168b2o572b2o4bo2bo<br />
269bo$161b2o5b2o572b2o5bobo$142b2o17b2o579b2o6bo$143bo599bo$140b3o599b<br />
obo9b2o$140bo600b2obo9bo247b2o$755b3o245bo23b2o$757bo242b3o24bo$742b2o<br />
256bo7b2o15bobo$742b2o264b2o15b2o10$4b2o$2obo2bob2o$2o2bo4bo997b2o$5bo<br />
1000bobo$6bobo997bo$1005b2o2$9bo$8bobo$7bo2bo$8b2o$1023b2o$1023bo$4b2o<br />
1018b3o$3bobo1020bo$3bo$2b2o4$1015b2o$1006b2o7b2o$1007bo$921b2o84bobo$<br />
921b2o2b2o81b2o$925bobo$926bo$929b3o$923b2o3bo$924bo3bo3bo$921b3o4bo2b<br />
obo$921bo8bobo2bo$931bo3bo$935bo150b2o$692bo239b3o151b2o$105b2o2bo580b<br />
3o346b2o4b2o$101b2o2b2o3bo578bo348bo2bo3b2o$101b2o7bo578b2o348b2o$106b<br />
4o$1013bo$162b2o848bobo$161bo2bo4b2o841bobo$110bo50bobo5b2o497b2o343bo<br />
$109bobo50bo504bobo401b2o$108bo2bo57bo497bo376b2o25b2o$109b2o46b2o9bob<br />
o495b2o353b2o21b2o$158bo9bo2bo840b2o7b2o$155b3o11bo2bo229b2o5b2o601b2o<br />
33b2o$105b2o48bo247bo5b2o260b2o374b2o$104bobo62bo2bo230bobo264bobo384b<br />
2o$104bo64b2o233b2o264bo386bo$103b2o303b2o259b2o384bobo$407bobo645b2o$<br />
408bo$404bo686b2o$1091bo$402b3obo685b3o$401bob2o275b2o412bo$401b2obo<br />
275b2o$399bob3o284b2o$688bo$401bo287b3o359b2o22b2o$691bo359bobo20bobo$<br />
1053bo20bo25b2o$690bo362b2o18b2o25bo$689bobo389b2o15bobo$420b2o267bobo<br />
389b2o15b2o$420b2o2b2o262b2ob3o$424bobo267bo$425bo262b2ob3o$428b3o257b<br />
2obo344b2o$422b2o3bo608b2o$423bo3bo3bo248b2o362b2o$420b3o4bo2bobo238b<br />
2o7b2o362bo$420bo8bobo2bo237bo372b3o$430bo3bo237bobo372bo$434bo238b2o$<br />
431b3o612bo$1045bobo32b2o$1045bobo31bobo$693b2o349b2ob3o29bo$693b2o<br />
355bo27b2o$74b2o968b2ob3o$74b2o968b2obo2$1036b2o63b2o5b2o$678bo348b2o<br />
7b2o63b2o5bo$677bobo348bo77bobo$677bobo348bobo75b2o$678bo350b2o71b2o$<br />
675b3o412b2o10bobo$675bo414b2o11bo3bo$1106b2o$1049b2o54bob2o$1049b2o<br />
53b3o2bo35b2o$1106bobobo34b2o$25b2o1080bobobo$25b2o1052b2o27bo2b3o$<br />
1080bo19b2o7b2obo$1034bo45bobo17bo9b2o$1033bobo45b2o15bobo9bo$1033bobo<br />
57bo4b2o$1034bo57bobo$1031b3o58bobo$33b2o996bo49b2o10bo36b2o$33b2o<br />
1045bobo47b2o$1080bo$1079b2o$710bo383b2o$708b3o383bo$707bo387b3o$707b<br />
2o388bo4$1150b2o$686b2o462bo$685bobo463b3o$685bo467bo$684b2o3$574bo<br />
114b2o$574b3o111bobo443b2o$577bo110bo446bo23b2o$576bobo108b2o443b3o24b<br />
o$576bobo553bo24bobo$577bo579b2o2$2o$2o$698b2o$592b2o62bo41b2o442b2o$<br />
592b2o62b3o47b2o434b2o7b2o$659bo46bo444bo$658bobo46b3o439bobo$658bobo<br />
48bo439b2o$572b2o85bo472b2o$571bobo134bo423b2o$571bo135bobo412b2o$570b<br />
2o7b2o126bobo413bo$579b2o125b2ob3o411bobo$674b2o36bo411b2o$587b2obo83b<br />
2o30b2ob3o$587b2ob3o113b2obo$593bo$587b2ob3o105b2o$588bobo63b2o33b2o7b<br />
2o$588bobo62bobo34bo$589bo63bo36bobo$652b2o7b2o28b2o$590bo70b2o465b2o$<br />
588b3o536bobo$587bo81b2obo454bo$587b2o80b2ob3o36b2o413b2o$579b2o94bo<br />
35b2o$579b2o88b2ob3o$670bobo$670bobo$671bo$696bo446b2o$672bo22bobo445b<br />
2o$568b2o100b3o22bobo437b2o$569bo99bo26bo439bo$569bobo97b2o22b3o437b3o<br />
$570b2o89b2o30bo439bo$661b2o$1134bo$565b2o566bobo$566bo566bobo$566bobo<br />
562b3ob2o$567b2o561bo$650b2o479b3ob2o$651bo481bob2o$651bobo$652b2o489b<br />
2o$588b2o553b2o7b2o72b2o$588bo563bo73b2o$589b3o55b2o501bobo$591bo56bo<br />
501b2o$648bobo$649b2o2$1130b2o$1130b2o2$670b2o539b2o$670bo540b2o$671b<br />
3o$673bo472bo$1145bobo$1145bobo$1146bo$1147b3o$502bo646bo$502b3o$505bo<br />
$504bobo724b2o$504bobo724bo$505bo726b3o$1234bo$1134b2o11bo$1134b2o10bo<br />
bo$1146bobo31b2o21b2o5b2o$520b2o62bo560b2ob3o2b2o25bo23bo5b2o$520b2o<br />
62b3o564bo2bo23bobo23bobo$587bo557b2ob3o3bobo21b2o25b2o$586bobo556b2ob<br />
o6b2o52b2o$586bobo619bobo10b2o$500b2o85bo621bo11b2o$499bobo$499bo704b<br />
3o$498b2o7b2o695b3o$507b2o695b3o$602b2o538b2o13b2o42b3o$515b2obo83b2o<br />
538b2o13b2o42b3o28b2o$515b2ob3o606b2o72b3o7b2o19bo$521bo604bo2bo82bo<br />
17bobo$515b2ob3o604bob2o83bobo15b2o$516bobo63b2o541bo87b2o4bo$516bobo<br />
62bobo540b2o92bobo$517bo63bo557b2o77bobo$580b2o7b2o548bo79bo10b2o$518b<br />
o70b2o549b3o23b2o62bobo$516b3o623bo24bo64bo$515bo81b2obo563b3o4b2o59b<br />
2o$515b2o80b2ob3o561bo6b2o44b2o$507b2o94bo614bo$507b2o88b2ob3o612b3o$<br />
598bobo614bo$598bobo$599bo2$600bo$496b2o100b3o$497bo99bo$497bobo97b2o$<br />
498b2o89b2o$589b2o$893bo$493b2o398b3o$494bo401bo364b2o$494bobo398bobo<br />
363b3o$495b2o398bobo357b2o2bo2bobo$578b2o316bo358b2o2b2o2b2o$579bo679b<br />
2o56b2o$579bobo735b2o$580b2o$516b2o$516bo394b2o342bo$517b3o55b2o334b2o<br />
341bobo$519bo56bo677bo2bo$576bobo676b2o$577b2o$891b2o$890bobo366b2o$<br />
890bo368bobo$889b2o7b2o361bo$598b2o298b2o361b2o$598bo$599b3o304b2obo$<br />
601bo304b2ob3o$912bo$906b2ob3o$907bobo$907bobo$908bo2$909bo$907b3o$<br />
906bo$906b2o$898b2o$898b2o6$887b2o$888bo$888bobo$889b2o4$887b2o$887b2o<br />
6$907b2o$907bo$908b3o$910bo32$737bo$737b3o$740bo$739bobo$739bobo$740bo<br />
5$755b2o$755b2o4$735b2o$734bobo$734bo$733b2o7b2o$742b2o2$750b2obo$750b<br />
2ob3o$756bo$750b2ob3o$751bobo$751bobo$752bo2$753bo$751b3o$750bo$750b2o<br />
$742b2o$742b2o6$731b2o$732bo$732bobo$733b2o4$731b2o$731b2o6$751b2o$<br />
751bo$752b3o$754bo21$887bo$887b3o$890bo$889bobo$889bobo$890bo5$905b2o$<br />
905b2o4$885b2o$884bobo$884bo$883b2o7b2o$892b2o2$900b2obo$900b2ob3o$<br />
906bo$900b2ob3o$901bobo$901bobo$902bo2$903bo$901b3o$686b2o212bo$686b2o<br />
2b2o208b2o$690bobo199b2o$691bo200b2o$695bo$688b2o4bobo$689bo3bo3bo$<br />
686b3o5bo3bo$686bo8bo3bo$696bo3bo180b2o$697bobo182bo$698bo183bobo$883b<br />
2o4$881b2o$881b2o5$1046b2o$901b2o142bo2bo4b2o$901bo143bobo4bo2bo$902b<br />
3o141bo5bo$904bo147bo$1041b2o9bob2o$1042bo11b2o$1039b3o$1039bo$1053b2o<br />
$1053b2o46$836b2o$836b2o2b2o$840bobo$841bo$845bo$838b2o4bobo$839bo3bo<br />
3bo$836b3o5bo3bo$836bo8bo3bo$846bo3bo$847bobo$848bo654$1300b3o11$1280b<br />
o$1279bobo$1278bo3bo$1277bo3bo$1276bo3bo$1275bo3bo$1276bobo$1277bo$<br />
1273bo$1272bobo$1272b2o$1276b2o$1276bobo$1271b2o5bo$1271b2o5b2o23$<br />
1250b2o$1248bob2o$1247bo$1250bo$1246b2obo$1246b2o2$1243bo$1242bobo$<br />
1242b2o$1246b2o$1246bobo$1241b2o5bo$1241b2o5b2o360$874bo2$871b3o$873bo<br />
$872bo39$824b2o$823bobo$825bo!<br />
#C [[ THEME Blues STEP 16 X 0 Y -200 Z -4 ]]<br />
#C [[ LABELANGLE 45 ]]<br />
#C [[ LABEL 300 500 2 "FIRE_CC_ODD_DEC1" ]]<br />
#C [[ LABEL 336 464 2 "FIRE_CP_EVEN_DEC1" ]]<br />
#C [[ LABEL 372 428 2 "FIRE_CC_EVEN_DEC1" ]]<br />
#C [[ LABEL 408 392 2 "FIRE_CP_ODD_DEC1" ]]<br />
#C [[ LABEL 444 356 2 "INC16" ]]<br />
#C [[ LABEL 480 320 2 "DEC8" ]]<br />
#C [[ LABEL 516 284 2 "INC4" ]]<br />
#C [[ LABEL 552 248 2 "DEC2" ]]<br />
#C [[ LABEL 588 212 2 "INC1" ]]<br />
#C [[ PASTET 1024 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ PASTET 2048 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ PASTET 3072 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ PASTET 4096 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ PASTET 12288 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ PASTET 16384 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ PASTET 18432 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ PASTET 20480 PASTE 2110$874bo2$871b3o$873bo$872bo39$824b2o$823bobo$825bo! 0 0 ]]<br />
#C [[ STOP 33000 ]]<br />
</code></div></div>
<canvas height="540" style="margin-left: 1px;" width="420"></canvas></div>
<p>With a combination of some subset of these nine operations, the DBCA can generally fire exactly the right next glider in its recipe, at a standard cost of just nine bits on the tape (one "codon"). In any bit position, two incoming gliders will suppress the output and nothing will happen; one incoming glider will allow that operation to happen.
<h3>Slow And Steady Wins The Race</h3>
<p>Notice what happens when the unary decoder in the northwest reaches the ninth output position, and the entire <a href="https://conwaylife.com/wiki/Bistable_switch">bistable switch</a> stack has to be reset to return to zero position. Feeding the final bistable switch output back into one of its inputs does a great job of resetting the entire stack -- eventually. It's all done in 35,000 ticks or so -- see below.
<div class="rle">
<div class="codebox">
<div class="selall">Code:
<a href="#" onclick="selectCode(this); return false;">Select all</a>
</div>
<div><code>x = 636, y = 595, rule = LifeHistory<br />
583.2A$583.2A$569.A13.2A$569.3A12.A$572.A10.A.A$571.2A9.2A.A2$576.A$<br />
575.A.A5.2A$575.A2.A4.2A$576.2A10$547.A.A$550.A$546.A4.A2.2A30.A.A$<br />
546.2A.A2.A.2A31.2A$550.2A35.A4$555.A$554.A.A$553.A2.A$554.2A3$550.2A<br />
$549.A.A$549.A$548.2A5$598.2A$591.2A5.2A15.F$591.2A22.F$615.F$615.F$<br />
593.2A27.2A$593.2A27.2A$587.2A$587.2A$628.2A$628.2A$624.2A$624.2A$<br />
550.2A$549.A2.A$536.A15.A$536.3A13.A66.3A7.2A$539.A9.2A.A34.2A30.A2.A<br />
6.2A$538.2A9.2A35.2A30.A3.A$588.A34.A$619.3A.2A$543.A.2A3.2A71.A$541.<br />
3A.3A2.2A66.A3.2A$542.A.A.2A74.A$543.3A$543.3A$615.A.A$615.2A18.F$<br />
616.A18.F$635.F$626.F8.F$582.2A42.F$582.2A42.F$626.F3$587.2A$587.2A$<br />
583.2A$583.2A$624.2A$624.2A$589.2A27.2A$589.2A27.2A3$620.2A$613.2A5.<br />
2A$613.2A24$533.2A$533.A$531.A.A$516.2A13.2A$516.2A3$496.2A$496.2A3$<br />
495.A$494.A.A$495.A$480.2A10.3A$481.2A9.A$480.A3$535.2A$535.2A7$532.<br />
2A$532.A$533.3A$535.A6$503.2A$503.2A2$480.2A$480.2A$502.2A$502.A$460.<br />
2A38.A.A$460.2A38.2A3$459.A$458.A.A$459.A$456.3A$456.A29.2A$485.A.A$<br />
486.A10$496.2A$496.A$497.3A$499.A6$467.2A$467.2A2$444.2A$444.2A$466.<br />
2A$416.2A48.A$417.2A5.2A38.A.A$416.A7.2A38.2A3$423.A$422.A.A$423.A$<br />
420.3A$420.A29.2A$449.A.A$450.A10$460.2A$460.A45.4B$461.3A43.4B$463.A<br />
44.4B$509.4B$510.4B$511.4B$512.4B$513.4B$431.2A$431.2A2$408.2A$408.2A<br />
$430.2A$430.A$388.2A38.A.A$388.2A38.2A3$387.A$386.A.A$387.A$384.3A$<br />
384.A29.2A$413.A.A$414.A10$424.2A43.4B$424.A45.4B$425.3A43.4B$427.A<br />
44.4B$473.4B$474.4B$475.4B$352.2A122.4B$353.2A122.4B$352.A42.2A81.4B$<br />
395.2A82.3B$480.2B$372.2A107.B$372.2A$394.2A$394.A$352.2A38.A.A$352.<br />
2A38.2A3$351.A$350.A.A$351.A$348.3A$348.A29.2A$377.A.A$378.A7$433.B$<br />
433.2B$433.3B$388.2A43.4B$388.A45.4B$389.3A43.4B$391.A44.4B$437.4B$<br />
438.4B$439.4B$440.4B$441.4B$359.2A81.4B$359.2A82.4B$444.4B$336.2A107.<br />
4B$336.2A108.4B$358.2A87.4B$358.A89.4B$316.2A38.A.A90.4B$316.2A38.2A<br />
92.4B$451.4B$452.4B$315.A137.4B$314.A.A137.4B$315.A139.4B$312.3A141.<br />
4B$312.A29.2A113.4B$341.A.A114.4B$342.A116.4B$460.4B$461.4B2$394.B$<br />
394.2B$394.3B$394.4B$395.4B$288.2A106.4B$289.2A61.2A43.4B$288.A63.A<br />
45.4B$353.3A43.4B$355.A44.4B$401.4B$402.4B$403.4B$404.4B$405.4B$323.<br />
2A81.4B$323.2A82.4B$408.4B$300.2A107.4B$300.2A108.4B$322.2A87.4B$322.<br />
A89.4B$280.2A38.A.A90.4B$280.2A38.2A92.4B$415.4B$416.4B$279.A137.4B$<br />
278.A.A137.4B$279.A139.4B$276.3A141.4B$276.A29.2A113.4B$305.A.A114.4B<br />
$306.A116.4B$424.4B$425.4B$426.4B$427.4B6$316.2A43.4B$316.A45.4B$317.<br />
3A43.4B$319.A44.4B$365.4B$366.4B$367.4B$368.4B$369.4B$287.2A81.4B$<br />
287.2A82.4B$372.4B$264.2A107.4B$264.2A108.4B$286.2A87.4B$286.A89.4B$<br />
244.2A38.A.A90.4B$244.2A38.2A92.4B$379.4B$380.4B$243.A137.4B$242.A.A<br />
137.4B$243.A139.4B$240.3A141.4B$240.A29.2A113.4B$269.A.A114.4B$270.A<br />
116.4B$224.2A162.4B$225.2A162.4B$224.A165.4B$391.4B$392.4B$393.4B$<br />
394.4B$395.4B$396.4B$280.2A115.4B$280.A117.4B$281.3A43.4B68.4B$283.A<br />
44.4B$329.4B$330.4B$331.4B$332.4B$333.4B$251.2A81.4B$251.2A82.4B$336.<br />
4B$228.2A107.4B$228.2A108.4B$250.2A87.4B$250.A89.4B$208.2A38.A.A90.4B<br />
$208.2A38.2A92.4B$343.4B$344.4B$207.A137.4B$206.A.A137.4B$207.A139.4B<br />
$204.3A141.4B$204.A29.2A113.4B$233.A.A114.4B$234.A116.4B$352.4B$353.<br />
4B$354.4B$355.4B$356.4B$357.4B$358.4B$359.4B$360.4B$244.2A43.4B68.4B$<br />
244.A45.4B68.4B$245.3A43.4B68.4B$247.A44.4B68.4B$293.4B68.4B$294.4B<br />
68.4B$295.4B68.4B$296.4B68.4B$297.4B68.4B$215.2A81.4B68.4B$215.2A82.<br />
4B68.4B$191.A108.4B68.4B$187.2A2.2A.3A104.4B68.4B$187.2A4.4A105.4B68.<br />
4B$191.2A110.4B$146.2A156.4B$139.2A5.2A157.4B$79.2A58.2A165.4B$78.B2A<br />
2B113.A110.4B$65.A13.2A2B77.2A33.A.A110.4B$65.3A11.BA2B58.2A18.2A7.2A<br />
22.A2.A111.4B$68.A9.BABA59.2A17.A9.2A23.2A113.4B$67.2A9.2ABA53.2A174.<br />
4B$77.4B54.2A175.4B$72.A4.4B95.2A13.2A120.4B$71.A.A3.2B2AB94.2A12.A.A<br />
121.4B$71.A2.A4.2A91.2A16.A124.4B$72.2A98.2A15.2A125.4B$317.4B$318.4B<br />
$319.4B$177.2A141.4B$134.2A41.2A142.4B$135.A186.4B$135.A.A185.4B$136.<br />
2A186.4B$325.4B$326.4B$327.4B$328.4B$216.2A42.B68.4B$209.2A4.A2.A41.<br />
2B68.4B$209.A2.A3.A.A41.3B68.4B$217.A42.4B68.4B$171.2A36.A2.A48.4B68.<br />
4B$171.A36.A2.A9.2A39.4B68.4B$130.2A40.3A33.A.A10.A41.4B68.4B$130.2A<br />
19.A22.A34.A12.3A39.4B68.4B$150.2A72.A40.4B68.4B$150.A.A56.2A55.4B68.<br />
4B$209.2A56.4B68.4B$135.2A23.3A105.4B68.4B$135.2A20.A.A.A.A105.4B68.<br />
4B$131.2A23.2A.A3.A106.4B68.4B$131.2A24.A.A2.2A107.4B68.4B$155.A5.A<br />
10.2A98.4B68.4B$155.2A.A2.A10.2A99.4B$137.2A18.2A.A5.2A106.4B$137.2A<br />
27.2A107.4B$276.4B$277.4B$168.2A108.4B$161.2A5.2A109.4B$142.2A17.2A<br />
117.4B$143.A137.4B$140.3A139.4B$140.A142.4B$284.4B$285.4B$286.4B$287.<br />
4B$288.4B$289.4B$290.4B$291.4B$292.4B$293.4B$294.4B$295.4B$.ABA292.4B<br />
$.3BAB2.B288.4B$A4BA2B2A288.4B$2ABA2BAB2A289.4B$.B2.2A3B291.4B$6.3B<br />
292.4B$302.4B$303.4B$9.A294.4B$8.A.A294.4B$7.A2.A295.4B$8.2A297.4B$<br />
308.4B$309.4B$4.2A304.4B$3.A.A$3.A$2.2A19$102.4A$101.A7.2A$101.A3.2A<br />
2.2A$102.A2.2A2$162.2A$161.A2.A4.2A$110.A50.A.A3.A2.A$109.A.A50.A$<br />
108.A2.A55.A2.A$109.2A46.2A9.A2.A$158.A10.A.A$155.3A12.A$105.2A48.A$<br />
104.A.A62.2A$104.A64.2A$103.2A32$153.A$152.2A$152.A.A!<br />
#C [[ THEME Blues ]]<br /></code></div></div>
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<p>Compared to the amount of time between successive bits coming in from the RCT mechanism, 35,000 ticks is practically instantaneous. This is a case where the simplicity of the mechanism is paramount (because we're trying to minimize the total number of bits that have to be stored in the RCT mechanism). The length of time that the mechanism takes to recover doesn't matter at all, compared to how much it costs to build it -- and Paul Callahan's bistable switch is made out of just a few Spartan still lifes, and is very cheap to construct.
<h1>What Comes Next</h1>
<p>Current RCT plans call for a <i>second</i> optional bootstrap stage, further improving the encoding efficiency of the system. The ECCA (Extreme Compression Construction Arm) uses 4-bit and 7-bit codons instead of 9-bit codons, and will be constructed with its own integrated self-destruct circuitry. As described in the next post, the ECCA will be responsible for several cleanup tasks, as well as for building the ATBC -- the Actual Thing Being Constructed, which we should be careful not to lose sight of because it's really supposed to be the whole point of this RCT exercise.Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-66433693355106839052022-04-24T22:09:00.024-05:002022-07-05T11:52:06.930-05:00Current RCT Technology, Part 1 (Build Anything Constructible, Now With Just 16 Gliders)<p>... This is an ambitious title in a couple of ways, but I'll try to keep this post up to date as new developments inevitably come along. The most recent update was 28 April 2022.
<h3>The Reverse Caber Tosser (RCT)</h3>
<p>The idea of fixed-cost glider construction recipes got its start in <a href="https://conwaylife.com/forums/viewtopic.php?p=16517#p16517" target="_blank">2015</a>, when Gustavo Rehermann inspired the idea of encoding recipes for large patterns using vast distances between a small number of gliders. Actual prototype patterns started showing up in <a href="https://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html" target="_blank">2018</a>. Rather than directly colliding large number of gliders to build a large structure, these "RCT" patterns essentially measure the distance between two structures, convert those measurements into a very long <a href="https://conwaylife.com/wiki/Construction_arm" target="_blank">universal construction arm</a> recipe of a type that <a href="https://b3s23life.blogspot.com/2014/06/new-wrinkles-in-slow-salvo-construction.html" target="_blank">we already know about</a> -- and then use that recipe to incrementally build the large structure.
<p>The RCT construction method produces recipes with a very small initial population, only 80 cells... at the cost of an unimaginably enormous bounding box, and a similarly huge number of ticks needed to complete the construction.
<p>The first estimates (by Chris Cain) of cost in gliders for a fixed-cost construction system were somewhere in the high three-digit or low four-digit range. This was then reduced to a surprisingly small <a href="https://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html" target="_blank">329</a> gliders, and then gradually over the next several years to a series of ever smaller and more surprising numbers. We're currently at a fixed cost of 16 gliders to build any glider-constructible pattern, no matter how large -- and there's still no guarantee that 16 is the minimum.
<h3>Some Terminology To Start Out</h3>
<p>We'll need a few key terms from <a h/ref="https://conwaylife.com/forums/viewtopic.php?p=104511#p104511">this source</a>, for this post and future posts in the series:
<p><b>epicentre</b>: the area of interest where all of the gliders collide<br />
<b>parsec</b>: the distance between the construction site of the southeastern GPSE and the epicentre<br />
<b>aeon</b>: the time it takes for a lightspeed diagonal signal to traverse a parsec<br />
<b>singularity</b>: the moment when all construction bits have been read<br />
<b>BS</b>: Before Singularity<br />
<b>AS</b>: After Singularity<br />
<b>GPSE</b>: <a href="https://conwaylife.com/wiki/GPSE">glider-producing switch engine</a><br />
<b>BRG</b>: Bit-Reading Glider -- see below.<br />
<b>DBCA</b>: Decoder and Better Construction Arm, an optimization stage described in the next post
<b>BSRD</b>: Bit Storage and Retrieval Device, a method of delaying construction to simplify some cleanup problems, described in a future post
<b>ATBC</b>: the Actual Thing Being Constructed -- the RCT's target object. The goal is to eventually turn 16 gliders into this object, with nothing else left in the infinite Life universe.
<h3>How RCT Works, From the Beginning</h3>
<p>A template RCT pattern that's easy to zoom in on and watch, in Golly if not in LifeViewer, can be found in <a href="https://conwaylife.com/forums/viewtopic.php?p=144445#p144445">this forum post</a>. It's slightly out of date, in that it contains 17 gliders rather than 16. I will probably add an embedded LifeViewer copy here once we have a 16G version of the template available, but all the main ideas are the same.
<p><b>1)</b> In the southwest corner of any RCT pattern, 7 gliders crash to produce a pair of GPSEs (glider-producing switch engines) that produce a specific two-glider salvo of gliders heading northeast. Until recently this construction needed 8 gliders, so this is the <a href="https://conwaylife.com/forums/viewtopic.php?p=144533#p144533">improvement</a> that reduced the minimum fixed cost from 17 to 16.
<p><b>2)</b> A very long way north, in the northwest corner, four more gliders collide to make another GPSE. We can't use just three gliders; there are known 3G GPSE recipes, but they create a lot of uncontrolled gliders flying off in different directions.
<p><b>3)</b> Much later, four more gliders collide, southeast of the epicentre. The long delay here ultimately reduces the cost of the RCT: a potentially very long series of gliders being reflected back from the northwest GPSE would normally need an extra glider to handle, e.g., by setting up a <a href="https://conwaylife.com/wiki/Crystal">crystal</a> to absorb them. With the extra delay, these gliders can instead be harmlessly caught by an eater built by the construction arm (see below).
<p><b>4)</b> All glider streams meet at the epicentre with specific timing, so that one glider escapes southeastward, and then all four gliders mutually annihilate each other, repeatedly building and destroying a temporary blinker. Let's call that one key escaped glider the "Bit-Reading Glider".
<p><b>5)</b> Bit-Reading Gliders always travel southeast from the four-stream collision point, to the GPSE whose position encodes the RCT recipe. The return signal after a Bit-Reading Glider reaches its destination may be a glider, or it may be a "hole" -- a glider missing from the standard northwest-traveling GPSE glider stream.
<p><b>6)</b> Every time a signal bounces back and forth, it allows either one or two gliders to escape past the blocking blinker to strike the central target -- depending on which phase of the GPSE is encountered by each of the Bit-Reading Gliders (BRGs).
<h3>How the Math Works</h3>
<p>Each new return signal arrives twice as quickly as the previous one. The entire system is designed to retrieve a series of bits from the large distance between the epicentre and the southeast GPSE, in an operation that amounts to repeatedly dividing the distance by two and taking the remainder. See the next section for the specific mechanisms.
<p>If a period-256 stream of gliders could be arranged to bounce off of an approaching c/12 Cordership, the returning glider stream would be period 128 instead of period 256, due to the Doppler effect. Something similar is happening here, but in the 17G and 16G RCT designs, the p256 glider stream is very very intermittent. An occasional BRG manages to escape, but all the rest of the gliders in that southeast-traveling p256 stream are suppressed at the epicentre.
<p>Each BRG may reach the approaching GPSE at either time 0 (mod 256) or 128 (mod 256) -- and the gliders colliding at the epicentre are very carefully arranged to do something different with the results of those two possible BRG + GPSE collisions. Each time the distance from the epicentre to that southeast GPSE is divided by two, there's another free choice of possible original starting positions for the GPSE -- one producing the 0 (mod 256) collision, and one producing the 128 (mod 256) collision.
<h3>Something To Try Out In Golly</h3>
<p>For a bigger and more functional example, download the "shillelagh_final_cropped.mc" pattern <a href="https://conwaylife.com/forums/viewtopic.php?p=144345#p144345">here</a> and open it in <a href="https://sourceforge.net/projects/golly/">Golly</a>.
<p>At around T=2500 in this cropped pattern, a Bit-Reading Glider is approaching the southeast GPSE for the first time. The BRG is circled in the northwest corner of this snapshot:
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<div><code>x = 221, y = 174, rule = B3/S23<br />
3bobo$bo5bo2$o2bobo2bo$4b2o$o3bo3bo2$bo5bo$3bobo50$53bo$52b2o$52bobo4$<br />
132b3o$131bo$130bo4b2o$129bo3bo15b3o$129bo2bo4bo4b2o$129bo3bo3bo4b3obo<br />
$130b2obob3o$133bo$134b4o20b2o$136b2o11bob2o5b2o$149bo2bo$149b3o5$166b<br />
2o$166b2o2$153b3o$138b2o13bo$138b2o14bo3$158b3o$159b2o2$173b2o$146b2o<br />
9b3o13bobo$146b2o11bo14bo$165b2o$156bob2o5b2o$151bo7bo$150b3o6bo$149b<br />
2obo3b2obo$150bobo3b3o$150b3o3bo$151b2o3$190b2o$190b2o13b2o$204bo2bo$<br />
205b2o$179bo$178bobo$165bo12b2o$164bobo$164b2o$208bo$208bo2bo6b2o$208b<br />
o3bo5b2o$174bo34bo2bo5bo$173bobo37bo$173b2o36b2ob2ob2o$213bo3$117bo$<br />
116b2o$116bobo2$209bo$209bo$211b2o$174b2o30b3ob2obo$173bo2bo29b2o2b2ob<br />
obo$174b2o30b3o3b3o$208b4o$170b3o36b3o$210bo$174bo$174bo$174bo2$176b2o<br />
$176b2o2$197bo$196bobo$196b2o4$206bo$205bobo$205b2o2$168b2o$168b2o7$<br />
164b2o$164b2o40b2o$205bo2bo$206b2o2$202b3o2$206bo$206bo$206bo$174b2o$<br />
173bobo32b2o$173b2o33b2o$218b3o!<br />
#C [[ THEME Blues ]]<br /></code></div></div>
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<p> Run the above for about a thousand ticks to see the returning "1" signal glider being generated, to head northwest parallel to the regular GPSE glider stream.
<p>At around T=13800 in the "shillelagh_final_cropped.mc" pattern (not in the above snapshot of it!), you'll see this in the center:
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<div><code>x = 175, y = 163, rule = B3/S23<br />
21bobo$22b2o$22bo62$85bobo$86b2o$86bo4$84b3o3$81bo$81b2o$80bobo16$73bo<br />
bo$71bo5bo$109bo$70bo3bo3bo29b2o$73b2o33bobo$64b2o4bo2bobo2bo$65b2o$<br />
64bo6bo5bo$73bobo38$17bo$17b2o$16bobo18$173bo$172b2o$172bobo$2o$b2o$o!<br />
#C [[ THEME Blues ]]<br /></code></div></div>
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<p>Here I've circled the returning "1" signal from the Bit-Reading Glider. This is the same northwest-traveling glider that we saw being created in the previous snapshot.
<p>The collision releases a single construction-arm glider headed northeast, and a new Bit-Reading Glider heads southeast. There's also an extra glider heading northwest, but these are absorbed harmlessly by the ash of the incoming GPSE, and that ash will get cleaned up later. In one possible phase of the collision a glider is created heading back towards the epicentre, but we've already talked about how an eater will be constructed to catch those.
<p>At around T=24550 there's another central collision, resulting in another singleton glider heading northeast.
<p>At around T=29900 another central collision, another singleton glider -- the bouncing glider gets back twice as quickly for each new collision.
<p>At around T=30800, the next Bit-Reading Glider is approaching the GPSE in the southeast:
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<div><code>x = 189, y = 139, rule = B3/S23<br />
3bobo$bo5bo2$o2bobo2bo$4b2o$o3bo3bo2$bo5bo$3bobo31$110b2obo$109b3obo6b<br />
obo$108bo4bobo4bo$109b2o6bobo3bo$110bo3bo2bo2b2o$113bob2o3bo$112bobo<br />
16b2o$112bobo16b2o6$47bo$46b2o$46bobo$117bo10b2o$112bo3b5o5bo2b3o$111b<br />
obo7b2ob3ob2ob2o$111bo7bob2o2bo2bobob2o$112bo8b2o3b2obo2bo$113bo3b4o6b<br />
3obo$118b3o8b2o$125b2o11bo$125b2o7bo2bo$134bo2bo$119b2o12bo$119b2o12b<br />
2o$133b2o2$155b2o$131b3o21b2o$131bo2b2o$132b3o$133bo10bo$143bobo$143b<br />
2o$135b2o$134bo2bo$134b5o31bo$135b3o31b3o$159b2o8b2obo4bo$139bo18bo3bo<br />
6b3ob6o$138bobo17bo5bo3b4o2b2o2b2o$138b2o18b2o4bo3bob2obo2bo2b2o$153b<br />
2o6bo3b2o4b2ob4obo$153b2o6b4o7b3ob2obo$164b3o$164b2o$165bobo$164bo2bo$<br />
165bob2o4bo$167b2obo3b2o$162b3o3bobo2b2o$164bo$139b2o22bo$138bo2bo$<br />
139b2o2$135b3o2$139bo$139bo47b2o$139bo47b2o2$141b2o$141b2o33bo$175bobo<br />
$162bo12b2o$161bobo$161b2o4$171bo$170bobo$170b2o$111bo$110b2o21b2o$<br />
110bobo20b2o2$129bo$128bo$127b2o$123b3o3bo$122bo6b2o$120b3o$119bo2bob<br />
2o2b2o41b2o$119b4ob5o41bo2bo$121b8o21bo20b2o$123b4o22b3o$148bo18b3o$<br />
149b2o$171bo$171bo$171bo$139b2o$138bobo32b2o$138b2o33b2o$183b3o!<br />
#C [[ THEME Blues ]]<br /></code></div></div>
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<p>This time, though, thanks to the magic of Dividing By Two And Checking The Remainder, the mod-256 timing of the collision is clearly very different! It's offset by 128 ticks from what we've seen before. Instead of hitting a block and making an extra offset glider, here the Bit-Reading Glider strikes an active part of the GPSE glider-generating reaction, and no return glider is released at all for one cycle -- no extra offset glider, and no glider in the GPSE stream either.
<p><b>Side note</b>: If you're paying close attention here, when you run the above snapshot you'll see a worrisome detail: an extra glider gets generated that heads off to the southeast! It turns out that this glider gets absorbed by the ash of the next Bit-Reading Glider collision to the southeast, without generating any new gliders. The resulting variation in BRG collision ash is still a concern, because it complicates the problem of cleaning up all that ash -- but we'll deal with that in future episodes!
<p>At around T=32750 another central collision is about to happen:
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<div><code>x = 181, y = 169, rule = B3/S23<br />
21bobo$22b2o$22bo62$85bobo$86b2o$86bo7$87b3o6$81bo$81b2o$80bobo15$114b<br />
obo$112bo5bo2$111bo7bo2$111bo7bo$64b2o$65b2o45bo5bo$64bo49bobo39$17bo$<br />
17b2o$16bobo18$179bo$178b2o$178bobo$2o$b2o$o!<br />
#C [[ THEME Blues ]]<br /></code></div></div>
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<p>In the snapshot above I've circled the location where that suppressed glider would ordinarily be in the standard GPSE stream. The result of that missing glider is that <b>two</b> construction-arm gliders will be released toward the target in the northeast, instead of just one. Run the pattern and watch it happen.
This is all a very tricky and clever series of interactions, originally invented by MathAndCode (Daniel Vargas) and proved out by Adam P. Goucher in <a href="https://conwaylife.com/forums/viewtopic.php?p=104461#p104461">late 2020</a>.
<h3>Universality Achieved</h3>
<p>The above patterns show the binary choice of one glider versus two gliders, that turns out to give us just enough control to create slow salvos of gliders that can build any glider-constructible object. See <a href="https://conwaylife.com/forums/viewtopic.php?p=144315#p144315">this forum post</a> for an actual example of the full 17-glider macrocell pattern, openable in Golly, that constructs a small example object, a <a href="https://conwaylife.com/wiki/Shillelagh">shillelagh</a> -- but leaves a lot of ash to clean up (to put things very mildly). Forum posts following that post document a way of reducing the initial population of an RCT pattern to 16 gliders.
<p>The final fate of that shillelagh-making macrocell pattern's central area is the shillelagh_final_cropped.mc pattern that we were looking at above. The two-glider output is the last bit that can be retrieved by the Bit-Reading Glider. After that point the GPSEs all reach the epicentre, crash into the construction area, and make a big mess.
That big mess is obviously no good: for this RCT trick to work, we really want to end up with just a our intended object, and nothing else. What we're getting instead is, in this case, a shillelagh at the center of several incredibly long trails of GPSE ash. Blog posts yet to come will describe the details of the cleanup process for those ash trails.
<h3>See, It Actually Works</h3>
<p><b>4)</b>The "binary slow salvo" described above (a free choice at each point of either a single glider, or two gliders) is <a href="https://conwaylife.com/forums/viewtopic.php?p=143781#p143781">known to be capable of</a> very slowly generating new target objects at a safe distance from the construction lanes, and also clean 90-degree gliders on any lane we choose, aimed at those targets. We know from previous experience that this is sufficient for universal construction.
<p>In <a href="https://conwaylife.com/forums/viewtopic.php?p=143781#p143781">this forum post by Adam P. Goucher</a> is a demonstration of the 1-glider and 2-glider operations being sent in a very precisely chosen order to one of these construction arms, to build the shillelagh from the example macrocell pattern. The demo skips the part about encoding the recipe in a ridiculously large 16-glider macrocell pattern, and instead just sends the recipe gliders one after another (so there are a lot more than sixteen of them).
<p>I may add a version of the demo pattern here as a LifeViewer animation eventually. In the meantime, the demo is <i>still</i> far too large to fit in LifeViewer without PASTET scripting commands. However, it will run very quickly if loaded into Golly and run with a high step size.
<h3>This Is Where It Starts To Get Complicated (!)</h3>
<p>The <a href="https://b3s23life.blogspot.com/2022/05/current-rct-technology-part-2-dbca.html">next post</a> will talk more about about the DBCA -- "Decoder and Better Construction Arm" -- which is an optional stage of the RCT that allows us to build much more complex objects with the same number of bits encoded in the RCT distance. That is to say, with roughly the same sized <b>parsec</b> (to use the terminology from the top of this post) you can produce a much more complex final pattern if you include something like a DBCA stage. In fact, for a very wide range of parsec sizes, the DBCA will be the only thing that makes it possible to build any recognizable object at all, as opposed to just creating a truly humongous quantity of repetitive junk plus a (relatively) tiny constructed object at the RCT epicentre.
<p>The third post will briefly describe the rationale behind a <i>second</i> optional bootstrap stage, the ECCA -- "Extreme Compression Construction Arm". This stage really only improves the efficiency of construction data storage by a relatively minor percentage, but it turns out that it's worth building it anyway because it's very useful to have a construction arm pointing in a different direction.
<p>The fourth and final post will walk through current plans for completely cleaning up all of that repetitive junk, leaving only the constructed ATBC object behind. Again, ATBC just means the Actual Thing Being Constructed -- the shillelagh, or whatever object the main construction recipe codes for, up to and including a pi-calculator pattern or a fleet of a million Gemini spaceships.Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-34398802148477424712020-08-29T17:28:00.009-05:002022-05-12T12:31:47.936-05:00Self-constructing diagonal spaceships, now with limit speed c/4![<b>EDIT 4/24/2022</b>: Recently another feat of seed-construction legerdemain created an adjustable self-constructing spaceship analogous to the one in the title, with an orthogonal limit speed of c/2. Details can be found <a href="https://conwaylife.com/forums/viewtopic.php?p=144242#p144242">here</a>.]
<p>For several years the upper speed limit for diagonally-traveling self-constructing spaceships has been c/12, the speed of a Cordership. This is because self-constructing spaceships speeds are always limited to the maximum speed at which a target object can be moved by a given <a href="https://conwaylife.com/wiki/Construction_arm">construction arm</a>. We can build structures that come as close as we want to that maximum speed, simply by increasing the period of the spaceship and spending a longer time moving the target object at top speed. Only a constant amount of time is needed to construct a copy of the spaceship's circuitry, so with a long enough period, the construction time can be made to be as small a percentage of the elbow-push time as you want.
<p>Until recently, the fastest Demonoids used a "Corderpush" method to move their elbows and target blocks: i.e., first a Cordership was constructed and allowed to travel a long distance, and eventually it was shot down by a following salvo of gliders to produce faraway target <a href="https://conwaylife.com/wiki/Ash">ash</a>, which was then converted into a new copy of the spaceship's circuitry by a <a href="https://conwaylife.com/wiki/Slow_salvo">slow salvo</a>.</p>
<p>In late July 2020, Goldtiger997 constructed a new type of Demonoid puffer with the record-breaking velocity of (4825784,4825784)c/45679544 -- slightly slower than c/10 diagonally. This is a speed that can't be attained by Corderpush technology. What was used instead was a new and very large <a href="https://conwaylife.com/wiki/Seed">seed</a> for a c/5 diagonal spaceship, which like a Cordership can be followed by a slow salvo of gliders to stop it after it travels a long distance, producing target objects for construction without releasing any stray gliders.</p>
<p>Here is the incredibly large and complex seed used by the new Demonoid spaceship:</p>
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<div><code>x = 1296, y = 1352, rule = B3/S23<br />
939bo$938bobo$938b2o16$925bo$924bobo$923bobo$923b2o3$925b2o$925bobo$<br />
926bo6$922bo$921bobo$922b2o$622bo$621bobo283bo$622b2o282bobo$905bobo$<br />
905b2o23b2o$929bobo$928bobo$907b2o20bo$907bobo$908bo7$903bo$902bobo$<br />
902bo2bo55bo$903bobo54bobo$638bo249bo15bo56b2o$637bobo247bobo$638bobo<br />
245bobo12b2o51b2o$639b2o245b2o12bo2bo49bo2bo$900bobo50bo2bo$901bo52b2o<br />
$637b2o249b2o$636bobo249bobo$637bo251bo7$889bo$637b2o249bobo$636bo2bo<br />
231bo11bo3bo2bo$637b2o231bobo9bobo3b2o$644b2o11bo211bobo10bobo$643bo2b<br />
o9bobo210b2o12bo$644bobo10bobo$645bo12b2o$871b2o$871bobo$656b2o214bo$<br />
655bobo$656bo3$870bo$869bobo$868bo2bo$869b2o$656bo197bo11bo$655bobo<br />
195bobo9bobo$655bo2bo3bo11bo177bobo10bo2bo$656b2o3bobo9bobo176b2o12b2o<br />
$661bobo10bobo$662bo12b2o$854b2o$854bobo$673b2o180bo$672bobo$673bo3$<br />
997bo$996bobo$996b2o48bo$675b2o368bobo$674bo2bo159bo16b2o189bo2bo$675b<br />
2o159bobo8b2o5bobo189b2o11bo$835bobo9b2o6bo202bobo$835b2o221b2o$876bo<br />
105bo$875bobo103bobo$837b2o37b2o104b2o$837bobo$679bo158bo30b2o104b2o<br />
59b2o$678bobo187bo2bo102bo2bo58bobo16bo$679b2o187bo2bo102bo2bo59bo16bo<br />
bo$869b2o104b2o77b2o$535bo$534bobo165bo268bo$535b2o164bobo131b2o133bob<br />
o59b2o$702bobo129bo2bo132b2o59bo2bo$703b2o130b2o156b2o36bo2bo$569bo<br />
397b2o24b2o37b2o$568bobo396bobo$568b2o131b2o265b2o49b2o$700bobo114bo<br />
170b2o29bobo$575b2o124bo114bobo169b2o30bo$574bo2bo237bobo144bo45bo$<br />
533bo40bo2bo237b2o15bo128bobo43bobo$532bobo40b2o254bobo128b2o43b2o$<br />
533bobo295b2o182b2o$534b2o167bo113b2o136b2o57bo2bo$702bobo112bobo113bo<br />
20bo2bo56bo2bo$538bo163bo2bo112bo113bobo19bo2bo57b2o$537bobo163b2o228b<br />
2o20b2o$538bo168bo$706bobo160bo56b2o$705bo2bo159bobo54bo2bo$706b2o14bo<br />
93b2o51b2o54bo2bo$721bobo92bobo107b2o$722bobo92bo44b2o$723b2o76bo59bo<br />
2bo137b2o$800bobo58bo2bo74bo13b2o47bobo$799bobo60b2o74bobo12b2o48bo$<br />
721b2o76b2o137b2o$720bobo94b2o155b2o$721bo94bo2bo154b2o$801b2o13bo2bo<br />
129b2o47b2o$801bobo13b2o130b2o46bo2bo$802bo166b2o26bo2bo$969b2o27b2o2$<br />
667bo$666bobo57bo$666b2o57bobo$726b2o$673b2o65bo56bo$606bo65bo2bo63bob<br />
o54bobo$605bobo64bo2bo64bobo53b2o$605b2o66b2o51b2o13b2o40bo36bo$726bob<br />
o53bobo34bobo$612b2o113bo53bobo36b2o$567bo43bo2bo124b2o40b2o13b2o$566b<br />
obo42bo2bo123bobo54bobo15b2o41bo$566b2o44b2o125bo56bo15bo2bo39bobo$<br />
783b2o27bo2bo40b2o$573b2o118bo89bobo27b2o$572bo2bo116bobo83b2o4bo64b2o<br />
$572bo2bo116b2o84b2o68bo2bo69bo$573b2o165b2o106bo2bo68bobo$699b2o38bob<br />
o107b2o69b2o$698bo2bo38bo$698bo2bo54bo25b2o$529bo169b2o54bobo24bobo$<br />
528bobo225bobo24bo$529b2o226b2o233b2o$739b2o251bobo$738bo2bo251bo$738b<br />
o2bo13b2o198bo$501b2o236b2o13bobo26b2o169bobo$500bobo252bo26bo2bo168b<br />
2o$501bo280bo2bo202b2o$783b2o202bo2bo$559bo192b2o233bo2bo$558bobo190bo<br />
2bo233b2o139bo$505b2o52b2o189bo2bo374bobo$504bo2bo243b2o17bo357b2o$<br />
504bo2bo54b2o205bobo$505b2o54bobo206bobo322b2o$531bo29b2o193bo14b2o<br />
321bobo$530bobo222bobo335bobo$531b2o22b2o197bobo177bo159bo$555b2o197b<br />
2o13b2o162bobo174bo$768bobo162b2o174bobo4bo$524b2o243bo142b2o196b2o3bo<br />
bo$523bobo34b2o350b2o200bobo$524bo35b2o539b2o11b2o$1101bobo$907b2o193b<br />
o$907b2o$528b2o$527bo2bo242b2o$527bo2bo222bo18bo2bo128b2o$528b2o51bo<br />
170bobo17bobo129b2o$580bobo169b2o19bo55bo54bo$581b2o245bobo52bobo$759b<br />
2o18bo49b2o52b2o201b2o8bo$758bo2bo16bobo119b2o183bo2bo6bobo4bo$758bo2b<br />
o16b2o42b2o56b2o18b2o183bobo8b2o3bobo$759b2o60bo2bo55bobo203bo13bobo$<br />
821bo2bo56b2o217b2o$822b2o$1084b2o$1083bo2bo$1084b2o2$800bo$799bobo63b<br />
o44bo$800bobo61bobo42bobo$801b2o61b2o43b2o$905b2o$572b2o287b2o42bobo$<br />
572b2o225b2o60bobo42b2o$798bobo61b2o215bo$799bo266bo11bobo4bo$1065bobo<br />
11b2o3bobo$576b2o487bobo15bobo$576b2o488bo16b2o$581bo$580bobo$581b2o$<br />
585b2o$584bobo$584b2o213b2o16bo27bo$798bobo5b2o8bobo25bobo215b2o$799bo<br />
6b2o9bobo24b2o215bo2bo$818b2o241bobo$841b2o219bo$841bobo$816b2o24b2o<br />
49bo$815bobo74bobo130b2o$816bo4b2o69b2o88b2o41bobo$821b2o65b2o92bobo<br />
41bo$888bobo92bo$889b2o$598bo458bo$597bobo217b2o202b2o33bobo4bo$598b2o<br />
216bobo159b2o40bo2bo33b2o3bobo$817bo159bo2bo39bo2bo18b2o5bo11bobo$977b<br />
o2bo40b2o19bobo3bobo10b2o$978b2o63bo4bobo$644bo404bo$508b2o88bo44bobo$<br />
418bo88bobo87bobo43b2o171b2o68b2o$417bobo88bo89b2o215bo2bo67bobo$418b<br />
2o11bo13bo156b2o46b2o163bo2bo68bo72b2o$425bo4bobo11bobo93b2o59bobo45bo<br />
2bo163b2o142bobo$424bobo3b2o12bo2bo91bobo59b2o46bo2bo308bo$425bobo17b<br />
2o65b2o26bo109b2o$426b2o83bo2bo367b2o$511bo2bo152bo213bo2bo$512b2o152b<br />
obo212bo2bo71b2o83bo$544b2o120b2o214b2o71bo2bo69bo11bobo4bo$443b2o98bo<br />
2bo73bo24bo309bo2bo68bobo11b2o3bobo$443bobo97bo2bo72bobo22bobo26b2o<br />
281b2o69bobo15bobo$444b2o98b2o74b2o23b2o25bo2bo352bo16b2o$604b2o66bo2b<br />
o$603bobo42b2o23b2o$604bo42bobo219b2o$647b2o220b2o2$559b2o$558bobo47b<br />
2o254b2o158b2o$559bo47bo2bo253b2o157bo2bo$450bo9bo146bo2bo412bobo$444b<br />
o4bobo7bobo146b2o414bo$443bobo3b2o8bobo152bo48bo$444bobo13bo102b2o48bo<br />
bo46bobo$445b2o115bo2bo48b2o47b2o$562bo2bo52b2o330b2o$563b2o52bobo46b<br />
2o282bobo$463bo153b2o46bobo283bo$462bobo200b2o$462bo2bo542bo10bo$463b<br />
2o542bobo8bobo4bo$946b2o60b2o9b2o3bobo$945bo2bo74bobo$945bo2bo74b2o$<br />
946b2o3$1007b2o$1007b2o3$471bo10bo$465bo4bobo8bobo$464bobo3b2o9b2o$<br />
465bobo174b2o32bo$466b2o174b2o31bobo72bo$676b2o71bobo$609b2o138b2o250b<br />
o$608bobo36b2o351bobo4bo$482b2o125bo37b2o107b2o235b2o6b2o3bobo$482b2o<br />
271bo2bo233bo2bo9bobo$755bo2bo123bo109bobo10b2o$756b2o123bobo105bo3bo$<br />
613b2o93bo172bo2bo103bobo$612bo2bo91bobo172b2o104bo2bo$612bo2bo91b2o<br />
280b2o$613b2o$714b2o$713bo2bo180b2o$489bo223bo2bo180b2o$483bo4bobo223b<br />
2o$482bobo3b2o6b2o388bo16b2o$483bobo9bo2bo386bobo15bobo$484b2o10bobo<br />
386bobo11b2o3bobo$497bo3bo384bo11bobo4bo68bo9bo$500bobo396bo73bobo7bob<br />
o4bo$499bo2bo470bobo8b2o3bobo$500b2o205bo266bo13bobo$706bobo279b2o$<br />
667bo39b2o$666bobo$667b2o41b2o259bo$709bobo258bobo$709b2o258bo2bo$970b<br />
2o$671bo$506bo163bobo$500bo4bobo163b2o228b2o$499bobo3b2o7bo160b2o224bo<br />
bo$500bobo10bobo158bobo225bo$501b2o10bobo158b2o235bo381b2o$514bo395bob<br />
o10b2o368bobo$523bo386bobo10bobo368bo$522bobo386bo7b2o3bobo38bo$523b2o<br />
393bobo4bo26bo11bobo4bo$919bo31bobo11b2o3bobo$951bobo15bobo$641b2o309b<br />
o16b2o$640bobo$641bo321b2o$963b2o$727b2o$727b2o538b2o$645b2o278bo341bo<br />
bo$644bo2bo276bobo21b2o318b2o$644bo2bo276b2o21bo2bo$526bo118b2o84b2o<br />
214bobo$520bo4bobo203b2o215bo$519bobo3b2o7bo395bo$520bobo10bobo393bobo<br />
353b2o$521b2o10bobo162b2o228bo2bo344b2o7bobo$534bo163b2o229b2o12b2o<br />
330bobo8bo$543bo399bobo329b2o$542bobo394b2o3bobo$543b2o158b2o233bobo4b<br />
o$703b2o234bo9$582b2o361b2o$581bobo360bo2bo$546bo35bo358bo3b2o$540bo4b<br />
obo392bobo16b2o$539bobo3b2o7bo384bobo17bobo$540bobo10bobo384bo14b2o3bo<br />
bo$541b2o10bobo30b2o366bobo4bo$554bo30bo2bo366bo$563bo21bo2bo$562bobo<br />
21b2o$563b2o2$640b2o$639bobo$640bo$960bo$959bobo$825b2o132bo2bo$644b2o<br />
178bo2bo132b2o$643bo2bo177bo2bo$643bo2bo178b2o107b2o$644b2o287bo2bo$<br />
566bo13b2o351bo2bo$560bo4bobo5bo5bo2bo351b2o$559bobo3b2o5bobo4bo2bo<br />
247bo$560bobo9b2o6b2o247bobo132bo16b2o$499bo61b2o266b2o132bobo15bobo$<br />
498bobo438bo23bobo11b2o3bobo$497bo2bo437bobo23bo11bobo4bo$498b2o438b2o<br />
37bo3$781b2o$483b2o296b2o$483b2o2$477b2o16bo290b2o$476bobo15bobo289b2o<br />
$475bobo3b2o11bobo85bo9bo$476bo4bobo11bo80bo4bobo7bobo$482bo92bobo3b2o<br />
8bobo145b2o$576bobo13bo145bobo140b2o$577b2o159b2o140bo2bo$880bo2bo115b<br />
2o$741b2o138b2o71b2o28bo14bobo$595bo145bobo209bo2bo26bobo9b2o3bobo$<br />
594bobo145bo210bo2bo25bobo9bobo4bo$594bo2bo356b2o26b2o6bo4bo$476bo118b<br />
2o289bo102bobo$475bobo407bobo100bo2bo$463b2o11b2o407b2o101bobo$462bobo<br />
271b2o221bo29bo$461bobo3b2o266bo2bo219bobo$462bo4bobo265bo2bo219b2o$<br />
468bo267b2o19b2o$484bo271bobo$483bobo257b2o11b2o$482bobo116bo140bobo<br />
38b2o25b2o191bo$482b2o111bo4bobo11bo128bo15b2o22bobo23bobo185bo4bobo$<br />
594bobo3b2o11bobo143bobo22bo24b2o185bobo3bobo10b2o$595bobo15bobo144bo<br />
52b2o181b2o5bo11bobo$596b2o16bo198bobo195b2o3bobo$462bo351bo5b2o188bob<br />
o4bo$461bobo138b2o215bo2bo188bo$449b2o11b2o138b2o215bo2bo$448bobo369b<br />
2o$447bobo3b2o$448bo4bobo$454bo162b2o$470bo145bo2bo205bo$469bobo145bob<br />
o204bobo$468bobo147bo205b2o190bo$468b2o545bobo$1015bo2bo$1016b2o4$451b<br />
o373b2o$445b2o3bobo371bobo$444bobo3b2o372b2o$445bo382b2o190bo16b2o$<br />
431b2o395bobo188bobo15bobo$430bobo396bo189bobo11b2o3bobo$429bobo3b2o<br />
583bo11bobo4bo$430bo4bobo595bo$436bo$798b2o$797bobo$797b2o2$800b2o$<br />
800bobo$801bo237bo$1038bobo$939b2o97b2o11b2o$938bo2bo109bobo$938bo2bo<br />
105b2o3bobo$433b2o504b2o105bobo4bo$432bobo612bo$433bo597bo$424bo605bob<br />
o$411b2o10bobo33b2o356b2o125bo86bobo$410bobo10bobo32bo2bo354bobo124bob<br />
o86b2o$409bobo3b2o7bo33bo2bo35b2o317b2o125b2o$410bo4bobo41b2o35bo2bo$<br />
416bo79bo2bo319b2o$497b2o320bobo13b2o$820bo14bobo$455bo380bo213b2o$<br />
454bobo592bo2bo$455b2o36bo38b2o516bobo3b2o$492bobo36bo2bo516bo3bo2bo$<br />
493b2o36bo2bo300b2o217bo2bo$410bo121b2o300bobo218b2o13b2o$409bobo422b<br />
2o234bobo$397b2o11b2o170b2o482b2o3bobo$396bobo35b2o146bobo117b2o133b2o<br />
226bobo4bo$395bobo3b2o30bo2bo91bo54b2o116bo2bo132bobo226bo$396bo4bobo<br />
29bo2bo90bobo49b2o77b2o41bo2bo133bo$402bo31b2o92b2o39b2o7bobo76bo2bo<br />
41b2o67b2o$418bo149bo2bo7bo77bo2bo109bo2bo$417bobo148bo2bo86b2o49b2o<br />
59bo2bo87b2o$416bobo150b2o137bobo60b2o88b2o$416b2o12bo278bo$429bobo<br />
346b2o$430b2o345bobo70b2o$565bo92bo119bo71bobo12b2o205b2o$396bo167bobo<br />
90bobo191bo13b2o204bo2bo$395bobo167b2o90b2o409bo3b2o$383b2o11b2o669bob<br />
o16b2o$382bobo550b2o129bobo17bobo$381bobo3b2o545bo2bo129bo14b2o3bobo$<br />
382bo4bobo263b2o279bo2bo143bobo4bo$388bo264b2o4bo275b2o145bo$404bo163b<br />
2o88bobo13b2o$403bobo162bobo87b2o13bo2bo$402bobo164b2o70b2o30bo2bo$<br />
402b2o161b2o74bobo30b2o264bo$564bobo75b2o12b2o281bobo$565bo90bobo280b<br />
2o159b2o$639b2o16bobo440bobo$638bobo17bo309b2o131bo$639bo34bo292bo2bo$<br />
673bobo291bo2bo$380bo292b2o107b2o184b2o$379bobo399bo2bo$378bo2bo399bo<br />
2bo$379b2o401b2o$973bo$675bo27b2o84b2o181bobo$674bobo25bo2bo82bobo80b<br />
2o99b2o$557b2o62b2o51b2o26bo2bo83bo81bobo$557bobo61bobo79b2o167bo$558b<br />
2o62b2o$358b2o16bo177b2o116b2o36b2o$357bobo15bobo175bobo63b2o31b2o18bo<br />
bo9b2o6bo16bobo$356bobo3b2o11bobo176bo63bobo30bo2bo18bobo8b2o5bobo16bo<br />
$357bo4bobo11bo242bo31bo2bo19bo16b2o$363bo288b2o$795b2o$450b2o193b2o<br />
147bo2bo$449bo2bo192bobo146bo2bo$449bo2bo193bo148b2o$450b2o$426b2o374b<br />
2o$425bo2bo372bobo$425bo2bo263bo109bo$426b2o18bo152b2o90bobo$445bobo<br />
151bobo89b2o$359bo86b2o152b2o$353b2o3bobo349bo$352bobo3b2o62bo153b2o<br />
19b2o90b2o18bobo$353bo67bobo114b2o35bobo18bobo90bobo10b2o5bo2bo$339b2o<br />
81b2o114bobo35bo20bo92bobo9bobo5b2o252b2o$338bobo198b2o150bo11b2o258bo<br />
2bo$337bobo3b2o190b2o426bo2bo$338bo4bobo188bobo342b2o83b2o$344bo190bo<br />
343bobo$880bo28b2o$909bobo$558b2o350bo58bo$558b2o408bobo$890b2o76b2o$<br />
889bobo$889b2o$554b2o155bo203b2o$554b2o154bobo179b2o21bobo$710b2o180bo<br />
bo21bo$723bo169bo$323b2o397bobo$322bobo9b2o6b2o299b2o63b2o13b2o219b2o$<br />
321bobo3b2o5bobo4bo2bo297bo2bo62bobo233bobo$322bo4bobo5bo5bo2bo297bo2b<br />
o63bobo233bo$328bo13b2o299b2o65bo$723b2o$636b2o85bobo$636bobo85bo$637b<br />
o2$803b2o$802bo2bo$802bo2bo$530b2o271b2o$325bo204b2o9b2o186bo$319b2o3b<br />
obo213bobo185bobo79b2o$318bobo3b2o215bo186b2o13b2o64bobo63b2o38b2o38b<br />
2o$319bo422bobo65bo63bo2bo37bobo36bobo$305b2o219b2o213bobo130bo2bo38bo<br />
37b2o$304bobo219b2o198b2o14bo132b2o81b2o$303bobo3b2o415bobo229bobo$<br />
304bo4bobo415bobo152b2o75bo$310bo417bo17b2o133bobo$500b2o243bo2bo133bo<br />
64b2o14b2o$499bobo136b2o104bo2bo199b2o13bo2bo$500bo136bo2bo104b2o215bo<br />
2bo$529b2o106bo2bo322b2o$529b2o107b2o$743bo207b2o$631b2o109bobo206b2o<br />
36b2o$524b2o105bobo108b2o224bo19bo2bo$304b2o218b2o106bo334bobo18bo2bo$<br />
303bo2bo660b2o20b2o$303bobo128b2o304b2o$304bo60b2o66bo2bo303bobo$364bo<br />
2bo65bo2bo304bobo$364bo2bo66b2o306bo251bo$286b2o77b2o394bo231bobo$285b<br />
obo13bo99b2o357bobo230b2o$284bobo3b2o8bobo97bo2bo80b2o275b2o$285bo4bob<br />
o7bobo97bo2bo26bo53b2o250b2o145b2o$291bo9bo59bo39b2o26bobo303bo2bo143b<br />
o2bo$360bobo67b2o303bo2bo143bo2bo$361b2o373b2o23b2o120b2o90b2o$480b2o<br />
279bobo211bobo$340b2o55bo77b2o3b2o280bo127b2o84bo33b2o$339bo2bo53bobo<br />
76b2o412bobo117bo2bo$339bo2bo54b2o491bo118bobo$340b2o395bo265bo6bo$<br />
470b2o264bobo263bobo$285b2o183b2o265b2o263bobo$284bo2bo715bo$284bobo<br />
49bo430bo135b2o$285bo49bobo428bobo133bo2bo$336b2o184b2o217b2o23b2o134b<br />
o2bo$521bobo212bo4b2o160b2o46b2o$267b2o253bo212bobo213bobo$266bobo13bo<br />
453b2o26b2o144b2o40bo53b2o$265bobo3b2o8bobo480bobo142bobo94bobo$266bo<br />
4bobo7bobo357b2o122bobo142bo96bo$272bo9bo357bo2bo81b2o11b2o26bo$640bo<br />
2bo80bo2bo9bobo$641b2o81bobo9bobo$725bo11bo$634b2o79b2o$634bobo77bo2bo<br />
216b2o$635bo79b2o216bo2bo$933bo2bo$934b2o$266b2o$265bo2bo672b2o$266b2o<br />
672bobo$941bo$250b2o204b2o$249bobo13bo190b2o$248bobo3b2o8bobo$249bo4bo<br />
bo6bo2bo$255bo8b2o185b2o261bo$451b2o39b2o219bobo$492b2o205b2o13b2o84bo<br />
$699bobo97bobo149b2o$700bobo96bobo3b2o143bo2bo$701bo14b2o82bo3bo2bo<br />
142bo2bo$488b2o225bobo87bobo143b2o$488b2o224bobo89bo$2o633b2o59b2o17bo<br />
242b2o$2o632bo2bo57bo2bo258bobo$5b2o245bo381bo2bo58bo2bo258bo$6bo239b<br />
2o3bobo381b2o60b2o$3b3o239bobo3b2o$3bo242bo100b2o115b2o162b2o$232b2o<br />
112bo2bo113bobo162bobo69bo105bo$231bobo112bo2bo114bo164bo56bo12bobo<br />
103bobo12bo$230bobo3b2o109b2o336bobo12b2o103b2o12bobo$231bo4bobo447bob<br />
o129bobo$237bo449bo131bo$702b2o99b2o$343bo345bo11bobo99bobo11bo$342bob<br />
o251b2o90bobo9bobo101bobo9bobo$23b2o318b2o250bo2bo89bobo10bo103bo10bob<br />
o$22bobo419b2o149bo2bo90bo127bo$23bo419bobo150b2o$444bo$589b2o$28b2o<br />
559bobo$28b2o204bo355bo$228b2o3bobo$227bobo3b2o449bo137bo$228bo454bobo<br />
135bobo$214b2o454b2o12b2o135b2o12b2o$213bobo454bobo161bobo$212bobo3b2o<br />
193b2o256bo163bo$213bo4bobo191bobo271b2o131b2o$219bo193bo271bobo131bob<br />
o$684bobo133bobo$671b2o12bo135bo12b2o$442b2o226bo2bo159bo2bo$442bobo<br />
226b2o161b2o$443b2o2$440b2o$439bobo$213b2o225bo$212bo2bo452bo169bo$<br />
212bo2bo216b2o233bobo167bobo$213b2o216bobo234b2o167b2o$432bo2$208b2o<br />
460b2o163b2o11b2o$194b2o11bobo459bobo163bobo9bo2bo$193bobo11b2o459bobo<br />
165bobo9bobo$192bobo3b2o5b2o314b2o146bo167bo11bo$193bo4bobo3bobo313bo<br />
2bo334b2o$199bo4b2o314bo2bo333bo2bo$521b2o335b2o2$514b2o38b2o$514bobo<br />
36bo2bo84b2o$357b2o156bo37bo2bo84bobo$356bo2bo194b2o86bobo$356bo2bo12b<br />
2o269bo$193bo163b2o13bobo172b2o$192bobo178b2o172bobo$193b2o174b2o42b2o<br />
133bo89b2o$368bobo42bobo221bo2bo$353bo15bo44b2o222bo2bo218bo$188bo163b<br />
obo55b2o227b2o218bobo13b2o$187bobo163b2o54bobo447b2o13bo2bo$187bo2bo<br />
219bo463bo2bo$174b2o12b2o417b2o33bo232b2o$173bobo430bo2bo31bobo213b2o$<br />
172bobo3b2o426bo2bo32b2o213bobo$173bo4bobo120b2o304b2o249bobo$179bo<br />
120bo2bo555bo$300bo2bo35b2o259b2o28b2o12b2o229bo$301b2o35bo2bo258bobo<br />
26bo2bo10bobo228bobo$338bo2bo259bo27bo2bo9bobo229b2o$339b2o289b2o11bo<br />
2$297bo$296bobo326b2o$297b2o36bo87b2o199bobo249bo$334bobo86bobo198b2o<br />
249bobo$171bo163b2o19b2o66b2o87b2o107b2o251b2o$170bobo4bo178bobo40b2o<br />
111bo2bo105bobo$158b2o10bobo3bobo178b2o39bobo20b2o89bo2bo105b2o$157bob<br />
o11bo5b2o174b2o44bo20bobo90b2o358b2o$156bobo3b2o188bobo66bo451bobo$<br />
157bo4bobo188bo152b2o366bobo$163bo342bobo113bo252bo$507bo113bobo$622b<br />
2o$285b2o139b2o180b2o$284bo2bo137bo2bo178bobo$284bo2bo137bo2bo179bo15b<br />
2o251b2o$285b2o139b2o195bobo251bobo$622bobo253bo$419b2o202bo$378b2o39b<br />
obo46b2o26b2o$281bo95bobo40bo46bo2bo24bo2bo$280bobo95bo88bo2bo24bo2bo$<br />
281b2o185b2o26b2o106b2o$603bo2bo$461b2o26b2o113b2o$461bobo25bobo$341b<br />
2o119bo27bo$340bobo$341bo243bo$584bobo$583bobo16bo$129b2o221b2o229b2o<br />
16bobo$128bobo220bobo248b2o$129bo222bo2$604b2o$591b2o10bobo$591bobo8bo<br />
bo$592bo10bo2$272b2o$271bo2bo$271bo2bo$272b2o46b2o$319bobo266bo$320bo<br />
266bobo$588b2o$268bo$267bobo$268b2o320b2o$577b2o10bobo$577bobo8bobo$<br />
578bo10bo2$435b2o135bo$434bo2bo133bobo$434bo2bo133bo2bo$435b2o135b2o2$<br />
428b2o$409b2o17bobo$408bo2bo17bo$408bo2bo$409b2o$349b2o217bo$348bobo<br />
51b2o148b2o13bobo$349bo52bobo146bo2bo13b2o$403bo147bo2bo$552b2o$261b2o<br />
307b2o$260bo2bo305bobo$260bo2bo304bobo$261b2o306bo$553bo$552bobo$553b<br />
2o$257bo$256bobo$257b2o$302b2o$302b2o81b2o165bo$384bo2bo163bobo$384bo<br />
2bo149b2o13b2o$243b2o52b2o86b2o150bobo$242bo2bo51b2o36b2o201bobo$242bo<br />
2bo88bobo41b2o159bo14b2o$243b2o90bo42bobo172bobo$379bo172bobo$534b2o<br />
17bo$533bo2bo$239bo48b2o244bo2bo$238bobo46bobo245b2o$239b2o47bo35b2o$<br />
324bobo$325b2o211bo$537bobo$322b2o214b2o$321bobo202bo$322bo202bobo$<br />
525b2o13b2o$539bobo$538bobo$359b2o178bo$358bo2bo163b2o$358bo2bo162bobo<br />
$359b2o164bo2$352b2o$352bobo$353bo$275b2o52b2o$275bobo50bo2bo$276b2o<br />
50bo2bo188bo$272b2o55b2o173b2o13bobo$271bobo229bo2bo13b2o$272bo49b2o<br />
179bo2bo$322bobo179b2o$323bo198b2o$521bobo$520bobo16b2o$273b2o246bo16b<br />
o2bo$272bobo230bo32bobo$273bo230bobo32bo$505b2o$540bo$539bobo$539b2o2$<br />
504bo$503bobo$490b2o12b2o$490bobo$491bo$318b2o186b2o$317bo2bo184bobo$<br />
317bo2bo183bobo$318b2o171b2o12bo$490bo2bo$311b2o178b2o$311bobo$312bo4$<br />
488bo$487bobo$488b2o3$490b2o$489bobo$488bobo$468b2o19bo$468bobo$469bo<br />
4$291b2o176b2o$290bo2bo174bo2bo$290bo2bo175b2o$291b2o2$276bo7b2o$275bo<br />
bo6bobo$276bo8bo$466bo$272b2o191bobo$271bobo192b2o$270bobo$271bo$468b<br />
2o$467bobo$448b2o16bobo$447bobo17bo$448bo2$266b2o$265bobo$266bo3$444b<br />
2o$443bo2bo$444b2o6$442bo$441bobo$442b2o3$431bo12b2o$430bobo10bobo$<br />
429bo2bo9bobo$430b2o11bo$423b2o$422bo2bo$423b2o8$423bo$422bobo$423b2o<br />
3$412bo12b2o$411bobo10bobo$406b2o3bobo9bobo$405bo2bo3bo11bo$405bobo$<br />
406bo7$406bo$405bobo$406b2o3$408b2o$407bobo$406bobo$407bo$386b2o$385bo<br />
bo$386bo7$382b2o$381bo2bo$382b2o6$380bo$379bobo$380b2o288bo$669bobo$<br />
670bobo$382b2o287b2o$381bobo$380bobo$381bo5$378b2o$377bobo$378bo25$<br />
360b2o$360bobo$361bo337$30b3o$32bo$31bo!<br />
[[ THEME 2 STEP 30 T 4500 X 0 Y -200 Z -2 STEP 30 T 7000 STEP 15 T 8200 STEP 10 T 8500 Z 3 Y -300 X 60 STEP 2 T 9000 THEME 3 ANGLE 315 ]]
</code></div></div>
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<p>This impressive piece of technology stirred up new interest in the subject. Less than a month later, a collaborative effort produced a new and much cheaper glider recipe for a c/4 diagonal wickstretcher based on a <a href="https://conwaylife.com/wiki/Crab">crab</a>. Crab spaceships are glide symmetric and have two attachment points for long barge/boat <a href="https://conwaylife.com/wiki/Wick">wicks</a>. These wicks can burn cleanly, faster than the wickstretcher can travel.</p>
<p>It turns out that just the right gliders traveling near a crab spaceship can allow a burning wick to either destroy the crab when it catches up with it, or else just stop the wickstretching activity and leave a target block behind, safely off to one side.</p>
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<div><code>x = 511, y = 511, rule = LifeSuper<br />
67.pA.pA$68.2pA$68.pA47$116.S$117.S$115.3S118$277.M$276.M.M$277.2M35.<br />
3N$316.N$315.N$312.2N$312.N2$310.N3.2N$309.N.N2.2N5.3N$258.2M48.N.N3.<br />
N.N6.N$257.M2.M46.N.N6.2N4.N$257.M.M33.3N10.N.N6.N.4N$258.M36.N9.N.N<br />
10.2N$280.2M5.2M5.N9.N.N8.N$279.M2.M3.M.M14.N.N8.N.N$265.2M13.M.M3.M<br />
15.N.N8.N.N$265.2M14.M3.2M14.N.N8.N.N$300.N.N8.N.N$299.N.N8.N.N$252.<br />
2M44.N.N8.N.N$251.M.M43.N.N8.N.N$251.2M43.N.N8.N.N$295.N.N8.N.N$294.N<br />
.N8.N.N3.3N$250.2M15.2M3.2M7.M11.N.N8.N.N6.N$249.M.M15.2M3.M.M4.3M10.<br />
N.N8.N.N6.N$248.M.M22.M4.M12.N.N8.N.N$249.M28.2M10.N.N8.N.N$289.N.N8.<br />
N.N$266.2M20.N.N8.N.N$266.2M19.N.N8.N.N$287.2N8.N.N8.2M$243.2M51.N.N<br />
10.M$242.M.M50.N.N8.3M$242.2M15.2M34.2N9.M$259.M.M$261.M10.N$243.M17.<br />
2M8.N.N33.2M$242.M.M27.2N32.M2.M$242.M.M25.2M35.M.M$243.M19.2M5.2M29.<br />
2M5.M$264.M10.2M24.M$264.M.M3.2M2.M.M22.M.M$234.2M29.2M2.M2.M2.M23.2M<br />
$234.2M33.M.M$231.M38.M45.2M6.M$230.M.M7.M65.2M8.M.M4.M.M$230.M.M5.3M<br />
33.M26.M4.M.M8.M.M4.2M$231.M5.M6.M28.M.M5.2M5.2N10.M.M4.2M9.M$237.2M<br />
4.M.M23.M3.M2.M3.M.M5.N.N10.2M$242.M.M18.2M4.M4.M.M4.M7.N$242.2M19.M.<br />
M3.M5.M31.M$265.M14.M25.M.M5.2M$265.2M12.M.M.2M20.M2.M5.2M$272.3M3.M<br />
2.M.2M21.2M$279.2M2$293.2M$257.2M8.2M11.2M11.2M$257.2M7.M2.M10.M$261.<br />
M4.M2.M11.3M$260.M.M4.2M14.M$260.2M24.M$286.3M$289.M$266.M21.2M14.M$<br />
265.M.M36.3M$264.M2.M32.M6.M$242.2M21.2M22.2M8.M.M4.2M$241.M.M16.2M<br />
27.M10.M.M$242.M16.M2.M24.M.M11.2M$260.2M21.M3.2M$282.M.M$281.M.M$<br />
281.2M$242.2M28.M$241.M2.M26.M.M$241.M2.M5.2M18.M.M$242.2M5.M2.M17.2M<br />
$249.M2.M31.M$250.2M22.2M7.M.M$274.M9.M$272.M.M$272.2M5.2M$279.2M3$<br />
265.M$264.M.M$255.2M7.2M$255.M.M20.2M$256.M20.M.M$278.M$233.3M$235.M$<br />
234.M87$125.3W$127.W$126.W5$111.3W$113.W$112.W3$427.2S$426.2S$428.S<br />
12$96.3S$98.S$97.S$132.3W$134.W$133.W21$71.2S$72.2S$71.S31$508.2pA$<br />
508.pA.pA$508.pA44$27.2pA$26.pA.pA$28.pA23$.pA$.2pA$pA.pA!<br />
#C [[ X 22 Y -37 Z 5 ]]</code></div></div>
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<p>Here the green gliders stand in for a slow-salvo cleanup of the wickstretcher activation reaction, the yellow gliders create a boat and convert it to an R-loaf to light the first wick, which burns without destroying the crab spaceship. The pink gliders perform the same wick-lighting trick later for the second wick, but this time when the reaction catches up to the crab, it destroys it, leaving a slow-salvo target behind.</p>
<p>This mechanism allows a wickstretcher to easily produce two targets separated by long distances. This is exactly what is needed by a Speed Demonoid design, where the recipe spends a fair fraction of its time traveling in the same direction as the full spaceship, zigzagging back and forth between its two halves. Each half will be made up of a Scorbie Splitter (which produces a copy of the recipe to be used by the splitter's construction arm) and a Snark reflector, separated from the Scorbie Splitter by a long distance in the direction of travel.</p>
<p>Here is a <a href="https://conwaylife.com/forums/viewtopic.php?p=103603#p103603">21-glider slow salvo</a> that produces two workable targets. They happen to be lined up one right behind the other, so they could be used as elbow blocks for a single-channel recipe, but. This is not a design requirement, though; slsparse could equally well compile two standard slow-salvo recipes that produce a Scorbie splitter and a Snark, a safe distance to the northwest of these two target blocks.</p>
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<div><code>x = 525, y = 530, rule = B3/S23
516b2o$515bobo$517bo$514bo$513b2o$513b2o$514b2o$511bo3b2o6b2o$510bobob
o2b2o3bobo$509bobo4b3o5bo$495b2o11bobo10bo$494bobo10bobo10b2o$496bo9bo
bo8bo$505bobo8bobo$504bobo8bobo$503bobo8bobo$502bobo8bobo$501bobo8bobo
$500bobo8bobo$499bobo8bobo$498bobo8bobo$497bobo8bobo$496bobo8bobo3b2o$
495bobo8bobo3bobo$494bobo8bobo6bo$493bobo8bobo$492bobo8bobo$491bobo8bo
bo$490bobo8bobo$489bobo8bobo$488bobo8bobo$487bobo8bobo$486bobo8bobo$
485bobo8bobo$484bobo8bobo$483bobo8bobo$482bobo8bobo$481bobo8bobo$480bo
bo8bobo$479bobo8bobo$478bobo8bobo$477bobo8bobo$476bobo8bobo$475bobo8bo
bo$474bobo8bobo$473bobo8bobo$472bobo8bobo$471bobo8bobo$470bobo8bobo$
469bobo8bobo$468bobo8bobo$467bobo8bobo$466bobo8bobo$465bobo8bobo$464bo
bo8bobo$463bobo8bobo$462bobo8bobo$461bobo8bobo$460bobo8bobo$459bobo8bo
bo$458bobo8bobo$457bobo8bobo$456bobo8bobo$455bobo8bobo$454bobo8bobo$
453bobo8bobo$452bobo8bobo$451bobo8bobo$450bobo8bobo$449bobo8bobo$448bo
bo8bobo$447bobo8bobo$446bobo8bobo$445bobo8bobo$444bobo8bobo$443bobo8bo
bo$442bobo8bobo$441bobo8bobo$440bobo8bobo$439bobo8bobo$438bobo8bobo$
437bobo8bobo$436bobo8bobo$435bobo8bobo$434bobo8bobo$433bobo8bobo$432bo
bo8bobo$431bobo8bobo$430bobo8bobo$429bobo8bobo$428bobo8bobo$427bobo8bo
bo$426bobo8bobo$425bobo8bobo$424bobo8bobo$423bobo8bobo$422bobo8bobo$
421bobo8bobo$420bobo8bobo$419bobo8bobo$418bobo8bobo$417bobo8bobo$416bo
bo8bobo$415bobo8bobo$414bobo8bobo$413bobo8bobo$412bobo8bobo$411bobo8bo
bo$410bobo8bobo$409bobo8bobo$408bobo8bobo$407bobo8bobo$406bobo8bobo$
405bobo8bobo$404bobo8bobo$403bobo8bobo$402bobo8bobo$392b2o7bobo8bobo$
391bobo6bobo8bobo$393bo5bobo8bobo$398bobo8bobo$397bobo8bobo$396bobo8bo
bo$395bobo8bobo$394bobo8bobo$393bobo8bobo$392bobo8bobo$391bobo8bobo$
390bobo8bobo$353b2o34bobo8bobo$352bobo33bobo8bobo$354bo32bobo8bobo$
386bobo8bobo$374b2o9bobo8bobo$373bobo8bobo8bobo$375bo7bobo8bobo$382bob
o8bobo$381bobo8bobo$380bobo8bobo$379bobo8bobo$378bobo8bobo$377bobo8bob
o$376bobo8bobo$375bobo8bobo$374bobo8bobo$373bobo8bobo$372bobo8bobo$
371bobo8bobo$370bobo8bobo$369bobo8bobo$368bobo8bobo$342b2o23bobo8bobo$
341bobo22bobo8bobo$343bo21bobo8bobo$364bobo8bobo$363bobo8bobo$362bobo
8bobo$361bobo8bobo$360bobo8bobo$359bobo8bobo$358bobo8bobo$357bobo8bobo
$356bobo8bobo$355bobo8bobo$354bobo8bobo$353bobo8bobo$352bobo8bobo$351b
obo8bobo$350bobo8bobo$349bobo8bobo$348bobo8bobo$347bobo8bobo$346bobo8b
obo$345bobo8bobo$312b2o30bobo8bobo$311bobo29bobo8bobo$313bo28bobo8bobo
$341bobo8bobo$340bobo8bobo$339bobo8bobo$338bobo8bobo$337bobo8bobo$336b
obo8bobo$335bobo8bobo$334bobo8bobo$333bobo8bobo$332bobo8bobo$331bobo8b
obo$330bobo8bobo$329bobo8bobo$328bobo8bobo$327bobo8bobo$326bobo8bobo$
325bobo8bobo$324bobo8bobo$323bobo8bobo$322bobo8bobo$321bobo8bobo$320bo
bo8bobo$300b2o17bobo8bobo$299bobo16bobo8bobo$301bo15bobo8bobo$316bobo
8bobo$315bobo8bobo$314bobo8bobo$313bobo8bobo$312bobo8bobo$311bobo8bobo
$310bobo8bobo$309bobo8bobo$308bobo8bobo$307bobo8bobo$306bobo8bobo$305b
obo8bobo$304bobo8bobo$294b2o7bobo8bobo$293bobo6bobo8bobo$295bo5bobo8bo
bo$300bobo8bobo$299bobo8bobo$298bobo8bobo$297bobo8bobo$296bobo8bobo$
295bobo8bobo$294bobo8bobo$293bobo8bobo$279b2o11bobo8bobo$278bobo10bobo
8bobo$280bo9bobo8bobo$289bobo8bobo$288bobo8bobo$287bobo8bobo$286bobo8b
obo$285bobo8bobo$284bobo8bobo$283bobo8bobo$282bobo8bobo$281bobo8bobo$
280bobo8bobo$253b2o24bobo8bobo$252bobo23bobo8bobo$254bo22bobo8bobo$
276bobo8bobo$275bobo8bobo$274bobo8bobo$273bobo8bobo$272bobo8bobo$271bo
bo8bobo$270bobo8bobo$269bobo8bobo$268bobo8bobo$267bobo8bobo$266bobo8bo
bo$265bobo8bobo$264bobo8bobo$263bobo8bobo$237b2o23bobo8bobo$236bobo22b
obo8bobo$238bo21bobo8bobo$259bobo8bobo$258bobo8bobo$257bobo8bobo$256bo
bo8bobo$255bobo8bobo$254bobo8bobo$253bobo8bobo$252bobo8bobo$251bobo8bo
bo$250bobo8bobo$249bobo8bobo$248bobo8bobo$247bobo8bobo$246bobo8bobo$
245bobo8bobo$244bobo8bobo$226b2o15bobo8bobo$225bobo14bobo8bobo$227bo
13bobo8bobo$240bobo8bobo$239bobo8bobo$238bobo8bobo$237bobo8bobo$236bob
o8bobo$235bobo8bobo$234bobo8bobo$207b2o24bobo8bobo$206bobo23bobo8bobo$
208bo22bobo8bobo$230bobo8bobo$229bobo8bobo$228bobo8bobo$227bobo8bobo$
226bobo8bobo$225bobo8bobo$224bobo8bobo$223bobo8bobo$222bobo8bobo$221bo
bo8bobo$220bobo8bobo$219bobo8bobo$218bobo8bobo$196b2o19bobo8bobo$195bo
bo18bobo8bobo$197bo17bobo8bobo$214bobo8bobo$213bobo8bobo$212bobo8bobo$
211bobo8bobo$210bobo8bobo$209bobo8bobo$208bobo8bobo$207bobo8bobo$206bo
bo8bobo$205bobo8bobo$178b2o24bobo8bobo$177bobo23bobo8bobo$179bo22bobo
8bobo$201bobo8bobo$200bobo8bobo$199bobo8bobo$198bobo8bobo$197bobo8bobo
$196bobo8bobo$195bobo8bobo$194bobo8bobo$193bobo8bobo$192bobo8bobo$191b
obo8bobo$154b2o34bobo8bobo$153bobo33bobo8bobo$155bo32bobo8bobo$187bobo
8bobo$186bobo8bobo$185bobo8bobo$184bobo8bobo$183bobo8bobo$182bobo8bobo
$181bobo8bobo$180bobo8bobo$179bobo8bobo$178bobo8bobo$177bobo8bobo$176b
obo8bobo$175bobo8bobo$174bobo8bobo$173bobo8bobo$172bobo8bobo$171bobo8b
obo$170bobo8bobo$169bobo8bobo$168bobo8bobo$167bobo8bobo$166bobo8bobo$
140b2o23bobo8bobo$139bobo22bobo8bobo$141bo21bobo8bobo$162bobo8bobo$
161bobo8bobo$160bobo8bobo$159bobo8bobo$158bobo8bobo$157bobo8bobo$156bo
bo8bobo$155bobo8bobo$154bobo8bobo$153bobo8bobo$114b2o36bobo8bobo$113bo
bo35bobo8bobo$115bo34bobo8bobo$149bobo8bobo$148bobo8bobo$147bobo8bobo$
146bobo8bobo$145bobo8bobo$144bobo8bobo$143bobo8bobo$142bobo8bobo$141bo
bo8bobo$140bobo8bobo$139bobo8bobo$138bobo8bobo$137bobo8bobo$136bobo8bo
bo$135bobo8bobo$134bobo8bobo$104b2o27bobo8bobo$103bobo26bobo8bobo$105b
o25bobo8bobo$130bobo8bobo$129bobo8bobo$128bobo8bobo$127bobo8bobo$126bo
bo8bobo$125bobo8bobo$124bobo8bobo$123bobo8bobo$122bobo8bobo$121bobo8bo
bo$120bobo8bobo$119bobo8bobo$118bobo8bobo$117bobo8bobo$94b2o20bobo8bob
o$93bobo19bobo8bobo$95bo18bobo8bobo$113bobo8bobo$112bobo8bobo$111bobo
8bobo$110bobo8bobo$109bobo8bobo$108bobo8bobo$107bobo8bobo$106bobo8bobo
$105bobo8bobo$104bobo8bobo$72b2o29bobo8bobo$71bobo28bobo8bobo$73bo27bo
bo8bobo$100bobo8bobo$99bobo8bobo$98bobo8bobo$97bobo8bobo$96bobo8bobo$
95bobo8bobo$94bobo8bobo$93bobo8bobo$92bobo8bobo$91bobo8bobo$90bobo8bob
o$89bobo8bobo$88bobo8bobo$87bobo8bobo$62b2o22bobo8bobo$61bobo21bobo8bo
bo$63bo20bobo8bobo$83bobo8bobo$82bobo8bobo$81bobo8bobo$80bobo8bobo$79b
obo8bobo$78bobo8bobo$77bobo8bobo$76bobo8bobo$75bobo8bobo$74bobo8bobo$
73bobo8bobo$72bobo8bobo$71bobo8bobo$70bobo8bobo$69bobo8bobo$68bobo8bob
o$67bobo8bobo$66bobo8bobo$65bobo8bobo$64bobo8bobo$63bobo8bobo$62bobo8b
obo$61bobo8bobo$60bobo8bobo$59bobo8bobo$58bobo8bobo$57bobo8bobo$56bobo
8bobo$55bobo8bobo$54bobo8bobo$53bobo8bobo$52bobo8bobo$51bobo8bobo$50bo
bo8bobo$49bobo8bobo$48bobo8bobo$47bobo8bobo$46bobo8bobo$45bobo8bobo$
44bobo8bobo$43bobo8bobo$42bobo8bobo$41bobo8bobo$40bobo8bobo$39bobo8bob
o$38bobo8bobo$37bobo8bobo$36bobo8bobo$35bobo8bobo$34bobo8bobo$33bobo8b
obo$32bobo8bobo$31bobo8bobo$30bobo8bobo$29bobo8bobo$28bobo8bobo$27bobo
8bobo$26bobo8bobo$25bobo8bobo$24bobo8bobo$23bobo8bobo$22bobo8bobo$21bo
bo8bobo$20bobo8bobo$19bobo8bobo$18bobo8bobo$17bobo8bobo$16bobo8bobo$
15bobo8bobo$14bobo8bobo$13bobo8bobo$12bobo8bobo$11bobo8bobo$9bo2bo8bob
o$9bobo8bobo$19bobo$10bo7bobo$8b2o7bobo$16bobo$15bobo$14bobo$13bobo$
12bobo$11bobo$10bobo$9bobo$8bobo$7bobo$6bobo$5bobo$4bobo$3bobo$bo$o2b
2o$o!
#C [[ TRACK 1/4 -1/4 STOP 7855 ]]</code></div></div>
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Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-17770086757012451252020-07-26T11:58:00.003-05:002020-07-26T15:34:04.988-05:00Spaceship Construction For Fun and Profit<p>Glider synthesis technology for Conway's Life spaceships -- i.e., the techniques needed to construct spaceships by crashing gliders into each other -- continues to improve. This is due in large part to the impressive efforts of a new generation of Lifenthusiasts. The current list of glider-constructible spaceships includes loafer, dart, crab, x66, weekender, puffership, B29, Pushalong 1, copperhead, fireship, spider, 25P3H1V0.1, 25P3H1V0.2, 27P4H1V1, 30P5H2V0, 30P4H2V0.4, 31P8H4V0, 46P4H1V0, 56P6H1V0, 58P5H1V1, 60P5H2V0, and 70P2H1V0.1.</p>
<p>The full list of spaceships with known glider recipes can be found <a href="https://conwaylife.com/wiki/Glider_synthesis#Spaceship_syntheses">on the LifeWiki Glider Synthesis page</a>. Considering that only one spaceship in the above list (<a href="">60P5H2V0</a>) had a known synthesis at the beginning of 2013, this is a lot of progress!</p>
<p>Here's a showcase animation created by <a href="https://conwaylife.com/wiki/User:Saka">Saka</a> a few months ago to document the construction of <a href="https://conwaylife.com/wiki/58P5H1V1">58P5H1V1</a>, a 58-bit c/5 spaceship:</p>
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<div><code>x = 536, y = 536, rule = B3/S23<br />
504bobo$504b2o$505bo2$503bo$501b2o$502b2o5bobo$17bo491b2o$18bo491bo$<br />
16b3o$492bo20bobo$491bo21b2o8bobo$491b3o20bo8b2o$20bo503bo$5bobo13b2o$<br />
6b2o12b2o$6bo2$4bo510bo$2bobo509bo$3b2o10bobo496b3o8bo$9bo6b2o505b2o$<br />
10b2o4bo507b2o$9b2o$529bo$527b2o$493bobo32b2o$481bobo9b2o$481b2o11bo$<br />
482bo52bo$533b2o$56bo430bobo44b2o$54bobo430b2o40bobo$55b2o431bo40b2o$<br />
530bo$62bo$63bo$61b3o$487bo$486bo$486b3o20bo$463bobo41b2o$463b2o43b2o<br />
13bo$464bo58bobo$523b2o$67bo$68bo435bo$66b3o426bo6b2o$470bo24bobo5b2o$<br />
31bo438bobo22b2o$32b2o436b2o$31b2o$508bo$506b2o$74bo432b2o$75bo$73b3o$<br />
461bo$461bobo$461b2o4$81bo404bo$82bo402bo$80b3o402b3o$452bo$452bobo$<br />
436bo15b2o$434b2o$426bobo6b2o57bo$426b2o64b2o$427bo49bo15b2o$73bo402bo<br />
$74bo401b3o$72b3o351bo$425bo$425b3o2$61bo$59bobo$60b2o406bo$467bo$65bo<br />
bo399b3o$66b2o3bo$66bo5bo6bo$70b3o7b2o$79b2o9$408bo$407bo$400bobo4b3o$<br />
114bo285b2o63bobo$115bo285bo63b2o$113b3o350bo6$465bo$458bo4b2o$458bobo<br />
3b2o$458b2o5$394bobo$123bo270b2o$124b2o269bo$123b2o$136bo$137bo$135b3o<br />
$398bo$397bo$397b3o$134bobo$135b2o300bo$135bo301bobo$437b2o$134bo$135b<br />
o$133b3o$385bo$384bo52bo$384b3o48b2o$436b2o$380bo30bo$373bo4b2o31bobo$<br />
371b2o6b2o30b2o$141bo230b2o46bo$139bobo276b2o$140b2o277b2o$372bo$129bo<br />
bo240bobo$130b2o240b2o$130bo4$363bo37bo$140bo222bobo35bobo$141b2o27bo<br />
192b2o36b2o$140b2o29b2o$170b2o6$382bo$382bobo$382b2o11$196bo$197b2o$<br />
196b2o4$364bo$348bo15bobo$348bobo13b2o$348b2o10$195bo$196b2o134bobo25b<br />
o$195b2o135b2o26bobo$333bo26b2o2$196bo$194bobo$195b2o$178bo21bobo151bo<br />
bo2bo$176bobo22b2o151b2o3bobo$177b2o22bo141bo11bo3b2o$341b2o$342b2o10$<br />
205bo$203bobo$204b2o2$212bo$213b2o$212b2o103$214bo$197b2o15b2o$198b2o<br />
7b3o3bobo$197bo11bo136b3o$208bo137bo$320b2o25bo$319b2o$321bo3$320b3o$<br />
320bo14b2o$182bo138bo12b2o$182b2o152bo$181bobo27bo$211b2o$210bobo130bo<br />
$337b3o2b2o$337bo4bobo$338bo15$346b2o10bo$185b3o158bobo8b2o$187bo158bo<br />
10bobo$186bo$181b2o$180bobo195bo$182bo7b2o185b2o$189bobo185bobo$191bo<br />
2$178b3o203b3o$180bo172b3o23bo4bo$179bo173bo24b2o5bo$354bo23bobo12$<br />
134b2o$135b2o$134bo2$140bo$140b2o$139bobo3$136b2o$137b2o$98b2o31bo4bo$<br />
97bobo31b2o$99bo30bobo239b2o$371b2o$373bo2$414b2o$409b2o3bobo$404b2o2b<br />
2o4bo$404bobo3bo$404bo8$418bo$417b2o$417bobo8$434b2o$434bobo$434bo14$<br />
141b3o$143bo$142bo$78b3o$80bo$79bo2$75bo$75b2o$65b2o7bobo$64bobo$66bo<br />
3$69bo$69b2o$68bobo$470b2o$449bo20bobo$95b2o351b2o20bo$94bobo351bobo$<br />
96bo2$90b2o$91b2o386b2o$90bo369b2o17bobo$460bobo16bo$449b2o9bo$449bobo<br />
$83b2o364bo$84b2o$83bo404b2o$451b2o35bobo$88b3o359b2o36bo$90bo361bo$<br />
89bo$498b2o$498bobo$454b3o41bo$454bo$455bo3$502b3o$502bo$503bo2$28b2o$<br />
27bobo$29bo7$15b2o$bo12bobo$b2o13bo$obo8bo$11b2o$10bobo4$2b2o$3b2o480b<br />
o$2bo481b2o$484bobo2$8b2o40b3o$9b2o41bo$8bo42bo5$12b3o506bo$14bo505b2o<br />
$13bo4b2o500bobo$17bobo$19bo506b2o$514b2o10bobo$41b3o469b2o11bo$43bo<br />
471bo$21b2o19bo$20bobo$22bo15b2o$39b2o472bo$28bo9bo473b2o$28b2o482bobo<br />
$27bobo$520b2o$519b2o$521bo$515b3o$515bo$40b2o474bo$41b2o$40bo!<br />
[[<br />
WIDTH 720<br />
AUTOSTART<br />
GPS 20<br />
PAUSE 2 "58P5H1V1 Synthesis"<br />
PAUSE 2 "By Kazyan (Tanner Jacobi)\nand Goldtiger997"<br />
PAUSE 2 "The synthesis was posted \non the forums on April 3, 2020."<br />
T 60 "At the time this animation was made,\nit cost 161 gliders."<br />
T 139 "It has since been reduced to 100 gliders."<br />
GPS 30 T 202 "Let's zoom in."<br />
ZOOM 12 GPS 60<br />
T 203 PAUSE 3 "First glider collision."<br />
T 216 PAUSE 3 "Beehive at beehive made."<br />
PAUSE 2 "This will become the 'centerpiece'\nof the consttruction."<br />
T 455 "A complex seed constellation is gradually\nbuilt up around the beehive at beehive."<br />
T 456 PAUSE 3 "OK, that last part was cool.\nIt will happen again on the other side."<br />
X -12<br />
PAUSE 2 "11 cells are added all at once."<br />
T 485 "\n"<br />
GPS 30 "Magic..."<br />
T 550 X 0<br />
COLOR POLY Red<br />
POLYT 550 650 50<br />
POLYLINE 266 252 269 255 264 260 261 257 266 252 12<br />
POLYLINE 280 266 283 269 278 274 275 271 280 266 12<br />
T 599 X 10 Y -10 "More of the superstructure is\nincrementally constructed."<br />
T 600 PAUSE 3 "See those 2 long barges? \n They're going to get extended 4 times."<br />
T 872 "\n"<br />
T 873 PAUSE 3 "...And now they're boats, I guess. \n (Barges are a type of boat, right?)"<br />
PAUSE 1 X 0 Y 0<br />
T 936 PAUSE 3 "Here comes the really fun part!" ZOOM 5.5<br />
PAUSE 2 "Hope you don't mind some SFX..."<br />
PAUSE 0.5 LAYERS 10 DEPTH 2 THEME Fire<br />
PAUSE 0.5 ZOOM 1 ANGLE 45 T 945<br />
PAUSE 1 T 960 ZOOM 7.7 ANGLE 0 THEME Poison LAYERS 1<br />
T 1000 "And the ship is done!"<br />
T 1094 "Wait, don't forget cleanup!" THEME Blues X -6 Y 3<br />
T 1100 PAUSE 3 X 25 Y -25 "The construction is complete!" ZOOM 15<br />
LOOP 1500<br />
]]<br />
#C By: Saka<br /></code></div></div>
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<p>As the pop-up captions mention, the synthesis has already been improved significantly to less than two-thirds of its original cost. Below is a recipe using just 100 gliders. Type J / Shift+J or use the onscreen < and > buttons to move between the incremental construction stages.</p>
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<div><code>x = 425, y = 162, rule = B3/S23<br />
241bo159bo$240bo159bo$240b3o157b3o3$172bo234bo$173bo12bo218b2o$171b3o<br />
12bobo213bo3b2o$186b2o212b2o$401b2o$130bo280bo$131bo278bo$71bo13b2o42b<br />
3o104bo44bo53bo54bo19b3o$71b2o12bobo147bobo42bobo51bobo52bobo$70bobo<br />
12bo148bobo37b2o3bobo46b2o3bobo47b2o3bobo$6bo120b2o10bo38b2o54bo39bo4b<br />
o16bo31bo4bo49bo4bo$7bo118bobo11bo36bobo51b2obo40b3obo15bo33b3obo21bo<br />
28b3obo$5b3o117bobo10b3o35bobo51bo2bo44bo16b3o34bo22bobo29bo$125b2o49b<br />
2o53b2o44bo53bo23b2o29bo$79b2o48b2o49b2o53b2o39bo3b2o48bo3b2o49bo3b2o$<br />
78bo2bo46bo2bo47bo2bo51bo2bo37bo3bo2bo39bo6bo3bo2bo47bo3bo2bo13bo$79b<br />
2obo7b2o37b2obo47b2obo51b2obo36b2o3b2obo39b2o4b2o3b2obo6bo39b2o3b2obo<br />
6bo4b2o$81bobo6bobo38bobo48bobo29b3o20bobo42bobo37b2o12bobo4bobo45bobo<br />
4bobo3bobo$81bobo6bo40bobo48bobo31bo20bobo42bobo51bobo5bo46bobo5bo$82b<br />
o49bo50bo3b2o26bo22bo3b2o39bo3b2o48bo3b3o48bo3b3o$186bobo52bobo42bobo<br />
51bo54bo$185bobo52bobo42bobo51bobo52bobo$185b2o29bo23b2o43b2o52bobo49b<br />
obo2bo$216b2o122bo50b2o3bobo$215bobo179b2o$7b2o129b2o83b2o71b2o114b3o$<br />
bo4bobo130b2o81bobo71bobo113bo$b2o5bo129bo85bo71bo116bo$obo234bo$236b<br />
2o87b3o$22b3o195bo15bobo88bo$22bo23bo173b2o104bo$23bo22b2o171bobo98b2o<br />
$45bobo273b2o$320bo2$328b2o$329b2o3b2o$328bo4bobo$335bo11$114b2o$115b<br />
2o$114bo26$356bo$357b2o$356b2o$364bo$362bobo$363b2o$356bo$357b2o49bo$<br />
356b2o48b2o$400bobo4b2o$64bobo333b2o$65b2o334bo$65bo58bo235bo$125bo<br />
235bo$77bo45b3o233b3o29bo$75b2o314bobo$76b2o128bo141bo27bobo12b2o22bob<br />
o$134bobo70b2o137bobo28b2o27bo8b2o$135b2o69b2o139b2o28bo26b2o10bo$135b<br />
o75bobo191b2o$212b2o$212bo$415bo$413b2o$414b2o$208bo$209b2o$208b2o$<br />
218bobo$17bobo132bo66b2o15bo68bo74bo$18b2o36bo94bobo65bo10bo4bobo61bo<br />
4bobo67bo4bobo$18bo37b2o79b2o11bobo76bobo2bobo58b2obobo2bobo64b2obobo<br />
2bobo28bo$55bobo78bobo12bo77bo2bo2bo53bo6bobo2bo2bo66bobo2bo2bo28bo$<br />
138bo75b2o14b2o58bo5bo2b2o70bo2b2o32b3o$16bo50bo27bobo54bo60bobo20bo<br />
51b3o6b2o6bo51bo14b2o6bo$10b2o3bobo43b2o3bobo5b2o19b2o49b2o3bobo5b2o<br />
54bo14b2o3bobo5b2o54b2o3bobo5b2o43b2o15b2o3bobo5b2o$10bo4bo2bo42bo4bo<br />
2bo3bo2bo19bo49bo4bo2bo3bo2bo68bo4bo2bo3bo2bo53bo4bo2bo3bo2bo41bobo15b<br />
o4bo2bo3bo2bo$11b3obo3bo42b3obo3bo3bobo70b3obo3bo3bobo69b3obo3bo3bobo<br />
54b3obo3bo3bobo60b3obo3bo3bobo$14bo5bo44bo5bo3bo58b2o14bo5bo3bo73bo5bo<br />
3bo58bo5bo3bo58bo5bo5bo3bo$13bo7bo42bo7bo62b2o12bo7bo75bo7bo60bo7bo59b<br />
3o4bo7bo$12bo3b2o4bo40bo3b2o4bo60bo13bo3b2o4bo73bo3b2o4bo58bo3b2o4bo<br />
57bo6bo3b2o4bo$11bo3bo2bo4bo8b2o28bo3bo2bo4bo72bo3bo2bo4bo71bo3bo2bo4b<br />
o56bo3bo2bo4bo56b2o4bo3bo2bo4bo25bobo$11b2o3b2obo4bo6b2o29b2o3b2obo4bo<br />
71b2o3b2obo4bo70b2o3b2obo4bo55b2o3b2obo4bo61b2o3b2obo4bo24b2o$18bobo4b<br />
o7bo35bobo4bo77bobo4bo4bo71bobo4bo4bo56bobo4bo4bo62bobo4bo4bo19bo$18bo<br />
bo5bo42bobo5bo76bobo5bo2bobo50b2o18bobo5bo2bobo55bobo5bo2bobo61bobo5bo<br />
2bobo$19bo3b3o44bo3b3o23b2o53bo3b3o2bobo50bobo19bo3b3o2bobo57bo3b3o2bo<br />
bo63bo3b3o2bobo$22bo50bo25b2o57bo6bo53bo22bo6bo61bo6bo67bo6bo13b2o$21b<br />
obo48bobo26bo55bobo81bobo42b2o22bobo35b3o34bobo18b2o$18bobo2bo45bobo2b<br />
o79bobo2bo78bobo2bo4bo38b2o18bobo2bo4bo32bo31bobo2bo4bo15bo$18b2o3bobo<br />
43b2o3bobo77b2o3bobo76b2o3bobobobo36bo20b2o3bobobobo30bo32b2o3bobobobo<br />
$24b2o49b2o83b2o82b2obo2bo62b2obo2bo32b2o34b2obo2bo$212b3o33b2o65bob2o<br />
34b2o35bob2o$214bo100bo36bo32b2o3bo$213bo102b3o66bo5b3o$79b2o237bo64bo<br />
bo7bo$80b2o301b2o$79bo268b3o$350bo$163b3o183bo3bo$165bo149b2o36b2o$<br />
157bo6bo13b2o71b2o62bobo34bobo4bo59b3o$157b2o18b2o55b3o13b2o49bo13bo<br />
43b2o58bo$156bobo20bo56bo15bo48b2o55bobo24b2o33bo$235bo64bobo82bobo22b<br />
3o$385bo24bo$245b3o163bo$228b2o17bo169bo5bo$227bobo16bo13b2o154b2o4b2o<br />
$229bo29b2o155bobo3bobo$261bo96b3o$254bo105bo3b2o7bo$182b2o69b2o104bo<br />
5b2o6b2o$182bobo68bobo7bo100bo7bobo$182bo79b2o$262bobo102b2o7b2o$366bo<br />
bo6bobo$368bo8bo28b3o$406bo$407bo!<br />
#C [[ THEME Fire LOOP 150 ]]<br />
#C [[ POI X -196 Y -60 Z 11 ]]<br />
#C [[ POI X -130 Y -60 Z 11 ]]<br />
#C [[ POI X -80 Y -60 Z 11 ]]<br />
#C [[ POI X -29 Y -60 Z 11 ]]<br />
#C [[ POI X 26 Y -60 Z 11 ]]<br />
#C [[ POI X 71 Y -60 Z 11 ]]<br />
#C [[ POI X 125 Y -60 Z 11 ]]<br />
#C [[ POI X 180 Y -60 Z 11 ]]<br />
#C [[ POI X -193 Y 44 Z 11 ]]<br />
#C [[ POI X -142 Y 44 Z 11 ]]<br />
#C [[ POI X -57 Y 44 Z 11 ]]<br />
#C [[ POI X 27 Y 44 Z 8 ]]<br />
#C [[ POI X 96 Y 44 Z 8 ]]<br />
#C [[ POI X 171 Y 44 Z 7 ]]</code></div></div>
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<p>For anyone interested in the more convoluted side of Life technology, these glider constructions make it possible to create circuitry that converts one type of spaceship into another. The current status of this effort is also <a href="https://conwaylife.com/wiki/User:Goldtiger997/Spaceship_Stable_Circuitry">documented in a LifeWiki article</a>.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-59857726889300383022020-07-02T09:30:00.003-05:002020-07-02T13:50:45.551-05:00Newer Better Faster Smaller Stable Signal Circuits<p>In 2020 so far there's been a major surge in interest in stable circuitry. For example, on January 26 Entity Valkyrie constructed a <a href="">period-11040 spider gun</a>, and on May 22 a <a href="https://www.conwaylife.com/forums/viewtopic.php?p=97489#p97489">58P5H1V1 gun</a> -- the first-ever guns to fire c/5 orthogonal spaceships and c/5 diagonal spaceships, respectively. In both cases, as is almost inevitable for new glider synthesis, cheaper recipes have since been found, making it possible to construct significantly smaller guns.
</p><p>More recently, Entity Valkyrie also found the key cleanup mechanism for an incomplete color-changing glider lane shifter found by Martin Grant. The result was the <a href="https://conwaylife.com/wiki/Bandersnatch">Bandersnatch</a>, so named because of its association with Snarks and Boojums in Lewis Carroll's poem <u>The Hunting of the Snark</u> (appropriately subtitled "an agony in eight fits".)
</p>
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<div><code>#N Bandersnatch
#O Entity Valkyrie and Martin Grant, 5 June 2020<br />
#C Spartan 0-degree color-changing glider shifter<br />
x = 50, y = 46, rule = B3/S23<br />
o$b2o$2o16$45bo$44bobo$44bobo$43b2ob3o$31b2o16bo$31b2o10b2ob3o$43b2ob<br />
o7$46b2o$37bo8b2o$36bobo$36bo2bo$37b2o$20b2o$19bobo$19bo24b2o$18b2o24b<br />
2o5$35b2o$35b2o!<br />
#C [[ THUMBNAIL THUMBSIZE 3 AUTOSTART WIDTH 640 HEIGHT 540 X 7 Y 10 THUMBSIZE 2 ZOOM 16 GPS 40 LOOP 200 ]]</code></div></div>
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The Bandersnatch is a significant discovery, and has already helped to solve quite a few glider adjustment problems. For example, it enabled Goldtiger997 to build a highway robber with <a href="https://www.conwaylife.com/forums/viewtopic.php?p=98370#p98370">863-tick recovery time</a>. (The current record is a larger staged-recovery design with <a href="https://www.conwaylife.com/forums/viewtopic.php?p=98379#p99379">742-tick recovery time</a>.) The Bandersnatch consists of just seven well-separated still lifes, which is <a href="https://conwaylife.com/wiki/Spartan">Spartan</a> by the modern definition, so it is bound to become very useful in self-constructing circuitry as well.
</p><p>In April, Louis-François Handfield constructed a <a href="https://www.conwaylife.com/forums/viewtopic.php?p=93647#p93647">much more compact universal regulator</a> than the previous best known mechanism.
</p><p>The following month Handfield also adapted Martin Grant's <a href="https://www.conwaylife.com/forums/viewtopic.php?p=95988#p95988">new HL161H conduit</a> to make a useful color-changing edge shooter, <a href="https://www.conwaylife.com/forums/viewtopic.php?p=96093#p96093">HSW47T214</a>. Its output lane is transparent, so it can serve as a merge circuit in a fairly compact <a href="https://www.conwaylife.com/forums/viewtopic.php?p=96124#p96124">glider adjustment toolkit</a>.
</p><p>On June 8, a collaborative effort produced a fully universal *WSS-to-glider converter that recovers in only 588 ticks. It accepts LWSSes, MWSSes, and HWSSes equally well, and works even if the input spaceship is moved by an odd number of cells along the input lane. Previous spaceship signal converters usually only worked if the spaceship was moved in two-cell increments, since the phase of these spaceships is different in odd and even positions.
</p>
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<div><code>#C universal *WSS-to-glider converter, repeat time 588 ticks<br />
x = 679, y = 92, rule = B3/S23<br />
591bo$591b3o$594bo$593b2o8b2o$603bo$601bobo18bo11b2o$601b2o18bobo10b2o<br />
$587b2o32bobo$587b2o26b2o2b3ob2o$615bo2bo$613bobo3b3ob2o$613b2o6bob2o$<br />
587b2o$587b2o5$611b2o13b2o$611b2o13b2o16b2o4bob2o$641b2o2bo4b2obo$640b<br />
o2b2o3b2o$641bo5bo3b2o$642b3o2bob2obo$644bo3bobobob2obo$629b2o20b2obob<br />
2o$630bo$627b3o$627bo$634b2o$616b2o17bo$617bo17bobo$616bo19b2o16b2o$<br />
616b2o36b2o$607b2o$2b2o334bo268bobo$o4bo330bo3bo249bo2bo14bo$6bo334bo<br />
252bo3b2o54b2o$o5bo329bo4bo248bo3bo2bo2bo53b2o$b6o330b5o249b4o3b2o19b<br />
2o$619b2o$603b2o$603bobo$604bo$654bo$653bobo$654bo$629b2o$630bo$627b3o<br />
$591b2o34bo16b2o$586b2o2bo2bo17b2o30bobo$583bo2bo4bobo17bobo29bo$582bo<br />
bobo5bo20bo28b2o25bo$583bo2bob2o23b2o52b3o$586bo2bo76bo$587bo4bo73b2o$<br />
588b5o2$590bo83b2o$589bobo2b2o29bo49bo$590b2o3bo27b3o49bob2o$592b3o27b<br />
o44b2o4b3o2bo$592bo29b2o43b2o3bo3b2o$672b4o$642bo15b2o15bo$640b3o10b2o<br />
2bobo12b3o$639bo14bo2bo13bo$626b2o11b2o11bo2b3o14b5o$626b2o24b3o21bo$<br />
655bo18bo$654b2o18b2o$669bo$667b3o$666bo$595b2o68bo2b2o$595b2o69b2o2bo<br />
$601b2o48b2o16b2o$601b2o48b2o3$599b2o$599b2o5b2o$606b2o31b2o3bo$639bo<br />
3bobo$640bo3bobob2o$641bo4bob2o$627b2o10bob5o$627b2o9bobo4bob2obob2o$<br />
639bo2b2obo2bob2obo$640b2obob2o12b2o$659b2o!<br />
#C [[ X 285 Y 0 Z 5 AUTOSTART PAUSE 2 STEP 5 LOOP 2000 ]]</code></div></div>
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<p>As the MWSS collision shows, the mechanism even works if the next spaceship arrives before the second half of the bait constellation (the boat) has been reconstructed.
</p><p>Toward the end of June the stable-circuitry construction binge continued with a number of new <a href="https://conwaylife.com/forums/viewtopic.php?p=99885#p99885">stable eaters</a> and <a href="https://www.conwaylife.com/forums/viewtopic.php?p=99196#p99196">spaceship-to-X converters</a>, including a much smaller <a href="https://www.conwaylife.com/forums/viewtopic.php?p=99834#p99834">HWSS Heisenburp</a> -- but these will probably fit much better in a future post.Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-43255465944020153722020-01-17T16:38:00.000-05:002020-01-17T16:38:03.683-05:00A Gentleman and a Scholar<p>On 30 December 2019, almost a decade after constructing the <a href="https://conwaylife.com/wiki/Gemini">Gemini spaceship</a>, <a href="https://conwaylife.com/wiki/Andrew J. Wade">Andrew J. Wade</a> made a sudden reappearance in a very different corner of the Life spaceship construction field. This time the new discovery was the <a href="https://conwaylife.com/wiki/Scholar">"scholar"</a>, the second known elementary 2c/7 spaceship (after the <a href="https://conwaylife.com/wiki/Weekender">weekender</a>, which was found by David Eppstein very nearly two decades ago).</p>
<p>The new spaceship was discovered using a depth-first search program called <a href="https://gitlab.com/andrew-j-wade/life_slice_ship_search">life_slice_ship_search</a>. Details can be found on <a href="https://www.conwaylife.com/forums/viewtopic.php?f=9&t=3413">this conwaylife.com forum thread</a>.
</p>
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<div><code>#C 2c/7 elementary spaceship #2, "scholar",<br />
#C found by Andrew J. Wade with life_slice_ship_search, 30 Dec 2019.<br />
x = 23, y = 82, rule = B3/S23<br />
11bo$10b3o$10b3o2$6b3o5b3o2$6bobo5bobo$6bobo5bobo$7bo7bo$6bo2bo3bo2bo$<br />
7bob2ob2obo$4bo4bo3bo4bo$4b6o3b6o$4bo4bo3bo4bo$5b2obo5bob2o$9bo3bo$5bo<br />
11bo$5bo3bo3bo3bo$6bo2bo3bo2bo$6bo2bo3bo2bo$b3o3bobo3bobo3b3o$o2bo3b9o<br />
3bo2bo$o2bo2b2ob5ob2o2bo2bo$7b2o2bo2b2o$6b2o3bo3b2o$6b2o7b2o$9b2ob2o$<br />
6bo3bobo3bo$6bo3bobo3bo$6b2o2bobo2b2o$8b3ob3o$4b2ob2o5b2ob2o$3bo2b2o7b<br />
2o2bo$2bo17bo$3bob3o7b3obo$6bo2bo3bo2bo$7b3o3b3o$4b2o4bobo4b2o$9bo3bo$<br />
5bo4bobo4bo$2bo6b2ob2o6bo$b2o2b3obo3bob3o2b2o$o5b4o3b4o5bo$bo3b2o2bo3b<br />
o2b2o3bo$2b3o2bobo3bobo2b3o2$7b3o3b3o$6b2o7b2o$5b2o9b2o$5bobo7bobo$6bo<br />
9bo$7bobo3bobo$7bobo3bobo$6bo9bo$6bo9bo$6bo3bobo3bo$7bo2bobo2bo$7bo2bo<br />
bo2bo2$8b3ob3o$8bobobobo$9b5o$3b3o11b3o$3b3o11b3o$bo3bo11bo3bo$5bo11bo<br />
$6bo9bo$bo3bo3bobobo3bo3bo$2b2o4bo5bo4b2o$3bo15bo$4b3o9b3o$5bo5bo5bo$<br />
10b3o$9b2ob2o$9b5o$6b3o2bo2b3o$4bo13bo$4bobo9bobo$6bo9bo$3bobo11bobo$<br />
2bo2bo11bo2bo$3b2o13b2o!<br />
#C [[ GRID THEME 7 TRACKLOOP 7 0 -2/7 THUMBSIZE 2 HEIGHT 680 ZOOM 7 GPS 7 AUTOSTART ]]</code></div></div>
<canvas width="420" height="680" style="margin-left:1px;"></canvas></div>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-76159965023368314822019-07-11T11:32:00.000-05:002019-09-21T21:15:25.084-05:00Less Than Two Gliders Per Cell, For All Constructible Still Lifes<p>On 19 June 2019 a surprising milestone was reached. Goldtiger997 made a final improvement to a 17-bit still-life synthesis -- ID <a href="http://catagolue.appspot.com/object?apgcode=xs17_03p6413z39c&rule=b3s23">xs17_03p6413z39c</a> -- to bring the cost down to 33 gliders. (It's since been reduced further, to 29 gliders, and eventually down to only 9 gliders as part of the long-running <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=3962">"17-in-16" project</a>.)
</p><p>This made it possible to announce a surprising result: there's a strict upper bound for the cost in gliders for any <a href="http://conwaylife.com/wiki/Strict_still_life#Strict_still_lifes">strict still life</a>, assuming it can be constructed by colliding gliders at all. If a glider-constructible still life contains N ON cells, then <a href="http://conwaylife.com/forums/viewtopic.php?p=78036#p78036">it can be constructed with less than 2N gliders</a>.
<h2>A Mix of Theory and Practice</h2>
</p><p>For still lifes larger than 17 bits, this result is supplied by the <a href="http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html">strange and wonderful RCT method</a>. The RCT (<a href="http://conwaylife.com/wiki/Reverse_caber-tosser">reverse caber tosser</a>) is a pattern that is constructible with only 35 gliders, that reads the very faraway position of an approaching object to produce a stream of bits, which are then interpreted as a construction recipe fed to a universal <a href="http://conwaylife.com/wiki/Construction_arm">construction arm</a>. Cleanup of the RCT's mechanism would also have to be done to produce a full synthesis, which makes it tricky to create these 35-glider recipes in practice; no working examples have yet been completed.
</p><p>The situation is much more straightforward for still lifes with up to 17 ON cells. Extensive soup searches recorded by <a href="https://catagolue.appspot.com/home">Catagolue</a>, and related technical advances, have allowed much more efficient recipes to be found for a large number of still lifes. In fact, almost all still lifes up to 17 bits can now be constructed with fewer than 1 glider per ON cell, let alone 2 gliders per ON cell.</p>
<h2>We've Come a Long Way, Conway</h2>
<p>For example, just a few years ago the best known recipe for an 8x6 17-bit still life with ID <a href="http://catagolue.appspot.com/object?apgcode=xs17_gbaikoz1252&rule=b3s23">xs17_gbaikoz1252</a> was around 73 gliders:
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<div><code>#C Incremental 73-glider synthesis of xs17_gbaikoz1252.<br />
#C Adapted from Mark Niemiec's database,<br />
#C http://conwaylife.com/ref/mniemiec/17/17-1202.rle<br />
x = 185, y = 236, rule = B3/S23<br />
143bo$143bobo$143b2o$140bo$138bobo$139b2o2$143bo$141b2o$142b2o2$133bob<br />
o15bo$133b2o15bo$96bo33bo3bo15b3o$91bo3bo15b2o15bobo10b2o$92b2ob3o12bo<br />
2bo15b2o9bo2bo$91b2o17bo2bo26bo2bo9bo$10bo100b2o17bo10b2o9b2o$11b2obo<br />
115b2o20bobo$10b2o2bobo112bobo34b2ob2o$14b2o12b2o18b2o18b2o18b2o18b2o<br />
28b2o27bobobobo$27bo2bob2o13bo2bob2o13bo2bob2o13bo2bob2o13bo2bob2o23bo<br />
2bob2o5b3o15bo2bob2o$23bo4bobobo15bobobo15bobobo15bobobo15bobobo25bobo<br />
bo6bo18bobo$22b2o5b2obobo14b2obobo14b2obo16b2obo16b2obo26b2obo7bo18b2o<br />
$22bobo8b2o18b2o17bob2o16bob2o16bob2o26bob2o$2b2o68bo2bo16bo2bo16bo2bo<br />
26bo2bo$3b2o68b2o18b2o18b2o28b2o$2bo2$151b2o$151bobo$53bo97bo$50bo2bob<br />
o$48bobo2b2o$49b2o6$50b3o$50bo$51bo11$19bo42bo$19bobo38b2o$19b2o40b2o$<br />
94bo$95bo4bo$93b3o3bo$6b2ob2o15b2ob2o15b2ob2o15b2ob2o15b2ob2o8b3o4b2ob<br />
2o4b2o9b2ob2o4b2o19b2ob2o4b2o$7bobobobo13bobobo15bobobo15bobobo15bobob<br />
o15bobobo3bo11bobobo3bo21bobobo3bo$7bo2bob2o13bo2bobobo12bo2bobobo12bo<br />
2bobo14bo2bobo14bo2bobo3bo10bo2bobo3bo20bo2bobo3bo$8bobo17bobo2b2o13bo<br />
bo2b2o13bobobo15bobobo15bobobo4bo10bobobo4bo20bobobo4bo$9b2o12bo5b2o<br />
18b2o18b2ob2o15b2ob2o5bo9b2ob2o2b2o11b2ob2o2b2o3bo17b2ob2o4bo$21b2o75b<br />
2o40bo28bo$22b2o74bobo39b3o27bo$56bobo77b2o33bo$15b2o39b2o37b3o37bobo<br />
32b2o$16b2ob3o35bo39bo39bo3b2o$15bo3bo76bo45b2o$20bo34b3o83bo$55bo$56b<br />
o2$58b3o$58bo$59bo13$6b2ob2o4b2o29b2ob2o4b2o29b2ob2o4b2o29b2ob2o4b2o$<br />
7bobobo3bo31bobobo3bo31bobobo3bo31bobobo3bo$7bo2bobo3bo30bo2bobo3bo30b<br />
o2bobo3bo30bo2bobo3bo$8bobobo4bo30bobobo4bo30bobobo4bo30bobobo4bo$9b2o<br />
b2o4bo30b2ob2o4bo30b2ob2o4bo30b2ob2o4bo$19bo39bo39bo39bo$20bo39bo39bo<br />
39bo$21bo39bo39bo39bo$20b2o3bo36bo39bo39bo$24bo38bo39bo39bo$24b3o35b2o<br />
38b2o3bo34b2o$20b2o84bo$19bobo84b3o$21bo3b2o75b2o$26b2o73bobo$25bo77bo<br />
3b2o$108b2o$107bo10$59bo$59bobo$59b2o$54bo$54bobo$54b2o5bobo$61b2o$53b<br />
o8bo55bo$54b2o60bobo$53b2o62b2o$120bo$61bo25bo19bo11bo17bo$60b2o23b3o<br />
17b3o11b3o13b3o$6b2ob2o4b2o9b2ob2o4b2o9b2ob2o4b2o3bobo13b2ob2o3bo11b2o<br />
b2o3bo21b2ob2o3bo$7bobobo3bo11bobobo3bo11bobobo3bo21bobobo3bo11bobobo<br />
3bo10bobo8bobobo3bo6b3o$7bo2bobo3bo10bo2bobo3bo10bo2bobo3bo20bo2bobo3b<br />
o10bo2bobo3bo10b2o8bo2bobo3bo4b3o$8bobobo4bo10bobobo4bo10bobobo4bo20bo<br />
bobo4bo10bobobo4bo9bo10bobobo4bo$9b2ob2o4bo10b2ob2o4bo10b2ob2o4bo20b2o<br />
b2o4bo10b2ob2o4bo20b2ob2o4bo$19bo19bo19bo29bo19bo29bo$20bo19bo19bo29bo<br />
19bo29bo$21bo10b2o7bo10b2o7bo20b2o7bo10b2o7bo20b2o7bo$22bo9b2o8bo9b2o<br />
8bo19b2o8bo9b2o8bo19b2o8bo$9b2o12bo19bo19bo29bo19bo29bo$6bo2bobo3b2o5b<br />
2o8b2o8b2o8b2o8b2o18b2o8b2o8b2o8b2o18b2o8b2o$4bobo2bo4b2o16b2o18b2o28b<br />
2o18b2o28b2o$5b2o9bo3$160bo$158b2o$159b2o4$143bobo$143b2o$144bo2$66bo$<br />
67bo29bo29bo$65b3o28bobo27bobo$96bobo27bobo$62b3o32bo29bo$64bo$13bo49b<br />
o$6bo5bo$7bo4b3o$5b3o$b3o$3bo126bo$2bo128bo$129b3o2$42bo29bo29bo29bo$<br />
41bobo27bobo27bobo27bobo$42b2o28b2o28b2o28b2o3$169b2o$169bo$170b3o$17b<br />
o29bo29bo29bo29bo34bo4bo$15b3o27b3o27b3o27b3o27b3o37b3o$6b2ob2o3bo21b<br />
2ob2o3bo21b2ob2o3bo21b2ob2o3bo21b2ob2o3bo31b2ob2o3bo$7bobobo3bo6b3o12b<br />
obobo3bo6b3o12bobobo3bo6b3o12bobobo3bo6b3o12bobobo3bo6b3o22bobobo3bo6b<br />
3o$7bo2bobo3bo4b3o13bo2bobo3bo4b3o13bo2bobo3bo4b3o13bo2bobo3bo4b3o13bo<br />
2bobo3bo4b3o23bo2bobo3bo4b3o$8bobobo4bo20bobobo4bo20bobobo4bo20bobobo<br />
4bo20bobobo4bo30bobobo4bo$9b2ob2o4bo20b2ob2o4bo20b2ob2o4bo20b2ob2o4bo<br />
20b2ob2o4bo30b2ob2o4bo$19bo29bo29bo29bo29bo39bo$20bo29bo29bo29bo29bo<br />
39bo$12b2o7bo20b2o7bo20b2o7bo20b2o7bo20b2o7bo30b2o7bo$12b2o8bo19b2o8bo<br />
19b2o8bo19b2o8bo19b2o8bo29b2o8bo$23bo29bo29bo29bo29bo39bo$12b2o8b2o18b<br />
2o8b2o18b2o8b2o18b2o8b2o18b2o8b2o28b2o8b2o$12b2o28b2o28b2o28b2o28b2o<br />
38b2o6$102bo$101bo$101b3o9$79bo$77b2o10bo$78b2o7b2o$88b2o$92bo$92bobo$<br />
92b2o$5bo3b2o28b2o38b2o65bo$3bobo3bo25b2o2bo28b3o4b2o2bo15bo49bo$4b2o<br />
4b3o22b2o3b3o27bo4b2o3b3o12bobo47b3o$b2o9bo4bo24bo4bo21bo12bo4bo7b2o$o<br />
bo12b3o27b3o37b3o32b2o18b2o6b2o10b2o$2bo3b2ob2o3bo21b2ob2o3bo31b2ob2o<br />
3bo31b2obo2bo13b2obo2bo5bobo5b2obo2bo$7bobobo3bo6b3o12bobobo3bo6b3o11b<br />
3o8bobobo3bo6b3o22bobobobo13bobobobo4bo8bobobobo$7bo2bobo3bo4b3o13bo2b<br />
obo3bo4b3o14bo8bo2bobo3bo4b3o23bo2bob2o13bo2bob2o13bo2bobo$8bobobo4bo<br />
20bobobo4bo19bo10bobobo4bo30bobo17bobo17bobo$9b2ob2o4bo20b2ob2o4bo30b<br />
2ob2o4bo30b2o18b2o18b2o$19bo29bo39bo$20bo29bo39bo$12b2o7bo20b2o7bo30b<br />
2o7bo7bo$12b2o8bo19b2o8bo29b2o8bo6bobo$23bo29bo39bo5b2o$12b2o8b2o18b2o<br />
8b2o28b2o8b2o$12b2o28b2o38b2o$97b2o3bo$88bo9b2obo$77bo10b2o7bo3b3o$77b<br />
2o8bobo$76bobo!<br />
<br />
#C [[ AUTOSTART X 137 Y 3 Z 2 PAUSE 2 GPS 25 LOOP 150 ]] </code></div></div>
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</p><p>Thanks to soup search data from Catagolue, that same still life can now be constructed with just 10 gliders:
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<div><code>#C 10-glider continuous synthesis of xs17_gbaikoz1252<br />
#C http://catagolue.appspot.com/object?apgcode=xs17_gbaikoz1252&rule=b3s23<br />
x = 30, y = 37, rule = B3/S23<br />
3bo$4bo$2b3o4$13bo$12bo$12b3o3$2bo24bo$obo24bobo$b2o24b2o11$15bo$14bo<br />
$4bo5bo3b3o8bo$4b2o4b2o12b2o$3bobo3bobo12bobo6$11bo8b2o$11b2o6b2o$10b<br />
obo8bo!<br />
#C [[ AUTOSTART PAUSE 2 GPS 25 T 150 X -5 Y 10 Z 12 PAUSE 2 LOOP 151 ]] </code></div></div>
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</p><p>At the time of writing (mid-July 2019), there are still <a href="http://conwaylife.com/forums/viewtopic.php?p=79235#p79235">several dozen 17-bit still lifes</a> that cost 1 glider per bit or more to synthesize -- but that number has been dropping quickly. All smaller still lifes have been below this limit for some time now, as described <a href="https://b3s23life.blogspot.com/2016/10/14-and-15-bit-still-life-syntheses.html">here</a>.</p>
<p> <b>UPDATE 9/9/2019:</b> Construction recipes with 16 gliders or fewer <a href="http://www.conwaylife.com/forums/viewtopic.php?p=82560#p82560">have now been found</a> for all 17-bit still lifes.
</p>
<h2>Some Related Open Questions</h2>
<p>It is technically possible that all constructible still lifes have recipes with fewer gliders than the number of ON cells. However, the number of distinct still lifes increases rapidly as the number of bits increases, and the number of unsolved still lifes in the 20-cell to 34-cell range is far too large to manage with current construction methods. The number of strict 34-bit still lifes has not even been calculated yet, but it should be quite close to 35 billion, and it will include a large number of objects that are difficult to construct because they are so delicately balanced.
</p><p>Notice for example that <a href="http://www.conwaylife.com/wiki/Quad_pseudo">quad pseudo</a> is 34 bits. It's technically a pseudo still life, not a strict one -- but just barely, since it can't be subdivided into two stable subpatterns, or even three. This kind of interdependence between different parts of an object becomes more common as the number of bits increases, and a larger area is out of reach of influence by colliding gliders around the object's perimeter. It seems possible that some object along these lines will turn out to be too delicately balanced, and it will be impossible to meet the less-than-one-glider-per-bit requirement.
</p><p>It's also possible that some still life will have so many mutually supporting parts that it's impossible to find any glider construction at all, no matter how expensive. However, experience so far seems to indicate that if a non-glider-constructible still life exists, it will be significantly larger than 34 bits.</p>
Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com1tag:blogger.com,1999:blog-8285929.post-84006558128230399932018-11-10T21:52:00.003-05:002018-11-18T17:23:55.371-05:00New Tools for Self-ConstructionTime for a new post on self-constructing circuitry! I've been updating the <a href="http://b3s23life.blogspot.com/2014/06/new-wrinkles-in-slow-salvo-construction.html">same old post</a> since 2014, but I think there's now some news that warrants a new article.<br />
<h1>
Self-Construction Just Got A Lot Easier</h1>
<p>For the last several years <a href="http://conwaylife.com/wiki/Adam_P._Goucher">Adam P. Goucher</a> has been incrementally working out the construction details for a "0E0P metacell". A <a href="http://conwaylife.com/wiki/metacell">metacell</a> is a piece of Life circuitry that simulates the behavior of a single cell in Life, or in many cases some other CA rule, depending on how it's programmed.</p>
<p>"0E0P" is short for "[state] zero equals zero population", meaning that no support circuitry is needed: when one of these 0E0P metacells turns off, it self-destructs completely! This means that when the metacell needs to turn back on again, it must be re-constructed from the ground up by its neighbors.
<p>One of the important effects of this design is that metacell patterns run at a sufficiently high step size, when viewed from very far away (e.g., at a size where an entire metacell takes up a single pixel in the display) will be indistinguishable from normal patterns that use the same rule -- except that the metacell patterns will run 2^36 times more slowly, of course.</p>
<h2>
Automatically Generated Construction Recipes</h2>
<p>A key breakthrough enabling the construction of the 0E0P metacell was a <a href="https://gitlab.com/apgoucher/slmake">publicly available search program</a> written by Goucher, capable of finding a <a href="http://www.conwaylife.com/wiki/Single_channel">single-channel</a> construction recipe for any constellation of still lifes -- provided the still lifes aren't too close together, and that recipes are known for each of them in isolation. This search program was originally called "slmake" but is now renamed to "slsparse" due to its ability to analyze a large constellation and automatically separate it into several well-separated sub-constellations, or "metaclusters" (when that's possible).</p>
<p>The first few self-constructing patterns -- Gemini, 10hd and 0hd Demonoids, linear propagator, and the first spiral-growth pattern -- all had slow-salvo recipes that were mostly compiled by hand. This was usually one of the most time-consuming parts of the construction process, and once a recipe was compiled it was often very difficult to make small adjustments to the design without recompiling everything from the ground up. Now that slsparse is available, it's much easier to produce new pattern variants and entirely new designs.</p>
<p>Here are three recently completed self-constructing spaceships that owe their existence to compilation with slsparse -- with images of each, since for a change they all look like something other than plain long straight lines from a distance.</p>
<div class="separator" style="clear: both; text-align: left;"><h3><a href="http://www.conwaylife.com/forums/viewtopic.php?p=65097#p65097">Fast HashLife-friendly Orthogonoid</a></h3>
<p>Older version with slow elbow push:</p>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrMgR8MLeXkVBLwpvXqy_FE_ACgKbsLBa19EXvoMoW3dR4tc3C5OdaQxOF8jWoi55hxuLIQXA6DOcPgadyBtKf7AGbxl77cAxPZ87zocFXK5hVmBQYBB5ouG-sd7gMCNas_D54bQ/s1600/Orthogonoid-to-scale.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="205" data-original-width="1293" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrMgR8MLeXkVBLwpvXqy_FE_ACgKbsLBa19EXvoMoW3dR4tc3C5OdaQxOF8jWoi55hxuLIQXA6DOcPgadyBtKf7AGbxl77cAxPZ87zocFXK5hVmBQYBB5ouG-sd7gMCNas_D54bQ/s1600/Orthogonoid-to-scale.png" /></a></div>
<p>Lower-population version with Cordership elbow push:</p>
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBu6v_6fgv-iArtax1xDc1HpsO1zsPsu5GN6FIDFTLNPhcpt6p_57r8kQuRaaM1X4xKcw9OmFPCdyaMV9J1Ycg9ZeyAPrkb8d1aIzd47g0PriAckP0qY_deuC6_hjkuVIeJrm3hA/s1600/orthogonoid16-diagram.png" imageanchor="1" ><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBu6v_6fgv-iArtax1xDc1HpsO1zsPsu5GN6FIDFTLNPhcpt6p_57r8kQuRaaM1X4xKcw9OmFPCdyaMV9J1Ycg9ZeyAPrkb8d1aIzd47g0PriAckP0qY_deuC6_hjkuVIeJrm3hA/s1600/orthogonoid16-diagram.png" data-original-width="1220" data-original-height="600" /></a>
The older Orthogonoid has a fairly continuous recipe, so it's a little easier to see what direction it's going. The newer recipe consists mostly of long gaps between gliders, waiting for Corderships to reach their target locations.
<ul><li>The blue arrow marks a slow salvo that has almost caught up with a three-engine Cordership, which it will convert into the main body of Orthogonoid circuitry.</li>
<li>The purple arrow marks a single-channel salvo just starting the long trip after a two-engine Cordership, which it will convert into an elbow block and then create the seed for a new three-engine Cordership heading at right angles to the first, to the northwest.</li>
<li>The green arrows show the direction the recipe travels.</li>
<li>The red arrows on the west side show the future path of an MWSS and glider that do the cleanup of previous circuitry that's no longer in use. The MWSS is constructed by the short segment of single-channel recipe that is just reaching the elbow ahead of the leftmost green arrow; it's a copy of a short final section of the last largest segment of the recipe.</li></ul>
<p>Features of slsparse used to build the new Orthognoid include</p>
<ul>
<li><b>automatic compilation of very widely separated metaclusters</b><br /><br /><i>This allows the MWSS-to-glider circuit to be moved a long distance from the glider-to-MWSS circuit, which allows the structure of the spaceship to be much more visible from a distance -- and incidentally reduces the number of required hashtiles enough that Golly can now "run away" with the pattern.</i></li><br />
<li><b>automatically compiled elbow push and hand push, with different Corderships</b><br /><br /><i>For historical reasons, slsparse currently uses 3-engine Corderships to move "hand" target blocks long distances at right angles to the construction lane. The more recently discovered two-engine Corderships are used to push elbow blocks long distances along the construction lane.</i><br /></li><br />
<li><b>automatically compiled non-Spartan objects</b><br /><br /><i>There's lots more available than the old standard Spartan still lifes -- even without counting the bespoke object collection, which allows for the construction of extra-difficult and extra-useful structures such as syringes and Snarks. For example, an aircraft carrier used to change a glider's color as part of the elbow Snark's self-destruct circuitry. This isn't strictly <a href="http://www.conwaylife.com/wiki/Spartan">Spartan</a>, but with slsparse the state of the art has moved well past that artificial limitation.</i></li><br />
</ul>
<h3>
<a href="http://www.conwaylife.com/forums/viewtopic.php?p=64590#p64590">Hashlife-friendly Demonoid</a></h3><br />
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOT8kGIJq8owgnbQR6KVhcV0GaCq8mwTdHMcUmHvPQ3Pi_IAATGB7vyerqvvbwwlDaVnmMHFD2a-dbR7VHO-YJzew_5cPw1KyKFUE2os7ZF8kHNTaKK8aBqujc_HADeDdKnC26mg/s320/Demonoid-not-to-scale.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="796" data-original-width="776" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOT8kGIJq8owgnbQR6KVhcV0GaCq8mwTdHMcUmHvPQ3Pi_IAATGB7vyerqvvbwwlDaVnmMHFD2a-dbR7VHO-YJzew_5cPw1KyKFUE2os7ZF8kHNTaKK8aBqujc_HADeDdKnC26mg/s320/Demonoid-not-to-scale.png" /></a>
<p>(The image at right is not exactly to scale, but it's close enough that it should be recognizable.)</p>
<p>Features of slsparse that appear in the new Demonoid include</p>
<ul>
<li><b>long-distance elbow pull</b><br /><br /><i>A counterpart to the 2-engine Cordership push is a long-distance elbow pull recipe, also recently added to slsparse. A faraway elbow is converted to a return glider, which allows for much quicker movement toward the recipe source than would be possible with a long series of classical elbow-block PULL operations.</i></li><br />
<li><b>Snarkbreaker</b><br /><br /><i>slsparse now knows a single-channel recipe that can add an additional lossless elbow to a construction arm -- a "Snarkmaker" -- and another recipe that can remove the added Snark when it is no longer needed ("Snarkbreaker"). This allows a single-channel arm to safely reach locations that are otherwise inaccessible, such as a construction area that overlaps the single-channel lane.</i></li></ul>
<p>The above recipes were actually compiled by hand into the current HashLife-friendly Demonoid, because the relevant features hadn't been added to slsparse yet. The long-distance Cordership elbow push had also not been added yet, so the elbow movement was done inefficiently with a long series of PUSH operations, which accounts for a large fraction of the gliders needed in the recipe.</p>
<p><mark><b>Challenge:</b> Install the latest <a href="https://gitlab.com/apgoucher/slmake">slsparse</a> and use it to build a lower-population Demonoid than the current model,</mark> with wider separation (but still a power of two, to keep HashLife happy!) between the back-and-forth glider streams. Reasonably up-to-date installation and usage instructions can be found in <a href="http://conwaylife.com/wiki/Tutorials/slsparse">this walkthrough on the LifeWiki</a>.</p></div>
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<p>------------------------------------------------</p>
<p>In this Demonoid design, only the Snarkbreaker is needed, and at the moment slsparse doesn't know how to do a Snarkbreaker without a matching Snarkmaker preceding it (see below). So the Snarkbreaker was added into the Demonoid recipe by hand after the compilation was completed.
<p>Another trick used in the Demonoid that slsparse doesn't know about yet is</p>
<ul>
<li><b>destruction of old circuitry by *WSS produced directly from construction elbow</b></li><br /><i>This destruction method is much more efficient than bending the construction arm around two 90-degree corners to reach the location of the old circuitry. At the moment slsparse is primarily concerned with construction and not destruction.</i></ul></div>
<div style="clear: both;">
<h3><a href="http://www.conwaylife.com/forums/viewtopic.php?p=65214#p65214">Loopship</a></h3>
<p>Features of slsparse used in building the loopship:</p>
<ul>
<li><b>automatically compiled on-lane construction</b><br /><br /><i>For the largest metacluster, slsparse automatically sends two Snarkmakers to move the construction arm sideways to a safe distance to complete the construction -- followed by two Snarkbreakers to return the arm to its original state.</i></li></ul>
<p>A new feature of slsparse that could be used to build a somewhat smaller loopship:</p>
<ul>
<li><b>automatically compiled 0-degree construction</b> for sufficiently narrow on-lane constellations<br /><br /><i>The largest metacluster is actually narrow enough that some reconfiguration of one-time turners could allow the entire constellation to be constructed directly by 0-degree gliders, with no Snarkmaker/Snarkbreaker combinations necessary.</i></li></ul>
<p>Other mechanisms used in the loopship</p>
<ul>
<li><b>destruction by GoL-destroy search result</b><br /><br /><i>A <a href="http://conwaylife.com/forums/viewtopic.php?f=9&t=2280">separate search program called GoL-destroy</a> written by Simon Ekström finds ways to interleave random still lifes into signal circuitry, out of the way of the actual signal paths, in such a way that the entire structure collapses cleanly down to zero population when it is hit by a single self-destruct signal. slsparse can compile these additional still lifes just as easily as the original circuitry.</i></li><br />
<li><b>one-time turners</b><br /><br /><i>A few classical one-time converters -- glider to MWSS, MWSS to glider, and glider to 2 glider -- were also included in the design, just for variety, though they're probably slightly less efficient than the best solution that a GoL-destroy search could come up with.</i><br /></li>
</ul>
The loopship's recipe gliders traverse parts of their path three times in a row, and some of those gliders (or rather a copy of them) travel the exact same path a fourth time, ahead of the full recipe. This happens along the zigzag central spine of the loopship.</p>
<p>A "working copy" of the recipe is split off from each loop to do the actual construction. The working copy first builds two Corderships and sends them off at 90 degrees to the left and right, to the next new loopship corners. After the necessary long pause, it follows those Cordership with cleanup salvos.</p>
<p>After that, the remainder of the working copy builds two temporary lossless elbows (Snarks) and constructs the biggest part of the loopship circuitry, which is a Scorbie Splitter combined with two Snark reflectors plus self-destruct circuitry. As the spaceship travels, a copy of this circuitry will appear at each 90-degree bend along the central spine.</p></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuEuPjB9JEy0caFguyCyJw4teP7ZGBo1cj6nEigPsiVrFAVIk2sPCdYkQ0LZhvImbKPUQowJGG0QvPvP1omLE5OR6v7of9idWArdLaqNqiRjzkYNiM-jdik49egOQElGnvb9bcmQ/s1600/loopship-diagram-accurate.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="607" data-original-width="528" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuEuPjB9JEy0caFguyCyJw4teP7ZGBo1cj6nEigPsiVrFAVIk2sPCdYkQ0LZhvImbKPUQowJGG0QvPvP1omLE5OR6v7of9idWArdLaqNqiRjzkYNiM-jdik49egOQElGnvb9bcmQ/s320/loopship-diagram-accurate.png" width="276" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4E3o2CDWo6tvjzIS_skLbVcK7oH5fJF5xIyiQ5eKsfx7ow0TcdYkHtkEe9Q4VMHnq9VF5D1JhsG0rpCWqaGg4B-umY5koeRao-rRcNfoQey_79yymTAc9VvfTNIh0uFcI2ck_9A/s1600/loopship-diagram-conceptual.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="647" data-original-width="555" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4E3o2CDWo6tvjzIS_skLbVcK7oH5fJF5xIyiQ5eKsfx7ow0TcdYkHtkEe9Q4VMHnq9VF5D1JhsG0rpCWqaGg4B-umY5koeRao-rRcNfoQey_79yymTAc9VvfTNIh0uFcI2ck_9A/s320/loopship-diagram-conceptual.png" width="274" /></a></div>
<p>An accurate diagram would show all these paths stacked exactly on top of each other, like the illustration at left.<p>
<p>However, it may be easier to visualize what's happening in the loopship, with a diagram has successive traverses offset slightly, as shown at right.</p>
<br />
</div>
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<p>The above diagrams represent one full period of the loopship, made up of two mirror-image half periods. Adding another half period would look something like this:</p>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj74r1s4BvNub2ZLJFMQe44sRJXnaSLM4YiiNC-V7yeVHS8gIyiPeqLfvnZZRgeBDyqTRTDx9zOuhsLHbtuQ6O1Mo9y_Vsn7eHhsHDJ4KcGwWRjwn3FBB603sRtmBjp_EM_7pLj3Q/s1600/loopship-diagram-continued.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="806" data-original-width="588" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj74r1s4BvNub2ZLJFMQe44sRJXnaSLM4YiiNC-V7yeVHS8gIyiPeqLfvnZZRgeBDyqTRTDx9zOuhsLHbtuQ6O1Mo9y_Vsn7eHhsHDJ4KcGwWRjwn3FBB603sRtmBjp_EM_7pLj3Q/s400/loopship-diagram-continued.png" width="291" /></a></div>
</div>
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<p>The actual loopship has significantly different shapes at different times in its construction cycle. Here's a snapshot diagram where
<br /></br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOTKRRgDJZItwtQA_dZgEpEtgJv_zag_OxycG4bI9tG_YdEgJ_0YjtxbFXeixdu_aLvewKBNt0TV5LMMy4DffuASu2dymOCDkdwmY8HhELMkTIpM9sccQBmfzHyW9wnzTLvzjDWg/s1600/loopship-diagram-in-progress.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="754" data-original-width="459" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOTKRRgDJZItwtQA_dZgEpEtgJv_zag_OxycG4bI9tG_YdEgJ_0YjtxbFXeixdu_aLvewKBNt0TV5LMMy4DffuASu2dymOCDkdwmY8HhELMkTIpM9sccQBmfzHyW9wnzTLvzjDWg/s1600/loopship-diagram-in-progress.png" /></a></div>
<ul>
<li>the two Corderships (orange dots) are each in the process of being chased down by a salvo of zero-degree gliders. The southeast salvo will convert the Cordership's leftover debris into a Snark, and the northwest salvo will reduce that Cordership to a single block.</li><br />
<li>the remainder of the recipe traveling northeast will construct a new splitter-plus-Snarks constellation (a future blue dot halfway between the two Corderships).</li>
<li>a copy of the full recipe is heading southwest around the left-hand loop (green arrows).</li><br />
<li>a cleanup MWSS and glider (red dots) have almost reached the splitter-plus-Snark (blue dot) and Snark (purple dot) to the south, which are no longer in use.
</li><br />
</ul>
</div>
<h4>The Switching System</h4>
<p>There are a few details of the loopship's operation that aren't covered by the diagram. In particular, an extra signal makes its way around the loop twice, following a chain of one-time turners. This is what triggers the two self-destruct signals, and also turns off one of the branches of each Scorbie Splitter so that the full recipe doesn't get copied again, to attempt a second disastrous trip around the delay loop.</p>
<h4>Final Challenges</h4>
<p><mark>The loopship is considerably bigger than it needs to be...</mark> and making it smaller requires only one minor adjustment to the recipe. It's quite possible to make this change without doing any recompiling with slsparse. Details of some open problems are posted on the <a href="http://www.conwaylife.com/forums/viewtopic.php?p=65214#p65214">loopship forum thread</a>.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-72585415638749008142018-06-16T17:59:00.005-05:002022-11-16T20:02:02.550-05:00Fixed Cost Glider Construction, Part II<h2>Design Summary for Fixed-Cost Glider Construction</h2>
<p><i>The <a href="https://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html">previous post</a> summarized the new 329-glider reverse caber tosser universal constructor design, but didn't go into detail about what exactly makes the design universal. Here are (most of) the fiddly details, some of which are already out of date now that a universal construction method has been found with as few as 15 gliders. See <a href="https://conwaylife.com/forums/viewtopic.php?p=144315#p144315">this conwaylife.com forum posting</a> for a sample RCT pattern with 17 gliders (a shillelagh). Following posts describe how it's possible to do the same kind of universal construction with just 16 gliders.</p>
<p>The "reverse caber tosser" idea, with two gliders reflected back 180 degrees by a Cordership (or Corderpuffer, anyway) still remains intact -- and so does the three-glider PUSH/DFIRE salvo and the idea of using a block-laying switch engine as a source of elbow blocks. However, all of the PUSH/DFIRE salvos are now produced by glider-producing switch engines. These various switch engines are almost the only things that need to be constructed. In the 50-glider UC model, no stationary circuitry is needed at all. The 35-glider model needs a single block as a catalyst, to cleanly generate a return glider to retrieve the next bit from the approaching Corderpuffer.</i></p>
<p>The idea of a fixed-cost glider recipe for any possible glider-constructible object has gone through several iterations in the past few years. The first completed construction was a <a href="http://conwaylife.com/forums/viewtopic.php?f=7&t=1792&start=25#p22050">decoder that used a double sliding-block memory</a>, and repeatedly divided the stored number by two or three, returning the remainder for each cycle. That information could then be used to run a construction arm. However, an explicit construction arm was never created for that design.</p>
<p>A newer "reverse caber tosser" design is an alternate storage mechanism for data feeding a universal constructor. The reverse caber tosser was designed by Adam P. Goucher, with Martin Grant finding the key glider-reflection reaction. A very large integer can be encoded in the position of a very faraway Cordership (instead of a block). If the distance to the Cordership is measured using circuitry designed to be as simple as possible, a complete decoder and universal constructor can be created by colliding exactly 329 gliders.</p>
<p>Normally a construction arm has at least four possible "elbow operations": PULL and PUSH to change the location of the elbow, and two different FIRE recipes to produce either of the two possible glider colors.</p>
<p>The <b>first</b> simplification for the reverse caber tosser is the use of only one color of output glider. This limits the output to monochromatic single-parity slow salvos (see below) but significantly simplifies the circuitry.</p>
<p>Usually FIRE operations also leave an elbow behind for the next elbow operation to make use of. The <b>second</b> simplification in the decoder design is to use up an elbow with every FIRE operation.</p>
</p>This makes construction recipes very much less efficient, because each new output glider needs a fresh elbow block to be pulled in from "elbow storage" (a line of blocks created by a block-laying switch engine) before the DFIRE (destructive fire) operation can be sent. As the number of output gliders increases, the pull distance increases proportionally, making the recipe progressively less efficient.</p>
<p>However, once again in this case, using up elbows makes the decoder mechanism significantly simpler, and that's the only kind of efficiency that matters from the point of view of reducing the total cost of the construction. The PULL and DFIRE combined salvo needs only three synchronized gliders. It appears that including an elbow-preserving FIRE option would require four gliders or more, with a correspondingly larger amount of circuitry that would then have to be constructed by the initial glider recipe.</p>
<h3>Summary of required parts and mechanisms</h3>
<ul>
<li>The glider recipe builds the decoder/constructor plus a very faraway Cordership.
<li>The recipe also builds a block-laying switch engine as a source of elbow blocks for the constructor arm.
<li>Two gliders are sent toward the Cordership.
<li>When they reach the Cordership, they are reflected 180 degrees and head back toward the decoder.
<li>The two return gliders may reach the decoder at two possible timings (mod 256). Let's call these two timings "PULL" and "DFIRE".
<li>Changing the position of the Cordership allows a free choice of "PULL" or "DFIRE" timings, for each of N sets of return gliders.</li>
<li>Adding another bit to the data stored in the Cordership's position requires increasing the Cordership's distance from the decoder by roughly a factor of two.</li>
<li>The return gliders always interrupt a suppressing glider stream, allowing a construction-arm shotgun to send a two-glider salvo southeast to the block-laying switch engine.</li>
<li>The two-glider salvo is the same one used in many previous construction arms including the Gemini spaceship.</li>
<li>When the salvo strikes a block -- an "elbow" of the construction arm -- the block moves forward by one diagonal.</li>
<li>If the gliders have the "DFIRE" timing, a third glider is also released, which destroys the elbow block but releases a sideways glider.</li>
<li>Because the block is used up, this is a "destructive FIRE" elbow operation, instead of the more normal "FIRE" which preserves the elbow.</li>
<li>"PULL" and "DFIRE" operations, when combined with an unlimited supply of elbow blocks, allow a series of same-color gliders to be released successively on any set of chosen lanes.</li>
<li>The gliders will all have the same phase, so this is a "monochromatic single-parity slow salvo".</li>
<li>It has been shown that monochromatic monoparity slow salvos are capable of constructing any pattern that can be constructed by colliding gliders together.</li></ul>
<p>More recent fixed-cost construction designs include the proposal that the Cordership should be replaced with a c/12 puffer that is cheaper to synthesize -- 7 gliders instead of 9. This leaves a much larger mess to clean up, but it's still doable... and reducing the initial cost is the only thing that matters for this particular project.</p>
<p>The Cordership, or puffer, eventually generates its last bit and comes to a crashing halt. In the sample pattern shown in the previous post, the block that the Cordership/puffer crashes into is generated by two loafers, to make it clear that this block is a placeholder, not an official part of the initial glider construction! In the actual construction process, that block would be built by the construction arm, according to PULL and DFIRE instructions coming from the Cordership/puffer.</p>
<p>The construction arm also has to build a number of other "maintenance mechanisms":</p>
<ul><li>a large structure made up of one-time glider splitters and glider turners, with four parts:</li>
<ol><li>a one-time circuit producing two gliders that stop the receding block-laying switch engine without releasing any gliders</li>
<li>a one-time circuit producing a slow salvo of many gliders aimed at the ash from the stopped switch engine, rebuilding it into a clean one-time-use specialized Cordership eater</li>
<li>a one-time circuit producing a specialized Cordership able to remove unused blocks from the block-laying switch engine's ash trail</li>
<li>a one-time circuit producing a "meteor shower" slow salvo that completely cleans up the entire decoder/constructor mechanism.</li></ol>
<li>a secondary "slow elbow" block at a safe distance from the construction arm (generated by colliding a series of monochromatic gliders into some of the block-laying switch engine's leftover ash).</li>
<li>a "hand block" to provide the construction arm with a usable target for incremental constructions</li></ul>
<p>All of the above are necessary only if the pattern must be built with the absolute minimum of 329 gliders. If a larger number of gliders is allowed, on the rough order of 1000, then all this cleanup can be accomplished by adding gliders to the initial recipe instead. The resulting complete pattern would be many orders of magnitude smaller, though still very large. It might include several hundred more gliders in the initial recipe, but would be considerably more efficient at completing constructions.</p>
<p>For example, a more expensive Cordership-based block puffer could be constructed, and then could be shot down with gliders after it has produced exactly the right number of blocks. This would completely avoid any need to build the complex structures outlined in #1 through #3 above.</p>
<p>Similarly, building the "slow elbow" block as part of the construction recipe would cost only one or two gliders more than the minimum, but would reduce the size of the final pattern by a hundred or more orders of magnitude. That's not just a reduction by a factor of a hundred -- it's a factor of a googol, 10^100, and that's just a bare-minimum estimate. An even larger size reduction would result from adding two gliders to build the block that stops the incoming Cordership (the one built by loafers in the sample pattern).</p>
<p>When the constructor is in operation, it builds a series of one-time turners. The recipes are all monochromatic slow salvos. The purpose of the one-time turners is to to aim gliders at the hand block. These one-time turners fall into one of four categories, since they may change the parity and/or the color of the output glider relative to the input glider. This allows the "slow elbow" to convert a monochromatic single-parity slow salvo into a standard "P2 slow" salvo where the gliders may be either parity and either color.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-79278165776626814262018-06-13T07:02:00.007-05:002024-01-03T05:26:30.977-05:00The Answer to Life's Ultimate Question is 42 -- But the Cost of Life Construction is Capped at 329...59...58...50...44... 43... 35...32...17...16...15<div class="rle">
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<code>#C universal constructor based on reverse caber tosser<br />
#C Completed 10 June 2018<br />
#C Original design by Adam P. Goucher<br />
#C Original glider synthesis by Goldtiger997<br />
x = 5379, y = 5173, rule = B3/S23<br />
bo$2bo361bo$3o360bo$363b3o16$36bo$34bobo$35b2o$355bo$354bo$354b3o14$<br />
29bo$30bo$28b3o2$335bo$335bobo$335b2o37$92bobo$93b2o$93bo2$356bo$72bo<br />
283bobo$73b2o281b2o$72b2o2$337bo$336bo$336b3o891$1177bo$1178b2o$1177b<br />
2o197$2925bo3b2o2bo$2925b2o3bo2bo$2926bo3bobo$2925bo5bo2$2926b2o$2925b<br />
o2bo$2925bobo$2926bo65$1275bo$1276bo$1274b3o6$1265bo$1266b2o$1265b2o<br />
15$1278bo$1279b2o$1278b2o$1291bo$1289bobo$1290b2o6$1287bobo$1277bobo8b<br />
2o$1278b2o8bo$1278bo295$4459bo$4458bo$4458b3o$1848bo$1849bo$1847b3o14b<br />
o$1865b2o$1864b2o$1717bo$1718b2o$1717b2o2$1865bobo2600bobo$1866b2o<br />
2600b2o$1725bo140bo2602bo$1726bo$1724b3o11$1732bobo$1733b2o$1733bo13$<br />
1749bo$1750b2o$1749b2o2$1761bobo$1762b2o$1762bo16$1765bobo$1766b2o$<br />
1766bo4$1774bo$1772bobo$1773b2o23$1854bo$1855bo$1853b3o6$1794bo$1795b<br />
2o$1794b2o32$1838bo$1839bo$1837b3o2$1851bo$1849bobo$1850b2o138$4513bob<br />
o$4513b2o$4514bo4$4506bo$4506bobo$4506b2o38$1876bo2193bo$1874bobo2192b<br />
o$1875b2o2192b3o412bo$4482b2o$4483b2o4$4063bobo$4063b2o$4064bo$2237bo$<br />
2235bobo16bo$2236b2o17bo$2246bo6b3o$2247bo$2238bo6b3o$2239bo$2237b3o<br />
23$4444bobo$4444b2o$4435bobo7bo$4435b2o$1822bo2613bo$1820bobo$1821b2o<br />
2626bobo$4449b2o$4450bo13$1843bo$1844b2o$1843b2o466bo$2312b2o$2311b2o<br />
4$1828bobo$1829b2o$1829bo$4095bo$4093b2o$4088bobo3b2o$4088b2o$1838bo<br />
2250bo$1839b2o$1838b2o473bobo$2314b2o$2314bo2$4090bobo$4090b2o$4091bo<br />
3$2222bo97bo$2223bo97bo$2221b3o95b3o$4092bobo$2234bobo1855b2o$2235b2o<br />
1856bo$2235bo4$4069bo$4069bobo$4069b2o$2246bo$2247b2o$2246b2o2$4073bob<br />
o$4073b2o$4074bo$4052bo$4050b2o$4051b2o5$4070bo13bo$2265bo1804bobo10bo<br />
$2266b2o1802b2o11b3o$2265b2o6$2267bobo$2268b2o$2268bo4$2276bo$2266bo<br />
10bo$2267bo7b3o$2265b3o55$2202bo$2203b2o$2202b2o$2215bo$2213bobo$2214b<br />
2o6$2211bobo$2201bobo8b2o$2202b2o8bo$2202bo36$4205bo$4205bobo$4205b2o<br />
4$4210bo$4209bo$4209b3o38$4154bobo$4154b2o$4155bo$4162bo$4162bobo$<br />
4162b2o2$4153bo$4151b2o$2105bo2046b2o$2106bo$2104b3o11$4137bo$4137bobo<br />
$4137b2o3$2103bobo$2104b2o$2104bo2040bo$4145bobo$4145b2o12$4122bo$<br />
4121bo$4121b3o2$4117bo$4116bo$4116b3o$2123bobo$2124b2o$2124bo2001bo$<br />
4126bobo$4126b2o16$2386bobo$2387b2o$2387bo13$3880bo$3879bo$3879b3o6$<br />
3873bobo$3873b2o$3874bo$2493bo$2491bobo$2335bo156b2o$2336bo$2334b3o$<br />
3861bo$2339bo1521bobo$2337bobo1521b2o$2338b2o$2484bo$2485b2o$2484b2o$<br />
2355bo$2356bo$2354b3o14bo16bobo$2372b2o15b2o1441bo$2371b2o16bo1441bo$<br />
3831b3o$2374bobo1467bo$2375b2o1467bobo$2375bo30bo1437b2o$2407b2o$2401b<br />
o4b2o$2402bo$2400b3o18bo$2364bo57b2o$2365b2o54b2o$2364b2o2$3832bo$<br />
3832bobo$3832b2o3$2311bo96bobo1455bo5bo$2312bo96b2o1454bo4b2o$2310b3o<br />
96bo1455b3o3b2o2$2413bo$2326bobo85bo$2327b2o83b3o$2327bo3$2336bo$2337b<br />
2o$2336b2o$2412bo1443bobo$2410bobo1443b2o$2411b2o1444bo4$2409bo$2407bo<br />
bo$2408b2o5$2414bo$2415b2o$2414b2o$3887bo$3886bo$3869bo16b3o$3869bobo$<br />
3869b2o7bo$3876b2o$3877b2o7bo$3884b2o$3885b2o62$3795bo$3793b2o$3794b2o<br />
3$3798bobo$3798b2o$3799bo2$2145bo$2146bo$2144b3o4$3794bo$3794bobo$<br />
3794b2o2$3789bo$3789bobo$2153bo1635b2o$2154b2o$2153b2o1644bo$3798bo$<br />
3798b3o83$2750bo$2751bo$2742bo6b3o$2743bo$2734bo6b3o$2735bo$2733b3o35$<br />
4006bo$4004b2o$4005b2o6$4008bo$4006b2o$4007b2o11$2572bo$2573bo$2571b3o<br />
2$2577bo2216bo$2578bo2214bo$2576b3o2214b3o$3995bobo$2573bo1421b2o$<br />
2568bo5b2o1420bo$2566bobo4b2o$2567b2o$3988bo$3987bo$3987b3o25$2856bobo<br />
$2857b2o$2857bo2$2852bo$2853b2o$2852b2o3$3693bo$3693bobo$3693b2o3$<br />
2857bo$2858bo$2856b3o2$2862bo$2863bo$2861b3o$3684bobo$3684b2o$2853bo<br />
831bo$2851bobo$2852b2o128$3522bo$3521bo$3521b3o4$2581bo$2582bo$2580b3o<br />
$2556bo$2557bo$2555b3o4$2580bo1181bobo$2559bo18bobo1181b2o$2557bobo19b<br />
2o1182bo$2558b2o$2569bobo$2570b2o$2570bo212bobo$2784b2o$2784bo2$2779bo<br />
$2780b2o$2779b2o3$4144bo$4144bobo$4144b2o11$2591bo$2589bobo$2590b2o5$<br />
2601bo$2602b2o1187bo4bobo$2601b2o1188bobo2b2o$3791b2o4bo44$3441bo$<br />
3441bobo$2629bo811b2o$2630b2o$2629b2o104$2797bo$2798bo$2796b3o4$2796bo<br />
bo$2797b2o809bobo$2797bo810b2o8bo$3609bo6b2o$3617b2o21$3571bo$2759bo<br />
811bobo$2760bo810b2o$2758b3o25$2767bo$2768bo$2766b3o41$3056bo$3054bobo<br />
$3055b2o2$3061bo$3059bobo$3060b2o803bo$3863b2o$3051bo812b2o$3052bo$<br />
3050b3o68$3774bo17bo$3772b2o17bo$3773b2o16b3o3$3781bobo12bo$3781b2o13b<br />
obo$3782bo13b2o3$3777bobo$3777b2o$3778bo174$2677b2o$2676bobo$2678bo<br />
813bo$3491b2o$3491bobo66$2747b2o$2748b2o$2747bo4$2737b3o$2739bo$2738bo<br />
40$3692bo$3678b2o11b2o$3677b2o12bobo$3679bo266$2251b2o$2252b2o$2251bo<br />
146b2o$2399b2o$2398bo2$2241b3o$2243bo135b3o12b2o$2227b2o13bo138bo13b2o<br />
$2226bobo151bo13bo$2228bo$2384b2o17bo$2383bobo17b2o$2385bo16bobo$2227b<br />
2o$2226bobo323b2o$2228bo194b3o127b2o1345bo$2425bo126bo1346b2o$2424bo<br />
1474bobo2$4097b2o$2545b2o1550bobo$2544bobo21bo1528bo$2546bo21b2o$2567b<br />
obo1322bo$3891b2o$2369b2o1520bobo211bo$2368bobo1733b2o$2370bo1733bobo<br />
12$2372bo$2372b2o$2371bobo5$2343bo$2343b2o14bo$2342bobo14b2o5b3o$2358b<br />
obo7bo$2367bo4$2344b2o$2343bobo$2345bo$3857b2o189b3o$3857bobo188bo$<br />
3857bo191bo$3608b3o$2284bo511b2o810bo$2284b2o509bobo811bo$2283bobo511b<br />
o$4076b3o$4076bo$2293b2o1782bo$2294b2o$2293bo2$2288b2o$2289b2o1562b2o$<br />
2288bo1563b2o$3854bo$3857bo$3856b2o228bo$3856bobo13bo212b2o$3871b2o<br />
212bobo$2271b2o1598bobo$2260b3o9b2o$2262bo8bo12b2o$2261bo21bobo$2285bo<br />
1595b2o$3880b2o$2750b2o1130bo$2288b3o460b2o6bo1135b3o$2290bo459bo8b2o<br />
810bo323bo$2289bo468bobo809b2o324bo$3570bobo$4082bo$4081b2o$4081bobo$<br />
2272b3o1295b3o$2274bo1295bo$2273bo1297bo2$2262b2o$2263b2o$2262bo60bo$<br />
2270b2o51b2o$2269bobo50bobo6bo$2271bo59b2o$2330bobo$2338b3o$2340bo$<br />
2339bo$2319b3o$2321bo$2320bo$2769bo1072b2o$2769b2o1070b2o$2768bobo<br />
1072bo5$3848b2o$3848bobo$3848bo28$2207b3o$2209bo$2208bo4$2212b2o$2211b<br />
obo$2213bo3$3858bo$3857b2o$3857bobo85$2573bo4b2o$2573b2o2bobo1184b2o$<br />
2572bobo4bo1183b2o$3765bo6$2952b3o$2954bo$2953bo4$3775b2o$3775bobo$<br />
3775bo5$2953b2o$2952bobo$2954bo832b2o$3786b2o214b2o$3788bo213bobo$<br />
4002bo3$2587b3o$2589bo1416bo$2588bo1416b2o$4005bobo2$4015b2o$4014b2o$<br />
4016bo$4012bo$4011b2o$2603bo1186b2o219bobo$2603b2o1185bobo$2602bobo<br />
1185bo7$3788b3o$3788bo$3789bo40$2146b2o12bo$2147b2o11b2o$2146bo12bobo<br />
73$4216bo$4206bo8b2o$4205b2o8bobo$4205bobo6$4203b2o$4203bobo$4203bo$<br />
4215b2o$4214b2o$4216bo4$4143bo$4142b2o$4142bobo35$1848b2o$1847bobo$<br />
1849bo15$4151b2o$4141b2o7b2o$4140b2o10bo$4142bo2$4132bo$1849b2o2280b2o<br />
$1850b2o2279bobo$1849bo2$2109b3o18b2o$2111bo19b2o$2110bo19bo4$4156b3o$<br />
4156bo$4157bo3$2105b3o$1760bo346bo$1760b2o344bo2052b2o$1759bobo2397bob<br />
o$4159bo21$1728bo$1728b2o46b2o$1727bobo47b2o$1776bo5$1737b2o$1736bobo$<br />
1738bo2660b2o$4398b2o$4400bo10$1791b2o$1790bobo$1792bo4$1784bo$1784b2o<br />
$1783bobo156$4503b2o$4502b2o$4504bo7$1912b2o$1913b2o$1912bo40$1863b3o$<br />
1865bo$1864bo$4428b2o$1864bo2562b2o$1864b2o2563bo$1863bobo2$1855b3o$<br />
1857bo2571b2o$1856bo2572bobo$4418b3o8bo$4418bo$4419bo38$4460b2o$4440b<br />
2o18bobo$4440bobo17bo$4440bo3$4453bo$4452b2o$4452bobo14$1824b2o$1823bo<br />
bo$1825bo2621bo$4446b2o$4446bobo3$1832bo$1832b2o$1831bobo2$1825b2o$<br />
1824bobo$1826bo2609bo$4435b2o24b3o$4435bobo23bo$4462bo2$1843b2o$1842bo<br />
bo$1844bo4$1836b2o$1835bobo$1837bo$1825b3o$1827bo$1826bo$4428b3o$4428b<br />
o$4429bo5$1840b3o$1842bo$1841bo$4443b3o$4443bo$4444bo25$2711b2o218b3o$<br />
2712b2o217b3o$2711bo218bo2$2933b2o1833b2o$2926b3o3bo1835bobo$2925bob2o<br />
4b2o1833bo$2925bo6bo$2926bobobo$1903b2o$1904b2o$1903bo2$4362b2o$4362bo<br />
bo$4362bo5$1940b2o$1939bobo$1941bo7$1935b2o$1934bobo$1936bo$1920b2o$<br />
1921b2o$1920bo2489b2o$4409b2o$4411bo385bo$4796b2o$4796bobo6$1917b3o$<br />
1919bo$1911b2o5bo$1910bobo$1912bo$4403bo$4402b2o$4402bobo6$4408b3o125b<br />
2o$4408bo127bobo$4409bo126bo47$2641b2o$2640bobo$2642bo29$1359b3o$1361b<br />
o$1360bo11$4614b2o$4614bobo$4614bo49$1295b3o$1297bo$1296bo3$1270b2o$<br />
1271b2o$1270bo$1283b3o$1285bo$1284bo4$1288b2o$1287bobo$1289bo$1262b2o$<br />
1261bobo$1263bo4$1255bo$1255b2o$1254bobo289$5377b2o$5376b2o$5378bo!<br />
#C [[ WIDTH 592 HEIGHT 500 X 5 Y -60 PAUSE 2 AUTOSTART ]]<br />
#C [[ T 800 STEP 5 ]]<br />
#C [[ T 2500 GPS 60 X 410 Y 456 Z 2 ]]<br />
#C [[ T 2600 STEP 4 ]]<br />
#C [[ T 2700 STEP 3 ]]<br />
#C [[ T 2800 STEP 2 ]]<br />
#C [[ T 2900 STEP 1 ]]<br />
#C [[ T 3000 STEP 2 ]]<br />
#C [[ T 3100 STEP 3 ]]<br />
#C [[ T 3200 STEP 4 ]]<br />
#C [[ T 3300 STEP 5 ]]<br />
#C [[ T 7850 GPS 60 STEP 50 X 555 Y 628 Z -1.5 ]]<br />
#C [[ T 28000 X 225 Y 300 Z -4 ]]<br />
#C [[ PAUSE 5 LOOP 28050 ]]</code></div>
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There has been speculation for <a href="http://conwaylife.com/forums/viewtopic.php?f=12&t=1596#p16517">at least a couple of years</a><a href="http://b3s23life.blogspot.com/2018/06/the-meaning-of-life-is-42-but-cost-of.html#footnote1">**</a> about the simplest possible form of universal constructor, where an arbitrarily complex construction recipe is encoded in the position of a single faraway object. The position of the object is measured by the simplest possible decoder mechanism, resulting in a series of bits that can then be interpreted to produce a <a href="http://conwaylife.com/wiki/Slow_salvo">slow salvo</a>.<br />
It has already been shown that slow salvos can construct any pattern that is constructible by gliders. So with the correct placement of the faraway object, the complete pattern is capable of building any possible glider-constructible pattern of any size. The same pattern is also capable of building a self-destruct mechanism that completely removes all trace of the universal constructor, after its work is done -- leaving only the constructed pattern and nothing else. A counterintuitive consequence is that any glider-constructible object, no matter what size, can be built with a specific fixed number of gliders.<br />
And now the actual number has been calculated, and it's surprisingly small. The initial upper limit was 329 gliders, based on the pattern shown above. This has since been reduced several times, as indicated by the series of numbers in this article's title.<br />
See <a href="http://b3s23life.blogspot.com/2018/06/fixed-cost-glider-construction-part-ii.html">the follow-up article</a> for a full summary of the tasks that the universal constructor has to accomplish to be enable the 329-glider recipe to to construct any arbitrary pattern. The plans for the 58-, 43-, and 35-glider recipes are similar, but greatly simplified by the fact that the streams of gliders can all be generated by faraway glider-producing switch engines instead of local glider guns and reflectors. With the 58-glider recipe, no stationary circuitry is needed at all; a single block is needed as a catalyst in the 43- and 35-glider recipes.<br />
<a href="https://www.blogger.com/null" name="footnote1">**</a> It seems likely that someone came up with this idea long before 2015 -- i.e., the inevitability of a fixed-cost construction with N gliders, for any possible glider-constructible object. Really it's more or less implied by the sliding-block memory units described in <u>Winning Ways</u>. But I don't know of anywhere that the fixed upper-limit cost of construction was mentioned explicitly. It would be interesting to see what early estimates of that upper limit might have been... it seems likely they were significantly higher than three digits, let alone two!<br />
<b>UPDATE 19 September 2020 and 11 November 2022</b>: Design improvements by MathAndCode, Adam P. Goucher, and danielle make possible a <a href="https://www.conwaylife.com/forums/viewtopic.php?p=104484#p104484">reduced reverse caber tosser design</a> requiring only 16 gliders, a 50% reduction from the previous fixed cost of 32 gliders.<br>
<b>UPDATE 15 September 2022</b>: The fixed cost has now been reduced to 15 gliders.Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com2tag:blogger.com,1999:blog-8285929.post-28468341281407287212018-03-10T08:49:00.004-05:002021-02-25T14:01:55.247-05:00It Happened One Knight<p>On 6 March 2018 the first member of a new class of Conway's Life spaceships was discovered. This is Sir Robin, the first elementary spaceship that travels in an oblique direction. Its displacement is two cells horizontally and one cell vertically (or vice versa) every six generations, which is the fastest possible knightship speed. The name is a reference to Monty Python's "Brave Sir Robin", who bravely runs away as fast as possible.</p>
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<div><code>#C (2,1)c/6 knightship found by Adam P. Goucher,<br />
#C based on a front end originally found by Josh Ball,<br />
#C rediscovered and extended by Tomas Rokicki,<br />
#C using a SAT solver-based search<br />
x = 79, y = 31, rule = B3/S23<br />
8bo$6bo2bo$4b2obo3bo$4bo2bo3bo$3o2bobo$o4bobobo$3bo2bo3bo$bobo6bo$2b2o<br />
6bo2$4b2ob2o4bob4o11bo$4b2ob2ob2ob3o2b2obob2o4bobo$4b2o4bo3bobobo6b2o$<br />
4b3o5bo4bobo6bob2o2b2o$6bo7bo5bo5bob3obo$6b2o2bobob4ob2o3bo3b2o2b2o$<br />
11b2obobo10bo3b3o22bo$17bo2bo6bob3obo24bo$13b3o5bo3bo2bo3b2o9bo8b3o3bo<br />
$18b4o3bo5bo2bo4bob2obo5b3o5bo$21bo3bo5bo3b2o2b2o3b2o3b2ob2obobo$23bob<br />
o5bo4b2obo5bob2obo2bo2b2o6bobo$24b2o11bo2bo4b2obobob2o2b2o5b2o2bo2b2o$<br />
32b2obobo3b2o2b2o3bob2o2b2o5b2o2bo2b3o$32b2obobo4bobo3bo2b3o2bob2obo3b<br />
2obob4o3bo$37b2o4bo13bo4bo2b3o5b3obo$38bobo4bo11bobo2bo3bob2o4bo3bo$<br />
41bobo2bo14b2o6bo3bo$39b2o2b2o15b2o3b3o4b2o$43b3o18bo3bob3o$65b2obo3bo!<br />
#C [[ GRID THEME 7 TRACKLOOP 6 -1/3 -1/6 THUMBSIZE 2 HEIGHT 480 ZOOM 7 GPS 12 AUTOSTART ]]</code></div></div>
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<p>The new knightship was found by Adam P. Goucher based on initial results by Tom Rokicki, after about a month of automated searching. The program that completed the knightship was <a href="https://gitlab.com/apgoucher/metasat/blob/master/ikpx.py">ikpx</a>, a <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=3303#p57354">"multithreaded hybrid of LLS and gfind"</a>.</p>
<p>A detailed summary of the discovery process <a href="https://cp4space.wordpress.com/2018/03/11/a-rather-satisfying-winter/">is now available</a>.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-29046645723396539572016-10-15T15:07:00.004-05:002019-07-12T05:33:13.113-05:0014-, 15-, and 16-bit still life syntheses<p><a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1452&start=1275#p36380">A week or so ago,</a> a better recipe was found for the last still life on Mark Niemiec's list of expensive 14-bit syntheses. Now all 14-bit still lifes can be constructed with less than 14 gliders -- less than 1 glider per bit, as the old saying goes.
</p><p>
<a href="http://catagolue.appspot.com">Catagolue</a> results continue to be very useful in finding new recipes.</p>
<br />
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<div><code>#C 12-glider synthesis for the last 14-bit still life,<br />
#C snake bridge snake / 12.105, which had previously cost at least<br />
#C one glider per bit.<br />
#C Goldtiger997, 6 October 2016, optimized by Mark Niemiec on 7 October.<br />
x = 79, y = 71, rule = LifeHistory<br />
7.A$.A6.A$2.A3.3A$3A2$16.A$14.A.A$15.2A6$36.A$34.A.A$35.2A8$30.3A$32.<br />
A$31.A4$31.3A$33.A11.2D.D$32.A12.D.2D$43.2D$39.2D.D$39.D.2D6$52.A$51.<br />
2A$20.2A5.3A21.A.A$21.2A6.A$20.A7.A22$3.3A$5.A70.2A$4.A4.2A65.A.A$10.<br />
2A64.A$9.A!<br />
#C [[ AUTOFIT AUTOSTART GPS 25 LOOP 150 ]] </code></div></div>
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<p>UPDATE: The next challenge along these lines was to similarly reduce 15-bit still life costs to below 1 glider per bit. The process started <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1452&start=1275#p36421">later in the same forum thread</a>, and was completed on <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2441&start=150#p37438">November 19, 2016</a>, with the following 14-glider synthesis:
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<div><code>#C 14-glider synthesis for the last 15-bit still life<br />
#C which had previously cost at least one glider per bit.<br />
#C Extrementhusiast, 19 November 2016<br />
x = 48, y = 38, rule = B3/S23<br />
17bobo$17b2o$18bo$4bobo$5b2o$5bo$18bo$18bobo$18b2o2$obo$b2o39b2o$bo40b<br />
o3b2o$20b3o21bo2bo$20bo22b2obo$21bo6bo16bo$8b2o18bobo14bobo$7bobo18b2o<br />
16b2o$9bo2$5b2o$4bobo$6bo9b2o$10b2o3bobo$11b2o4bo$10bo4$8b3o$7bo2bo$<br />
10bo$6bo3bo$10bo$7bobo$32b3o$32bo$33bo!<br />
#C [[ AUTOFIT AUTOSTART GPS 25 LOOP 150 ]] </code></div></div>
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<p>UPDATE 2: The next project involved a similar reduction for 16-bit still life recipes. The official project kickoff was on <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2642">December 16, 2016</a>, when 443 of the 3,286 16-bit still lifes had no synthesis in less than 16 gliders in <a href="https://github.com/ceebo/glider_synth">Chris Cain's database</a>. It concluded successfully on <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2642&start=250#p43734">May 24, 2017</a>.</p>
<p>UPDATE 3: As of 12 July 2019, every 15-bit still life has a recipe with at most 13 gliders. Other upper limits include a maximum of 12 gliders needed for 14-bit still lifes, and a maximum of only (N-4) gliders needed for 8-bit through 13-bit still lifes.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-16304795787550137202016-06-12T10:34:00.003-05:002016-06-12T21:55:53.588-05:00New spaceship speed: 3c/7<p>Tim Coe has found a symmetrical spaceship with a new speed, 3c/7 (left, below) after a series of searches that took a total of <a href=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2031&start=75#p31878>"one or two months"</a>. At 29 cells wide, it is the minimum width odd symmetric spaceship -- an <a href=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=2031&start=75#p31878>exhaustive width 27 search was run some time ago</a> by Paul Tooke. The author seems to have officially chosen a name of "Spaghetti Monster" for the new 3c/7 spaceship.</p>
<p>Matthias Merzenich has pointed out that two of these spaceships can support a known 3c/7 wave (right, below).</p>
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<div><code>#C 3c/7 FSM spaceship: Tim Coe, 11 June 2016<br />
#C Period-28 3c/7 wave found by Stephen Silver on Feb. 2, 2000<br />
x = 187, y = 139, rule = B3/S23<br />
10bo7bo65bo7bo$8b2ob2o3b2ob2o61b2ob2o3b2ob2o$8b2ob2o3b2ob2o61b2ob2o3b<br />
2ob2o73bo7bo$11b2o3b2o67b2o3b2o74b2ob2o3b2ob2o$7bo5b3o5bo59bo5b3o5bo<br />
70b2ob2o3b2ob2o$7bo13bo59bo13bo73b2o3b2o$8bo11bo61bo11bo70bo5b3o5bo$9b<br />
2o7b2o63b2o7b2o71bo13bo$6bobobobo3bobobobo57bobobobo3bobobobo69bo11bo$<br />
6bobob2o5b2obobo57bobob2o5b2obobo70b2o7b2o$6bobo11bobo57bobo11bobo67bo<br />
bobobo3bobobobo$164bobob2o5b2obobo$11bo5bo67bo5bo72bobo11bobo$10b2o5b<br />
2o65b2o5b2o$8b2o9b2o61b2o9b2o74bo5bo$8bo3bo3bo3bo61bo3bo3bo3bo73b2o5b<br />
2o$10bo2bobo2bo65bo2bobo2bo73b2o9b2o$10bobo3bobo65bobo3bobo73bo3bo3bo<br />
3bo$9bo9bo63bo9bo74bo2bobo2bo$7bo3bo5bo3bo59bo3bo5bo3bo72bobo3bobo$6b<br />
4o9b4o57b4o9b4o70bo9bo$4b2obo2bo7bo2bob2o53b2obo2bo7bo2bob2o66bo3bo5bo<br />
3bo$4b2o2b3o7b3o2b2o53b2o2b3o7b3o2b2o65b4o9b4o$7bobo2bo3bo2bobo59bobo<br />
2bo3bo2bobo66b2obo2bo7bo2bob2o$5bob3o2bo3bo2b3obo55bob3o2bo3bo2b3obo<br />
64b2o2b3o7b3o2b2o$5bo4bo7bo4bo55bo4bo7bo4bo67bobo2bo3bo2bobo$163bob3o<br />
2bo3bo2b3obo$6bo15bo57bo15bo66bo4bo7bo4bo$6b2obo9bob2o57b2obo9bob2o$5b<br />
o3b2o7b2o3bo55bo3b2o7b2o3bo66bo15bo$164b2obo9bob2o$5b2o4bo5bo4b2o55b2o<br />
4bo5bo4b2o65bo3b2o7b2o3bo2$8b2ob2o3b2ob2o61b2ob2o3b2ob2o68b2o4bo5bo4b<br />
2o$2bo5b2o3bobo3b2o5bo49bo5b2o3bobo3b2o5bo$bob2o5bobo3bobo5b2obo47bob<br />
2o5bobo3bobo5b2obo64b2ob2o3b2ob2o$2o2bo3b2obo5bob2o3bo2b2o45b2o2bo3b2o<br />
bo5bob2o3bo2b2o57bo5b2o3bobo3b2o5bo$2bob2ob6o3b6ob2obo49bob2ob6o3b6ob<br />
2obo58bob2o5bobo3bobo5b2obo$7bo2bobo3bobo2bo59bo2bobo3bobo2bo62b2o2bo<br />
3b2obo5bob2o3bo2b2o$4bobo2bo9bo2bobo53bobo2bo9bo2bobo61bob2ob6o3b6ob2o<br />
bo$2b3o3bo11bo3b3o49b3o3bo11bo3b3o64bo2bobo3bobo2bo$2b3obobo11bobob3o<br />
49b3obobo11bobob3o61bobo2bo9bo2bobo$3b3o17b3o51b3o17b3o60b3o3bo11bo3b<br />
3o$160b3obobo11bobob3o$4bo19bo53bo19bo62b3o17b3o$2b2o21b2o49b2o21b2o$b<br />
obo21bobo47bobo21bobo60bo19bo$b3o21b3o47b3o21b3o58b2o21b2o$159bobo21bo<br />
bo$b2o23b2o47b2o23b2o57b3o21b3o$b3o21b3o47b3o21b3o$4bo4b3o5b3o4bo53bo<br />
4b3o5b3o4bo60b2o23b2o$9bo2bo3bo2bo63bo2bo3bo2bo65b3o21b3o$2bobo4bo9bo<br />
4bobo49bobo4bo9bo4bobo61bo4b3o5b3o4bo$3bo7b2o3b2o7bo51bo7b2o3b2o7bo67b<br />
o2bo3bo2bo$6b5o7b5o57b5o7b5o63bobo4bo9bo4bobo$5b4o11b4o55b4o11b4o63bo<br />
7b2o3b2o7bo$4b2o17b2o53b2o17b2o65b5o7b5o$6bob2o9b2obo57bob2o9b2obo66b<br />
4o11b4o$5bob2obo7bob2obo55bob2obo7bob2obo64b2o17b2o$7b5ob3ob5o59b5ob3o<br />
b5o68bob2o9b2obo$2b3o2b2o2b2o3b2o2b2o2b3o49b3o2b2o2b2o3b2o2b2o2b3o62bo<br />
b2obo7bob2obo$4bo2b2o2b2obob2o2b2o2bo53bo2b2o2b2obob2o2b2o2bo66b5ob3ob<br />
5o$3bo3b2o2b3ob3o2b2o3bo51bo3b2o2b3ob3o2b2o3bo60b3o2b2o2b2o3b2o2b2o2b<br />
3o$3bo5bobob3obobo5bo51bo5bobob3obobo5bo62bo2b2o2b2obob2o2b2o2bo$3bo3b<br />
5o5b5o3bo51bo3b5o5b5o3bo61bo3b2o2b3ob3o2b2o3bo$4bo3b2o9b2o3bo53bo3b2o<br />
9b2o3bo62bo5bobob3obobo5bo$11bo2bo2bo67bo2bo2bo69bo3b5o5b5o3bo$11b2o3b<br />
2o67b2o3b2o70bo3b2o9b2o3bo$13bobo71bobo79bo2bo2bo$169b2o3b2o$8b3o7b3o<br />
61b3o7b3o76bobo$7bo3b2o3b2o3bo59bo3b2o3b2o3bo$8bo11bo61bo11bo71b3o7b3o<br />
$8bo4bobo4bo61bo4bobo4bo70bo3b2o3b2o3bo$7bobobo5bobobo59bobobo5bobobo<br />
70bo11bo$7bo3bo5bo3bo59bo3bo5bo3bo70bo4bobo4bo$7b2o3bo3bo3b2o59b2o3bo<br />
3bo3b2o69bobobo5bobobo$11bo5bo67bo5bo73bo3bo5bo3bo$9bo9bo63bo9bo71b2o<br />
3bo3bo3b2o$9b2o7b2o63b2o7b2o75bo5bo$10bo7bo65bo7bo74bo9bo$167b2o7b2o$<br />
168bo7bo$9b3o5b3o63b3o5b3o$9b2o7b2o63b2o7b2o$8bo3bo3bo3bo61bo3bo3bo3bo<br />
72b3o5b3o$9bo3bobo3bo63bo3bobo3bo73b2o7b2o$13bobo71bobo76bo3bo3bo3bo$<br />
11bo5bo67bo5bo75bo3bobo3bo$171bobo$11b3ob3o67b3ob3o77bo5bo$11b2obob2o<br />
67b2obob2o$9bobo5bobo63bobo5bobo75b3ob3o$8bob2o5b2obo61bob2o5b2obo74b<br />
2obob2o$8bo11bo61bo11bo72bobo5bobo$7bo2b2o5b2o2bo59bo2b2o5b2o2bo70bob<br />
2o5b2obo$8b2o9b2o61b2o9b2o71bo11bo$7bob2o7b2obo59bob2o7b2obo69bo2b2o5b<br />
2o2bo$9b2o7b2o63b2o7b2o72b2o9b2o$6bo15bo57bo15bo68bob2o7b2obo$6b2o3bo<br />
5bo3b2o57b2o3bo5bo3b2o70b2o7b2o$6b3o2bo5bo2b3o57b3o2bo5bo2b3o67bo15bo$<br />
7bo13bo59bo13bo68b2o3bo5bo3b2o$9b2ob2ob2ob2o63b2ob2ob2ob2o70b3o2bo5bo<br />
2b3o$10bob2ob2obo65bob2ob2obo72bo13bo$9b2ob2ob2ob2o63b2ob2ob2ob2o73b2o<br />
b2ob2ob2o$10bo7bo65bo7bo75bob2ob2obo$10bobobobobo65bobobobobo74b2ob2ob<br />
2ob2o$10bo7bo65bo7bo75bo7bo$168bobobobobo$8bo4bobo4bo61bo4bobo4bo7bo7b<br />
o7bo7bo41bo7bo$8bo3bo3bo3bo61bo3bo3bo3bo6b3o5b3o5b3o5b3o$7b2obo7bob2o<br />
59b2obo7bob2o4bo2b2o3b2o2bo3bo2b2o3b2o2bo5bo7bo7bo7bo7bo4bobo4bo$8bob<br />
2o5b2obo61bob2o5b2obo4b2o2b2o3b2o2b2ob2o2b2o3b2o2b2o3b3o5b3o5b3o5b3o6b<br />
o3bo3bo3bo$6bob3o7b3obo57bob3o7b3obo2b2o2b3ob3o2b2ob2o2b3ob3o2b2o2bo2b<br />
2o3b2o2bo3bo2b2o3b2o2bo4b2obo7bob2o$5bo17bo55bo17bob3o9b3ob3o9b3ob2o2b<br />
2o3b2o2b2ob2o2b2o3b2o2b2o4bob2o5b2obo$12bo3bo69bo3bo9b2o9b2o3b2o9b2o2b<br />
2o2b3ob3o2b2ob2o2b3ob3o2b2o2bob3o7b3obo$11bobobobo67bobobobo39b3o9b3ob<br />
3o9b3obo17bo$7b3o3bobo3b3o59b3o3bobo3b3o36b2o9b2o3b2o9b2o9bo3bo$7b4obo<br />
3bob4o59b4obo3bob4o73bobobobo$9b2o7b2o63b2o7b2o71b3o3bobo3b3o$7bob2o7b<br />
2obo59bob2o7b2obo69b4obo3bob4o$6b2ob2o3bo3b2ob2o57b2ob2o3bo3b2ob2o70b<br />
2o7b2o$5b2o2b2o2bobo2b2o2b2o55b2o2b2o2bobo2b2o2b2o67bob2o7b2obo$8b3obo<br />
3bob3o61b3obo3bob3o69b2ob2o3bo3b2ob2o$5b5o2bo3bo2b5o55b5o2bo3bo2b5o65b<br />
2o2b2o2bobo2b2o2b2o$4bo7b2ob2o7bo53bo7b2ob2o7bo67b3obo3bob3o$4bo3b2o3b<br />
obo3b2o3bo53bo3b2o3bobo3b2o3bo64b5o2bo3bo2b5o$4bobo2bo3bobo3bo2bobo53b<br />
obo2bo3bobo3bo2bobo63bo7b2ob2o7bo$11b3ob3o67b3ob3o70bo3b2o3bobo3b2o3bo<br />
$7b3ob3ob3ob3o59b3ob3ob3ob3o66bobo2bo3bobo3bo2bobo$13b3o71b3o79b3ob3o$<br />
13b3o71b3o75b3ob3ob3ob3o$171b3o$11bo5bo67bo5bo79b3o$11bobobobo67bobobo<br />
bo$169bo5bo$169bobobobo!<br />
#C [[ AUTOFIT AUTOSTART GPS 4 ]] </code></div></div>
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<p>This is the twenty-second spaceship velocity constructed in Conway's Life -- counting each of the four infinite families of spaceships (Gemini, HBK, Demonoid, Caterloopillar) as one velocity each.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-2750961613219136582016-03-10T22:04:00.000-05:002016-03-11T08:20:11.655-05:00New c/10 "copperhead" spaceshipReposted with permission from <a href="https://niginsblog.wordpress.com/2016/03/07/new-spaceship-speed-in-conways-game-of-life/">Alexey Nigin's blog</a>:<br />
<br />
The day before yesterday (March 6, 2016) <a href="http://conwaylife.com/forums/">ConwayLife.com forums</a> saw a new member named <a href="http://conwaylife.com/forums/memberlist.php?mode=viewprofile&u=1563">zdr</a>. When we the lifenthusiasts meet a newcomer, we expect to see things like “brand new” 30-cell 700-gen <a href="http://conwaylife.com/wiki/Methuselah">methuselah</a> and then have to explain why it is not notable. However, what zdr showed us made our jaws drop.<br />
<br />
It was a 28-cell <a href="http://conwaylife.com/wiki/C/10_orthogonal">c/10 orthogonal</a> <a href="http://conwaylife.com/wiki/Spaceship">spaceship</a>:<br />
<br />
<img alt="An animated image of the spaceship" src="https://i2.wp.com/conwaylife.com/w/images/f/f1/Copperhead.gif" /><br />
<br />
To explain why this is such a groundbreaking discovery, I should first tell you that Life spaceships can be loosely divided into two categories. <i>Engineered</i> ships are the ones that consist of various small components. They often have adjustable <a href="http://conwaylife.com/wiki/Speed">speed</a>. However, the population of <a href="http://conwaylife.com/wiki/Demonoid">tens of thousands</a> to <a href="http://conwaylife.com/wiki/Caterpillar">millions</a> of cells causes these spaceships to have no practical value.<br />
<br />
There is much more incentive in hunting for <i>elementary</i> spaceships, which can be used for complex constructions. They are found using programs such as gfind or WLS. The algorithms behind these programs are beyond the scope of my article, but the important thing is that the search time goes up exponentially as the <a href="http://conwaylife.com/wiki/Period">period</a> of the ship grows. It is most interesting to find spaceships of new speeds, and the number of speeds that low-period ships can have is unfortunately limited:<br />
<br />
<table border="1">
<tbody>
<tr>
<th></th>
<th>Orthogonal</th>
<th>Diagonal</th>
</tr>
<tr>
<th>c/2</th>
<td>Yes</td>
<td>Impossible</td>
</tr>
<tr>
<th>c/3</th>
<td>Yes</td>
<td>Impossible</td>
</tr>
<tr>
<th>c/4</th>
<td>Yes</td>
<td>Yes</td>
</tr>
<tr>
<th>c/5</th>
<td>Yes</td>
<td>Yes</td>
</tr>
<tr>
<th>2c/5</th>
<td>Yes</td>
<td>Impossible</td>
</tr>
<tr>
<th>c/6</th>
<td>Yes</td>
<td>Yes</td>
</tr>
<tr>
<th>c/7</th>
<td>Yes</td>
<td>Yes</td>
</tr>
<tr>
<th>2c/7</th>
<td>Yes</td>
<td>Impossible</td>
</tr>
<tr>
<th>3c/7</th>
<td>No</td>
<td>Impossible</td>
</tr>
<tr>
<th>c/8</th>
<td>No</td>
<td>No</td>
</tr>
<tr>
<th>3c/8</th>
<td>No</td>
<td>Impossible</td>
</tr>
</tbody></table>
<small>This table does not include oblique speeds, which causes little inconvenience because no elementary oblique ships are known.</small><br />
<small><br /></small>
The table above shows that ships exist for most of possible speeds, and it seems obvious that the speeds for which there are no ships have been searched by numerous people with good knowledge of search programs, powerful computers and lots of patience. As for higher periods, even the smallest searches would take years on modern computers. It appears that low-hanging fruit have been harvested clean during the 46 years of Life research… or, more precisely, it <i>appeared</i> so before zdr’s post.<br />
<br />
The idea we all missed is that if the ship is really microscopic, it can be found in reasonable time despite its high period. After zdr boldly went where no man has gone before, Josh Ball set up the <a href="http://conwaylife.com/forums/viewtopic.php?p=28065#p28065">corresponding search</a> in gfind and refound the spaceship in a little over an hour. zdr <a href="http://conwaylife.com/forums/viewtopic.php?p=28078#p28078">said</a> that their program found it in a matter of 19 seconds.<br />
<br />
To be frank, similar event did happen before when the aforementioned Josh Ball <a href="http://conwaylife.com/forums/viewtopic.php?p=7450#p7450">pulled</a> <a href="http://conwaylife.com/wiki/Loafer">loafer</a> <a href="http://pentadecathlon.com/lifeNews/2013/03/c7_orthogonal_spaceship.html">out of a hat</a>. However, zdr’s spaceship (which is now called <a href="http://conwaylife.com/wiki/Copperhead">Copperhead</a>, as <a href="http://conwaylife.com/forums/viewtopic.php?p=27995#p27995">proposed</a> by muzik) is much more awesome for a number of reasons:<br />
<ul>
<li>Loafer is not so mind-bogglingly high-period.</li>
<li>Copperhead was much easier to find, so it is more surprising that nobody found it before.</li>
<li>Copperhead’s tail is relatively strong and can interact with other objects without breaking down.</li>
</ul>
<hr />
The discovery of a new spaceship speed immediately opened a few new areas of research, which are being explored now.<br />
<h3>
Synthesis</h3>
Aidan F. Pierce <a href="http://conwaylife.com/forums/viewtopic.php?p=28033#p28033">came up</a> with a Copperhead <a href="http://conwaylife.com/wiki/Glider_synthesis">synthesis</a> only 10 hours after the completion of the spaceship. The synthesis was inefficient, and a few people discovered better ones. The <a href="http://conwaylife.com/forums/viewtopic.php?p=28085#p28085">current best synthesis</a>, made by Chris Cain, requires only 22 gliders. Its repeat time is 375 ticks, which means that a gun can start constructing the second spaceship 375 ticks after the first one. There is a 23-glider synthesis with a better repeat time of 373 ticks.<br />
<br />
<img alt="Incremental 22-glider synthesis of the copperhead" src="https://niginsblog.files.wordpress.com/2016/03/copperhead-synthesis.png?w=640" /><br />
<br />
The synthesis can be substantially improved if we find this spaceship crawling out of a random soup. Adam P. Goucher has written a wonderful program called <a href="https://catagolue.appspot.com/">apgsearch</a>, which is perfectly suited for this task. While the current version may be too slow to find a soup in reasonable time, highly anticipated version 3.0 can probably do the trick. Once it is found, it will appear <a href="http://catagolue.appspot.com/object/xq10_o5995ozes88sezw33/b3s23">here</a>.<br />
<h3>
Guns</h3>
Once the synthesis was complete, building a gun was nothing but <a href="https://cp4space.wordpress.com/2013/05/15/simultaneous-proofs/">corollary-sniping</a>. The <a href="http://conwaylife.com/forums/viewtopic.php?p=28101#p28101">first copperhead gun</a> was created by myself, and a video of it is available <a href="https://niginsblog.files.wordpress.com/2016/03/gun-1.gif">here</a>. It was put together in a hurry and is therefore extremely inefficient. In particular, skilled gun builders can spot a silly mistake in the Northeast.<br />
<br />
gmc_nxtman then made <a href="http://conwaylife.com/forums/viewtopic.php?p=28176#p28176">another gun</a> with an almost optimal period of 376 ticks.<br />
<h3>
Eaters</h3>
simeks found <a href="http://conwaylife.com/forums/viewtopic.php?p=28124#p28124">two</a> <a href="http://conwaylife.com/forums/viewtopic.php?p=28146#p28146">eaters</a> for this ship, the better of which is shown below:<br />
<br />
<img alt="A copperhead eater" src="https://i2.wp.com/conwaylife.com/w/images/b/b2/Copperhead_eater.gif" /><br />
<br />
It is now time to search for a good copperhead-to-something-useful converter. The <a href="http://conwaylife.com/forums/viewtopic.php?p=28129#p28129">only existing one</a> is clumsy and slow.<br />
<h3>
Sawtooths</h3>
<a href="http://conwaylife.com/wiki/Sawtooth">Sawtooths</a> often work by sending a flotilla of fast ships towards a slower ship. The more is the difference in speed, the less is the expansion factor of a sawtooth. Since expansion factor is proportional to how boring the sawtooth is, increasing the speed difference is a good thing. Dean Hickerson collided c/2 standard spaceships with c/10 copperhead to get a <a href="http://conwaylife.com/forums/viewtopic.php?p=28119#p28119">sawtooth</a> with expansion factor 6:<br />
<br />
<img alt="Hickerson's sawtooth" src="https://niginsblog.files.wordpress.com/2016/03/sawtooth.png?w=640" /><br />
<br />
He then made <a href="http://conwaylife.com/forums/viewtopic.php?p=28214#p28214">another sawtooth</a> with expansion factor 10/3.<br />
<h3>
Puffers and rakes</h3>
Suppose a c/10 flotilla is hit by a glider. The glider turns into loads of mess, but all copperheads somehow survive and move on. The mess releases a glider, which flies into strategically placed second flotilla that is identical to the first one. Gliders continue to bounce back and forth between flotillas leaving mess behind them, and a c/10 puffer is complete!<br />
<br />
Unfortunately, this cool technique doesn’t work out easily in our case. There are no interesting interactions between a glider and a single copperhead, and it is unclear how one can place two or more copperheads so close to each other that a glider interacts with all of them. Assuming we figure it out, we can try to make a rake by perturbing the mess with copperheads so that it evolves into gliders, but that seems even less likely.<br />
<br />
However, all this hand-waving can be turned it real puffers if we find…<br />
<h3>
Tagalongs</h3>
<a href="http://conwaylife.com/wiki/Tagalong">Tagalongs</a> are small things that are attached to the back of a spaceship and move with it. Here is an example tagalong, called the <a href="http://conwaylife.com/wiki/Schick_engine">Schick engine</a>:<br />
<br />
<img alt="Schick engine pulled by two LWSSs" src="https://i2.wp.com/conwaylife.com/w/images/7/7d/Schickengine.gif" /><br />
<br />
Finding a tagalong for the copperhead (or two copperheads) will be really nice. We can also try searching for pushalongs, but they are generally rarer.<br />
<h3>
Other patterns</h3>
There are a few other areas of Life exploration where the copperhead can be useful. For example, <a href="http://conwaylife.com/wiki/Universal_constructor">universal constructors</a> often need to create an elbow still life very far away. It can be done by producing a copperhead, waiting for some time, and then shooting the copperhead down with a LWSS. At the moment I do not see why the copperhead can be better than the loafer in this aspect, but who knows?Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-995028518708963612014-06-17T11:17:00.004-05:002022-04-24T22:30:05.332-05:00New Wrinkles in the Slow-Salvo Construction Game<a href="http://conwaylife.com/wiki/Salvo">Slow-salvo constructions</a> are starting to gain some traction as more uses are found for them. Most recently, <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1388&start=175#p12681">a (6,3) knightship has been built in Conway's Life</a> using a small synchronized glider salvo that activates long chains of half-bakeries, which cooperate to create a slow salvo that then re-creates the synchronized gliders at the correct offset. (See item #17 below.)
<br />
<div style="clear: both;">
</div>
<div class="figure">
<a href="http://conwaylife.com/forums/viewtopic.php?f=9&t=1296&start=100#p12251"><img alt="sample slow salvo" border="0" class="life" height="448" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOYvJC6zDcz4tJev4dqfCa84SdlQiq-CvdUBCyUlp6-Y-yVnpcq8sbG2a2bM2AxppFPGHsvM2Mb5tq3CA5_gPN8CLHvJVbRmzHXoPAj_IbWGT0Mi-AMDWbxVjHopLew7P5vy6ynA/s1600/sample-slow-salvo.png" width="407" /></a><br />
<div style="text-align: left;">
Slow salvo from 31c/240 spaceship project<br />
-- click the image to get the pattern RLE.</div>
</div>
<br />
<br />
<h3>
Quick Review</h3>
<br />
A "slow salvo" is a series of gliders all traveling the same direction. A "slow salvo construction" involves aiming a carefully designed slow salvo at a target object, and incrementally converting that target into some new object using a series of controlled collisions. Such a slow salvo is often described as a "recipe" for the new object.<br />
Some recipes may recreate the original target in a new location. Slow salvos can be proven to be universal, so other recipes might produce output gliders at 90 degrees from the original salvo, or larger spaceships, or any possible glider-constructible object.
<br />
In a slow salvo, arbitrarily long delays can be added between any two gliders. In other words, slow-salvo glider collisions must always settle into stable ash before the next glider arrives. In this context, "stable ash" might mean actual period-1 still lifes, but in "P2 slow salvos", low-period oscillators such as blinkers, beacons, or toads are also allowed as intermediate targets.
<br />
In the P2 case, of course, gliders can only be delayed by an even number of ticks. P3, P4, P5, P6, etc. slow salvos are technically possible, with restrictions analogous to the P2 case, but they don't seem to offer any practical advantages over P2 slow salvos.
<br />
<br />
<h3>
New Developments</h3>
<br />
Here's a list of known uses for slow-salvo technology, in rough chronological order:
<br />
<b>1) Conway's Universality Proof for B3/S23</b><br />
Unidirectional salvos were a significant component of John Conway's proof of construction universality in Life. The original proof was completed shortly after Gosper's glider gun was discovered (in 1970). Only an outline of the proof was ever published, many years later, in Volume 2 of <a href="http://en.wikipedia.org/wiki/Winning_Ways_for_your_Mathematical_Plays">Winning Ways for Your Mathematical Plays (1982)</a>. Part of the idea was to aim one or more "flotillas" -- long series of gliders all traveling in the same direction -- at a faraway simple object, or a faraway opposing flotilla produced by <a href="http://books.google.com/books?id=0FHqbtajb0wC&pg=PA217&lpg=PA217&dq=%22double+side-tracking%22&source=bl&ots=hyQdj14meE&sig=UKK2HvPoBSp4fyajr-yqvX58C1k&hl=en&sa=X&ei=QVCgU7XRCYaYyASDmoCwBA&ved=0CCEQ6AEwAA#v=onepage&q=%22double%20side-tracking%22&f=false">"double side-tracking"</a>. The glider collisions would gradually convert the target object into a complex piece of period-30N circuitry capable of performing calculations... including, eventually, the calculations needed to construct copies of the original flotillas.
<br />
These were unidirectional salvos, but not necessarily slow salvos. Some of Conway's construction recipes required multiple nearby gliders to be precisely synchronized with each other.
<br />
<b>2) Schroeppel's Speculations on Sparse Life Universe Fate</b><br />
By 1992 Rich Schroeppel and others had worked out the likely long-term fate of an infinite Life universe in which each cell had a very low but nonzero probability of being ON initially. After a few ticks, such a universe would consist predominantly of blocks and blinkers, since these only require three initial ON cells near each other to persist. Gliders would be very much rarer since they need five coordinated ON cells to get started -- but whenever a rare one did appear, it would travel until it eventually collided with something.
<br />
A glider hitting a blinker, or a block that has already been struck by another glider, can cause a chain reaction that releases multiple additional gliders. Schroeppel showed that arbitrarily long unidirectional salvos would eventually be created by chains of these kinds of collisions. Any glider could follow any other glider on nearby lanes, with few or no limitations -- except that most sets of closely-spaced gliders were much less likely.
<br />
Following Conway's universal-construction ideas, Schroeppel conjectured that a replicator would eventually appear that consisted of a long unidirectional flotilla of gliders aimed at a single faraway block. Here again this flotilla may have been visualized as containing some synchronized gliders, as long as they could be produced by gliders interacting with common random ash objects.
<br />
However, the key term "slow-unidirectional-salvo" appeared more than once in 1992. Also, Schroeppel's replicator blueprint used gliders of only a single color, analogous to the squares a bishop can reach on a chessboard. It appears that these monochromatic gliders were known or assumed to comprise a universal construction toolkit; this has recently (quite possibly not for the first time) been <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1388&start=25#p12232">proved by construction</a>. The concept of "slow synthesis" was introduced by Alan Wechsler and discussed in depth by Mark Niemiec in 1996.
<br />
<b>3) Nick Gotts and Sparse Life</b><br />
Nick Gotts introduced the term "slow salvo" into more general use in 1997, leaving "unidirectional" unstated (since that's implied by the definition of "salvo" in any case). Building on Schroeppel's earlier investigations, Gotts showed the feasibility of using pure slow salvos to construct arbitrarily complex objects, including rare infinitely growing objects. One early result was a <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1096&p=8145#p8145">53-glider slow-salvo recipe for a block-laying switch engine</a>. The <a href="http://nickgotts.weebly.com/research-interests.html">primary research focus</a> was on the <a href="http://books.google.com/books?id=5iz6C0zzWKcC&pg=PA387&lpg=PA387&dq=Nick+Gotts+life+emergence&source=bl&ots=P0fIVBfFQ7&sig=30m_qOhlz7MRNocLZFdEebpwl3g&hl=en&sa=X&ei=gHigU8jrAZGyyATMiIHICw&ved=0CFMQ6AEwBg#v=onepage&q=Nick%20Gotts%20life%20emergence&f=false">emergence of increasing levels of complexity starting from random initial conditions</a>, as opposed to universal construction or replicator design.
<br />
The appearance of actual construction recipes made it clearer that a complete universal toolkit could be built up from slow salvos alone, aimed at some very simple object -- a block, or pretty much <a href="http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html">any small common ash object</a>. Such objects could be placed at arbitrary distances by various "pusher" reactions, or by collisions between fast and slow glider-constructible spaceships. (Various <a href="http://conwaylife.com/wiki/Cordership">c/12 Corderships</a> were known by 1997.) This avoided a lot of worries about the slow and complicated side-tracking guns that had been part of earlier universality arguments.
<br />
<b>4) The Prototype Universal Constructor</b><br />
In 2004 Paul Chapman built a <a href="http://compgroups.net/comp.theory.cell-automata/a-prototype-programmable-universal/2571875">prototype Conway's Life universal constructor</a>. It was designed to read recipe data from a static tape and convert it into a slow salvo. Theoretically it was capable of being programmed to construct anything glider-constructible, up to and including itself. It did not include any mechanism for duplicating construction data to a new copy of itself, however, so it was not a candidate replicator.
<br />
The prototype was programmed to slow-construct a single eater. A small modification allowed the pattern to loop indefinitely, constructing an oblique line of eaters. But it was apparently too difficult to program -- no other slow-salvo recipes have ever been generated for it in its original form (!).
<br />
<b>5) Spartan Universal Computer-Constructor</b><br />
In 2009 Adam P. Goucher incorporated Chapman's prototype universal constructor into <a href="http://www.conwaylife.com/wiki/Spartan_universal_computer-constructor">a single programmable pattern that was both a universal constructor and a universal computer</a>. Here again, universal construction ability was theoretically provided by a single construction arm... but in practice, the UCC was never programmed to construct even as much as a line of eaters.
<br />
<b>6) O(sqrt(log t)) Diametric Growth Pattern</b><br />
In April 2010, just one month B.G. (Before Gemini), Adam Goucher also completed a pattern that grows at the slowest possible rate for a Conway's Life pattern -- or any other 2D Euclidean CA rule, for that matter. Of course it's possible to slow it down further by adding various delay mechanisms, but the new version would still have an O(sqrt(log t)) growth rate. Anything slower than that is provably impossible. Osqrtlogt.mc can be downloaded from within Golly 2.6 via Help > Online Archives > Very Large Patterns.
<br />
This rather mysterious and under-documented pattern uses two slow salvos, 28 gliders and 10 gliders respectively, to read and write bits in an unbounded triangular grid. Basically it counts in binary, using two-dimensional arrangements of boats on the Life plane separated by 16 full diagonals. The pattern uses copies of various pieces of the prototype constructor. The slow salvos were constructed manually using the <a href="http://b3s23life.blogspot.com/2004/09/glues-slow-salvo-block-move-table.html">original P1 block-move table</a>, so they are very far from optimal! A tighter bit spacing could now be found with many fewer gliders.
<br />
Honeyfarm targets for the salvos are created by a secondary arm that produces single gliders perpendicular to the primary slow-salvo shotgun direction. This initial collision is very similar to the construction method used by the (completely independently designed) Gemini spaceship -- see below.
<br />
<b>7) The Gemini Spaceship</b><br />
In May 2010 <a href="http://conwaylife.com/wiki/Gemini">Andrew Wade's self-constructing Gemini spaceship</a> was published, again based on Chapman's 2004 prototype. The Gemini <a href="http://pentadecathlon.com/lifeNews/2010/05/oblique_life_spaceship_created.html">broke new ground in many areas</a>, including the use of two construction arms firing coordinated 90-degree slow salvos to build Herschel-based signal circuitry. The Gemini's construction gliders are paired so that each glider in one slow salvo is synchronized with a glider in the other salvo. But as usual, successive gliders coming from the same direction don't have to be synchronized with each other -- only with their opposite number in the other salvo.
<br />
In most cases, construction by two perpendicular slow salvos is clearly much more efficient than construction with a single slow salvo. On the other hand, it takes extra circuitry to process the information for two separate slow salvos, and nontrivial signal-crossing problems can also show up in many cases. Single-salvo construction tends to minimize the complexity of the circuitry required for a universal constructor, at the cost of increasing the amount of construction data -- see #22.
<br />
<b>8) Universal Construction with Intermittent P30 Glider Streams</b><br />
Between 2009 and 2011, Frank Hoetmer put together a universal construction toolkit using collisions between slow salvos of *WSSes and gliders. The *WSSes and gliders were produced from 180-degree collisions of long streams of gliders. The two colliding streams were on fixed lanes, and were reflected with p30 technology, so the only variation available was the presence or absence of gliders in each p30 stream. Surprisingly, this <a href="http://conwaylife.com/forums/viewtopic.php?t=631">turns out to be enough to allow construction universality</a>, including the construction of new precisely-timed p30 gun/reflector components far away from the originals.
<br />
Like the Gemini spaceship, this was an independent project that showed up "out of the blue" and broke a lot of new ground. Intermittent P30 construction is impressively difficult -- among other things, very large recipes are needed, and child replicator components have to be constructed in exactly the right phase relative to the parent. As a result, this line of research was not continued once Geminoid technology became available.
<br />
<b>9) Pianola Breeders</b><br />
In 2010, Paul Tooke simplified and extended the Gemini's construction mechanism, producing a number of slow-salvo-constructed patterns with superlinear growth, including a <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=496&start=25#p3380">Gemini-based slide-gun puffer</a> and a series of <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=524">Pianola breeders</a>, which moved the Gemini's two construction arms to a permanent stationary platform, using fourteen glider-loop channels instead of twelve.
<br />
<b>10) Serizawa Geminoids and "Armless" Universal Constructors</b><br />
The extra complexity of multiple-arm circuitry has meant that since the original Gemini appeared, no two-arm constructor designs have been completed using Conway's Life rules. However, <a href="http://conwaylife.com/forums/viewtopic.php?f=11&t=1346">a self-constructing two-armed pattern</a> has recently been completed in Serizawa, another CA rule. Design features from this pattern can be applied to many other rules; among other things, it made possible a <a href="http://www.conwaylife.com/forums/viewtopic.php?f=11&t=1346&start=25#p11720">new "armless" universal constructor design in Conway's Life</a> that set new records for small size and population.
<br />
<b>11) Linear Replicators in Conway's Life</b><br />
The <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&start=125#p9901">linear Life replicator</a>, or "GoL propagator", demonstrated the universality of single-arm construction -- a single slow salvo aimed at simple targets can build anything that two arms can build. It is conjectured that either one or two slow construction arms can build anything that can be constructed with any number of colliding gliders (and/or spaceships). A proof is now <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1512&p=15224#p15208">within easy reach</a>.
<br />
<b>12) Freeze-Dried Seeds for Slow Salvos</b><br />
With linear-replicator technology as a model, <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&start=50#p9358">"freeze-dried" slow salvos</a> -- a variant of Nick Gotts' chain reactions, but with the seed still lifes deliberately built by a universal constructor -- can be designed that allow the construction of spaceships with very small step sizes, such as (1,0) or (1,1) -- or (2,1), a true (very slow) knightship. As of January 2017 no explicit example has been completed.
<br />
<b>13) Spiral Growth</b><br />
A <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1260#p12815">spiral-growth pattern</a> was constructed using four copies of a single-arm universal constructor. More recently, a <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1260#p44019">spiral-growth pattern smaller by a factor of 100</a> was completed, followed by <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1260#p44792">one that's 5000 times smaller than that</a>. The last pattern in the series uses an inline, 0-degree "Snarkmaker" recipe to build small lossless elbows using single-channel technology. See #23 below.
<br />
<b>14) Slow-Salvo Construction of Loafers</b><br />
In September 2013 <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1031&start=50#p9034">universal-constructor based loafer seed factory</a> was constructed, using an early version of the two-channel Demonoid (#22 below) construction arm design. This was along the same lines as Paul Tooke's Pianola breeders (#9), which were adapted from the Gemini's twelve channels.
<br />
<b>15) 31c/240 Spaceships</b><br />
In 2013 a <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1274">new reburnable fuse</a> was discovered that produced two gliders every 240 ticks, while the reaction moved forward 31 cells and the fuse moved forward 9 cells. 9 and 31 are relatively prime, and it turned out that the fuse could be modified in various ways to produce any possible slow salvo.
<br />
A <a href="http://www.conwaylife.com/forums/viewtopic.php?f=9&t=1296">new search utility</a> has been written to locate the most efficient recipes for lightweight, middleweight and heavyweight spaceships, which can move fast enough to overtake the front of the fuse and close the loop by building more blocks to support the 31c/240 "Herschel climber" reaction -- very much along the same lines as the <a href="http://www.conwaylife.com/wiki/Caterpillar">original Caterpillar spaceship</a>, but with a <a href="http://conwaylife.com/wiki/Centipede">new mechanism and new speed</a>.
<br />
<b>16) Caterpillar's Smaller Siblings</b><br />
It appears that the original Caterpillar <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1258">can now be made significantly smaller</a> using slow-salvo technology. For example, the Caterpillar builds a large number of HWSSes that travel forward to build new blinker trails ahead of its 17c/45 pi climbers. Each HWSS recipe requires a rake about 8000 cells high, made up of two separate sets of forerakes and backrakes running on blinker trails. The rakes' gliders collide a long distance from the trails, forming the large oblique triangles that make up most of the Caterpillar's body.
<br />
Spaceship constructions that are done entirely with a slow salvo seem likely to need rakes that are only a few hundred cells high instead of several thousand, and that can be packed very closely one after another. Even when the construction site is 1500 cells from the rakes, with a slow salvo there's no need to wait thousands of ticks between rakes to allow perpendicular glider streams to converge.
<br />
<b>17) Half-Baked Knightships</b><br />
Slow-salvo technology has now been used to construct <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1388&start=175#p12681">a (6,3) knightship</a> based on interactions between chains of <a href="http://conwaylife.com/wiki/Half_bakery">half-bakery reactions</a>. The new feature of this design is that slow-salvo gliders are generated on only one color -- every other lane -- of the Life grid. As mentioned in #2 above, this is not a new idea, but the half-baked knightships are the first completed patterns to use this type of slow salvo for actual constructions.
<br />
<b>18) Parallel HBK gun</b><br />
A gun was created for the parallel version of the half-baked knightship. To date (July 2017) this gun is the only other use of the original Gemini spaceship's slow-glider-pair construction technique, besides Paul Tooke's Pianola breeders and (in a very limited sense) Adam P. Goucher's O(sqrt(log t)) pattern.
<br />
<b>19) High-period 2c/7 "distaff" rake</b><br />
In May 2014, building on <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1259#p10169">2c/7 puffer results from the previous December</a>, Ivan Fomichev used a long chain of weekender conduits to generate gliders for a <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1259#p12047">modified slow-salvo construction of a single LWSS</a> ("modified" because it starts from two targets produced by glider-weekender collisions). The LWSS is then sent forward to the beginning of the chain to close the cycle and produce an adjustable high-period rake.
<br />
<b>20) 'Engineless Caterpillar' (Caterloopillar) project</b><br />
Starting in September 2014, Hartmut Holzwart proposed a slow-salvo-based version of <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1448#p13186">David Bell's idea for an "engineless Caterpillar"</a>, from a decade ago. Michael Simkin has since <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1448&start=125#p20726">worked out the necessary mechanisms</a> for an adjustable "strange-loop" Caterpillar-like spaceship. an adjustable-period Caterpillar design that doesn't need a period-specific "climber" reaction. Instead, streams of gliders are generated by repeatable interactions between stable objects and backward-traveling fleets of passing *WSSes. These streams of gliders can be used to perform <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1448#p14194">slow-salvo constructions</a> of fleets of spaceships traveling the opposite direction, which collide with other still lifes at the front to build more backward-traveling fleets, thus closing the cycle. To allow the period to be as adjustable as possible, only P1 slow-salvo recipes can be used. If a blinker, toad or other P2 object were allowed as an intermediate target, the adjustability would be limited to either odd periods or even periods.
<br />
The <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=2151">current model</a><a href="https://www.blogger.com/null"> can be fairly easily recalibrated to move at any sufficiently slow speed. For example, it can move at c/10, c/11, c/12, or any slower c/{integer}. The price of this adjustability is that only stable intermediate targets can be used; otherwise, very different construction recipes would be needed for even periods vs. odd periods. Slow construction of edge-shooter spaceship seeds, or any other stable seed object, appears to still be perfectly possible with this restriction. In fact, some </a><a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1448&start=100#p20569">preliminary searches</a> seemed to show that P1 slow monochromatic gliders (all gliders the same color) would be sufficient, so an engineless caterpillar with an even step length would be technically possible -- e.g., moving 38 instead of 59 cells with each cycle. However, such a spaceship would be considerably longer due to less efficient slow salvo recipes.
<br />
<b>21) (23,5)c/79 Caterpillar</b><br />
Also starting in September 2014, building on <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1142#p8458">discussion from the previous year</a>, Brett Berger ('biggiemac' on the forums) <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1142&start=50#p13311">steadily generated mechanisms and techniques</a> for constructing the first oblique caterpillar knightship, based on a known (23,5)c/79 Herschel reaction. The spaceship was completed on December 28th of the same year. Constructions are a mix of slow-salvo transformations and synchronized collisions.
<br />
Unlike the engineless Caterpillar which is designed so that the period can be either odd or even, this spaceship's rate of travel is fixed and slow salvo gliders will always be the same distance apart. This means that p2 intermediate targets can be used. For example, there's a line of traffic lights near the top of the triangle in the current front-end design; every other traffic light is in a different phase, but the glider that collides with it is always in the correct phase to convert the traffic light to a beehive to support the oncoming Herschel climber.
<br />
<b>22) Demonoid (diagonal Geminoid) spaceships</b><br />
Starting in late 2012, a number of designs were proposed for a self-constructing Geminoid variant where the two halves of the spaceship would be glide-reflected mirror images of each other, instead of exact copies. This would limit the travel direction to an exact diagonal, but would cut the amount of circuitry roughly in half (because it would no longer be necessary to support input from two different directions).
<br />
Over the next three years, the amount of required circuitry was gradually decreased until a <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1469&p=25716#p25702">complete Demonoid</a> needed only 48 still lifes to be built with a slow salvo, including all the self-destruct circuitry to clean up after each construction arm when its work is done.
<br />
As usual, this self-constructing spaceship has a trivial glider synthesis -- so trivial that for the first time in Life history, a gun for the 0hd Demonoid was built before the spaceship existed, and the very first 0hd Demonoid was fired by the gun.
<br />
In June 2017, a Demonoid using a single-channel recipe (see below) was constructed with only 19 still lifes per construction arm, and even more compact Demonoids were shown to be possible.
<br />
<b>23) Single-channel construction arms</b>
Research by Simon Ekström in <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1701&p=26063#p26024">December 2015</a> proved that a universal construction arm was possible with a stream of gliders on just a single lane, with gliders separated by at least 90 ticks. Unlike in the 0hd Demonoid where gliders could follow each other as closely as 15 ticks apart on the construction lane, a single-channel recipe can be safely reflected by a <a href="http://conwaylife.com/wiki/Snark">Snark</a> reflector, or even a <a href="http://conwaylife.com/wiki/Syringe">syringe</a> followed by signal-splitting Herschel circuitry.
<br />
This was a really radical simplification. Any spare glider output in any Herschel circuit with 90-tick recovery time could now be set up to function as a construction arm, with the addition of a single block anywhere along the output lane.
<br />
<b>24) Pan-directional construction elbows</b>
An idea that began its development in the 10hd and 0hd Demonoids has been almost fully realized in recent single-channel libraries of elbow operations: recipes are now known that can send a glider or spaceship directly from the construction elbow in any of eight directions. The first use was in a <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=2660&p=44384#p44377">Snark-chain-constructing triple wickstretcher</a>.
Two of these directions are used in the <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1469&start=200#p45264">single-channel Demonoid</a>. First, as in the wickstretcher, 0-degree gliders are send ahead of the construction elbow to build a Snark reflector exactly on the construction lane, as a lossless elbow. This allows the construction arm to reach around two corners instead of one, to build the next copy of the constructor/reflector. Second, backward LWSSes and MWSSes are fired from the same construction arm after the temporary Snark is removed, to destroy the previous constructor/reflector and complete the spaceship.
<br />
<b>25) Orthogonoid spaceship</b><br />
In June 2017 the first self-constructing spaceship with a slow orthogonal direction of travel was completed, using streams of MWSSes to store construction data instead of streams of gliders. It makes use of a temporary lossless elbow in its construction arm. Removing the Snark elbow allows the construction arm to function inexpensively as a destruction arm, at 90 degrees from its original direction of operation.
<br />
<b>26) Hydra</b><br />
In November 2017, Oscar Cunningham completed (+/-2sL) a single-channel self-constructing pattern called <a href="http://www.conwaylife.com/forums/viewtopic.php?f=2&t=3124#p53089">"Hydra"</a>, due to its ability to grow new "heads" at the corners of an expanding spiral pattern. Hydra is fairly similar to the 2017 spiral-growth pattern, but instead of adding an inline lossless elbow (a Snark) at every construction cycle, the Hydra adds a lossless glider splitter at the end of every active signal branch, creating more and more signal branches over time.
<br />
<b>27) Quadratic-Growth Replicator</b><br />
Adam Goucher's 0E0P metacell achieves quadratic growth as a by-product of its metacell functionality, by emulating an appropriate Life-like cellular automaton. The "ground state" for this very large unit cell is empty space, meaning that each set of megacells must create new neighboring copies of their entire structure and construction-recipe data, at every location where a birth is required. As a result, the 0E0P metacell is one of the largest Conway's Life structures ever assembled, and even though it was designed to be as "HashLife-friendly" as possible, Golly is not currently capable of simulating it through a complete cycle in any reasonable amount of time.
<br />
<b>28) Strict Volatility-1 Oscillator</b><br />
Self-constructing (and -destructing) mechanisms can easily produce an oscillator of any sufficiently high period, where every cell turns OFF at some time during the cycle. A <a href="http://www.conwaylife.com/forums/viewtopic.php?p=65835#p65835">first attempt</a> to build one of these used <a href="http://conwaylife.com/wiki/Freeze-dried">freeze-dried</a> slow salvos to shoot down and then rebuild reflector/constructors at each of four corners of a large diamond. Each freeze-dried salvo seed is activated by a single glider, to produce the entire destruction salvo, followed by the reconstruction salvo.
<br />
<b>29) Self-Constructing Camelship</b><br />
Chris Cain built a <a href="http://conwaylife.com/wiki/Camelship">(3,1) camelship</a> using as a template a later version of the volatility-1 oscillator (without the freeze-dried slow salvos).
<br />
<b>30)Loopship</b></br />
The <a href="http://www.conwaylife.com/forums/viewtopic.php?p=65214#p65214">loopship</a> is the first self-constructing spaceship that contains a construction recipe to build a memory loop big enough to hold that same construction recipe. The Geminis, Demonoids, or Orthogonoids all just reflect a recipe back and forth between two universal constructors. Here the idea is to "catch and release" the recipe instead. The loopship cheats a little bit by re-using some of the corner circuitry for multiple glide-reflected copies of the memory loop. A recipe capable of building a memory loop for itself in empty space, with no glide-reflect tricks or scaffolding, will be needed to complete a simpler quadratic-growth replicator (see below), self-synthesizing spaceship, RRO, or other similar structures.
<br />
<b>31)Remini</b><br />
The "Remini", or "retro Gemini", is an <a href="http://www.conwaylife.com/forums/viewtopic.php?p=74984#p74984">experimental self-constructing puffer</a> assembled by Michael Simkin in April 2019. It uses the same single-channel/slow-salvo construction mechanism as the 0E0P metacell (see above), but it is built from classic period-30 circuitry instead of stable Spartan circuits. The presence or absence of gliders in an intermittent p30 stream turns out to be enough to allow for universal control of a construction-arm elbow. The Remini is an implementation of modern single-channel construction methods using components available in the 1970s.
<br />
<b>32)Oblique Loopship and RRO</b><br />
Constructed by Goldtiger997 -- Pattern of the Year for 2021.
<br />
<b>33)Smaller Faster Quadratic Growth</b><br />
Pavel Grankovskiy used single-channel construction arms to build a <a href="https://conwaylife.com/forums/viewtopic.php?f=2&t=5480">quadratic-growth replicator</a> in Conway's Life, small and simple enough (at least relative to the 0E0P metacell!) that Golly can successfully run it through multiple cycles.
<br />
<b>34) QuickSilver Demonoid</b><br />
To be continued --
Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com1tag:blogger.com,1999:blog-8285929.post-42143943866742457122013-11-26T13:01:00.000-05:002013-11-26T13:12:31.147-05:00New Technology from the Replicator Project<p>Now that the <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&start=125#p9901">Conway's Life replicator pattern</a> is in working order, what might the next step be?
</p><p>
The phase-shifted linear replicator isn't really a very satisfactory design. Each parent pattern can produce only one child pattern, which then blocks it from any further replication. It seems as if a quadratic-growth, space-filling replicator would be much more in keeping with von Neumann's (and Conway's) original purpose.
</p><p>
One major limitation of essentially linear designs like the Gemini spaceship and Geminoid replicator is that replication and movement perpendicular to the long stream of gliders is fairly easy, but it's very hard to make a new copy in the other direction -- just because it means constructing the far end of the new copy millions of cells away.
</p><p>
It's certainly not impossible to reach that far out into empty space with a constructor arm, but it's bound to be very slow -- either in terms of the absolute number of ticks, or in the amount of time that it takes to simulate a construction cycle. Even Golly's Hashlife algorithm has difficulty with very long streams of information-carrying gliders traveling next to each other in opposite directions -- the number of combinations goes up exponentially, and beyond a certain point no reasonable amount of memory can hold all the different hashtiles.
</p><p>
<div class="separator" style="clear: both; text-align: left;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-xvCK2GwqMjTED-ZXbhknzuH12jgrqLXs1TKERFrRSf96aryp9eaCLI7MmA8chtbneU5aX1GgKFoDeLSyuH2DnMKY-C7xpnVXlVdpm2LeZq-7MHO3J_91EL4toO34SPUs2nDhww/s1600/Quadratic-replicator-diagram.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg-xvCK2GwqMjTED-ZXbhknzuH12jgrqLXs1TKERFrRSf96aryp9eaCLI7MmA8chtbneU5aX1GgKFoDeLSyuH2DnMKY-C7xpnVXlVdpm2LeZq-7MHO3J_91EL4toO34SPUs2nDhww/s1600/Quadratic-replicator-diagram.png" /></a>Luckily it may be possible to solve both of these problems at once with a diamond-shaped replicator. The memory loop would travel around the outside of a hollow square.
</p><p>
Hand blocks (or elbow blocks, if the UCs at the corners have two arms) can be trivially constructed in the correct starting locations by colliding LWSSes from one corner with gliders from an adjacent corner; glider pairs or slow salvos following the first glider will immediately have a target to work with.
</p><p>
To give Hashlife as much help as possible, it will make sense to adjust the reflection timings at the four corners so that the memory loop takes 2^N ticks per cycle; the spatial periodicity should also be a power of two.
</p><p>
The result will be a space-filling Life replicator with the same quadratic growth rate as Langton's Loops. It will be interesting to see how much memory will be needed to allow Golly to "run away" with the replicator simulation.
</p><p>
In the diagram at right, blue diamonds represent glider memory loops containing construction information. (A closed loop may not actually be needed, but that's another story.) Green objects are universal constructors and reflectors. The yellow arrows are eater groups that can absorb child replicators' attempts to build on top of a quiescent parent replicator. The white lines show the paths of starter LWSSes and construction gliders. The red numbers show replicators' generation number.</p></div>
<p style="clear:both"><b>The New Technology</b></p>
A number of the new construction and destruction mechanisms from the Geminoid project may be useful here:</p>
<ul>
<li><a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&p=8593#p8593">Ambidextrous glider-pair construction arms</a>, with lanes separated by either 9hd or 10hd;</li>
<li><a href="http://conwaylife.com/forums/viewtopic.php?f=7&t=1072#p8154">Construction arms with multiple elbows</a>, for building around awkward corners;</li>
<li><a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&start=50#p9358">"Freeze-dried" construction salvos</a> and <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&start=100#p9720">seeds</a>, when objects must be built within a short time window;</li>
<li><a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006&start=50#p9121">Self-destruct circuits</a>, to clean up temporary objects in a similarly short window.</li>
</ul>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com2tag:blogger.com,1999:blog-8285929.post-85081939917729648072013-01-12T00:59:00.000-05:002013-01-15T10:31:51.704-05:00Replicator Redux<h3>The Story So Far</h3>
<p>Self-replication in Conway's Life has been a topic for discussion and research from the very beginning, over forty years ago now (!). The <a href="http://en.wikipedia.org/wiki/Conway's_Game_of_Life#Origins">original purpose of Conway's Life</a> was to find a simplification of John von Neumann's self-replicating machine designs, which used a CA rule with 29 states. A couple of non-constructive universality proofs for B3/S23 Life were completed very early on, though they were never published in detail -- and my sense is that actual self-replicating patterns along the lines of these proofs would require something on the order of a planet-sized computer and a geological epoch or two to simulate a replication cycle.
</p><p>
The technology to build a Conway's Life replicator out of stable parts has been available since at least 2004. A working pattern could certainly have been put together in a few years by a full-time Herschel plumber, with a high-energy glider physicist or two as consultants. But unfortunately there seem to be very few multi-year grants available for large-scale CA pattern-building -- even for such obviously worthwhile Holy-Grail quests as this one!
</p><p>
In 2009, Adam P. Goucher put together a working <a href="http://pentadecathlon.com/lifeNews/2009/08/post.html">universal computer-constructor</a> that <i>could</i> be programmed to make a complete copy of itself. The pattern, however, is so huge and slow that it would have taken an enormous amount of work to program it to self-replicate -- it would have been easier to come up with a new replicator design from scratch. Clearly, in hindsight, everyone was waiting for something better to come along.
</p><h3>Lightning Strikes</h3><p>
In 2010, something better did come along: Andrew Wade's <a href="http://conwaylife.com/wiki/Gemini">Gemini spaceship</a> magically appeared on the scene, and things suddenly got much easier for would-be replicator designers. Self-constructing circuitry was no longer just a theoretical possibility but an accomplished fact -- and the Gemini made it look downright easy. Not that it <u>was</u> easy: Andrew Wade solved an impressive array of signal-crossing, synchronization and construction problems to make the Gemini fly.
</p><p>
The key insight was that it's much more efficient to store information about glider constructions directly in the distances between gliders. Previous efforts had tried to reduce complexity by relying on a limited instruction set of operations to operate a construction arm. Working examples can be found in Golly's Patterns/Life/Signal-Circuitry/constructor patterns.
</p><p>
But in these old prototypes, a lot of circuitry was needed to convert the coded instructions into the glider salvos that manipulate the construction elbow -- so the total size of self-constructing circuitry plus construction data was still very large. To build the Gemini, Wade borrowed the old construction arm with very few alterations, but took the radical step of simply throwing away most of the decoding circuitry (!).
</p><p>
Instead, he ran the Gemini's construction elbows directly with streams of gliders: if a glider was needed on lane L at time T, then there would be a glider in the Lane L data stream timed to produce a copy at the right spacetime location -- automatically, with no extra synchronization circuitry needed.
</p><p>
... It's actually a <u>little</u> more complicated than that -- most of the guns at the prototype construction-arm "shoulder" produce not single gliders but pairs of synchronized gliders. Sometimes two of these salvo shotguns combine to put gliders close behind each other on the same lane. This would not be possible if the Gemini had a separate channel for each glider lane, and the reflector arrays would have had to be even longer -- eighteen channels instead of twelve.
</p><p>
Still, the basic idea was there. The Gemini showed how to store precise timings for glider collisions on a linear data tape, and transfer that information efficiently to the construction area.
</p><h3>Limitations and Possibilities</h3><p>
However, a Gemini spaceship is <u>not</u> a replicator, any more than a glider or other small spaceship is! A replicator is a pattern that makes copies of itself: the total number of copies of the pattern has to increase over time. If a pattern is "used up" in some way by the copying process, and is not capable of completing another cycle of replication after the first, then to be a true replicator it would have to produce two or more children simultaneously. Otherwise the pattern falls into some other category.
</p><p>
Because there is only ever one primary copy of the glider streams that carry the construction data, a pair of Gemini replicator units can be programmed to produce an extremely slow puffer or a self-constructing spaceship, but can't make a complete copy of the entire Gemini pattern. Some new circuitry will have to be added to make a Geminoid design into a true replicator.
</p><p>
The twelve parallel channels and many signal crossings in the original Gemini spaceship would have made rewiring it into a replicator fairly difficult. New Geminoids have only a single channel and no signal crossings. It should be relatively trivial to duplicate the construction recipe into a new copy of the pattern, and also keep the old copy if necessary, to make a true replicator rather than a self-constructing spaceship.
</p><h3>What Counts As A Replicator, Anyway?</h3><p>
There are several possible types of Geminoid replicator. One of the easiest would be a one-dimensional <a href="http://www.ics.uci.edu/~eppstein/ca/replicators/">parity-rule replicator</a>. This is by far the most common type of natural replicator in Lifelike rules, and can be adapted to a Geminoid design by building in a self-destruct mechanism that is triggered by the presence of a neighbor pattern.
</p><p>
The only unsatisfactory thing about parity-rule replicators is their sawtooth growth pattern: eventually the population will exceed any given N, but it will also periodically return to a small constant value -- often just two replicators, or four. This doesn't quite match the standard vision of a replicator that copies itself relentlessly and eventually fills all available space, with a steadily growing population.
</p><p>
Another fairly straightforward category is a simple one-dimensional linear growth replicator. Each parent replicator will produce exactly one child pattern, which will then block the parent from making further copies of itself while constructing the next replicator in a growing line. If the parent pattern repeatedly returns to its initial state -- so it's still perfectly capable of making another copy of itself if its child pattern is removed -- it fits the technical definition of a replicator. This is a good design to start with, not least because no self-destruct circuitry is needed!
</p><p>
In the longer term it should be possible to design a Geminoid-based replicator with some form of exponential population growth in a two-dimensional pattern, similar for example to <a href="http://en.wikipedia.org/wiki/Langton's_loops">Langton's Loops</a>. This will have to be a much larger pattern, however. Gemini-like long narrow designs, with replication going on simultaneously at both ends, doesn't allow for easy construction of right-angle copies. A diamond-shaped version, with many back-and-forth reflections of the data tape, will probably be needed instead. So this is something to work up to gradually!
</p><h3>Radical Reductions, Continued</h3><p>
In the summer of 2010, with the Gemini for inspiration, Paul Chapman wrote a search utility to find a simpler set of elbow instructions -- the Gemini's minimal elbow-move instruction set involved salvos of three or four gliders on six possible lanes, performing just four operations -- INC, DEC, BLACK, and WHITE (the last two refer to the color of the emitted construction glider). Reducing the number of lanes cuts down enormously on the amount of synchronization circuitry. There turned out to be a wealth of possibilities using sets of three gliders on three glider lanes, and plenty of options to choose from even with just a pair of synchronized gliders on two lanes.
</p><p>
<a href="http://b3s23life.blogspot.com/2010/12/geminoid-research.html">My last post on this weblog</a> describes some Geminoid designs that are much more compact than the original Gemini spaceship. Below is a variant with a single construction arm, and no self-destruct circuitry: it's perfectly possible to do all the cleanup with "software" -- more gliders in the same input channel, after the construction of the new replicator unit is all finished, which bend the Geminoid's single arm in the other direction to clean up the previous replicator unit.
</p><p>
It's even possible to program the constructor arm to build a constellation that can be triggered by a single glider to generate a huge cleanup "meteor shower". So the very last input to a replicator unit would generate a signal that would destroy that same replicator unit, completely and immediately. (In the current design, the Gemini's destructor arm cleans up an old empty replicator unit left over from the previous construction cycle.)
</p>
<p style="clear: both"><div class="figure"><a href="http://cranemtn.com/life/weblog/2013-01-11-prototype-Geminoid.rle"><img border="0" height="231" width="400" class="life" alt="two prototype Geminoid replicator units" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlMSHukg-0XZQmg3X1Zvm57T83bqnzLUarkQHOVIk2Ro6WrOhJgdQMzlL6kiYWrJiPWMp8PFdZs82s_aHLxEU-GXxnssiK8fYXITUdToUfZKVEcXahh7kW0_Qe6XPunkrz1WswrA/s400/prototype-Geminoid.png" /></a><br /><div style="text-align: left">two copies of a prototype Geminoid replicator unit --<br>
normally these would be separated by a long distance diagonally.<br>
Click on the image to get the pattern file; <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlMSHukg-0XZQmg3X1Zvm57T83bqnzLUarkQHOVIk2Ro6WrOhJgdQMzlL6kiYWrJiPWMp8PFdZs82s_aHLxEU-GXxnssiK8fYXITUdToUfZKVEcXahh7kW0_Qe6XPunkrz1WswrA/s1600/prototype-Geminoid.png">larger image here</a>.</div></div>
</p><p>
I've posted some of these prototypes on a <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006">"Geminoid Challenge"</a> thread in the conwaylife.com forums, and am slowly working on more efficient variants.
</p><p>
The other half of this project involves finding more efficient ways to construct Geminoid circuitry using just a single construction arm. An arm run by glider pairs turns out to be much more versatile than the old prototype four-instruction arm. Not only are there <a href="http://conwaylife.com/forums/viewtopic.php?f=2&t=1006#p7340">many more INC and DEC operators</a> available, but it's also possible to find efficient recipes for a number of other useful actions: turn one elbow into two, use the second elbow for a while and then delete it, create debris off to the side of an elbow to make one or more new "hand" target blocks, build an LWSS directly or indirectly and then collide it with a glider to produce a new hand a long distance away -- and so on. I'll be posting samples of these new "elbow recipes" in the Geminoid Challenge thread.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com1tag:blogger.com,1999:blog-8285929.post-15533477897196528672012-11-03T18:50:00.004-05:002012-11-03T18:52:10.948-05:00ResurrectionI don't believe that there has yet been an official announcement (except for a <a href="http://cp4space.wordpress.com/2012/10/31/happy-halloween/">minor footnote</a>) that the entire pentadecathlon.com site is now irrevocably defunct. As such, Dave Greene suggested that we relocate LifeNews by merging it with <a href="http://b3s23life.blogspot.co.uk/">Conway's Life: Work in Progress</a>. There is going to be a programme of archiving the old LifeNews entries and making them available somewhere on the Internet.<br />
<br />
Until then, the LifeNews triumvirate humbly apologises for any inconvenience.Adam P. Goucherhttp://www.blogger.com/profile/17687726899833607532noreply@blogger.com3tag:blogger.com,1999:blog-8285929.post-3519059149007657242010-12-21T21:16:00.006-05:002012-10-18T09:23:16.016-05:00Geminoid Research<div class="separator" style="clear: both; text-align: center;"><a height="750" href="http://cranemtn.com/life/files/Geminoid-knightship-diagram.PNG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;" width="850"><img border="1" src="http://cranemtn.com/life/files/Geminoid-replicator-unit.PNG" /></a></div><br />
Since <a href="http://www.conwaylife.com/wiki/index.php?title=Andrew_J._Wade">Andrew Wade</a> built his amazing <a href="http://www.conwaylife.com/wiki/index.php?title=Gemini">Gemini spaceship</a> out of miscellaneous scraps from the Conway's Life junkyard (a feat somewhat equivalent to assembling a jet airplane out of Model T parts) I've been looking at possible ways to simplify the design. With a lot of help from Paul Chapman this summer, I think I'm finally making some progress.<br />
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Here's a diagram of a possible <a href="http://cranemtn.com/life/files/Geminoid-with-660-tick-cycles.rle">Geminoid replicator unit</a>. The original Gemini's base units are about 3750x4700, with about 16,000 live cells. This version fits into 580x540, with less than two thousand ON cells. In place of the Gemini spaceship's twelve input channels, there is now just a single stream of gliders. Four channels are encoded in the stream, two channels for each construction arm. Click on the image to the right to see how multiple copies of this unit will fit together.<br />
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There is no destruction arm in this design, and that's definitely its biggest weakness; I have quite a bit of programming left to do to produce a search utility that can "seed" the empty spaces between the signal channels with still lifes that will cause a chain reaction that destroys the entire replicator unit. The reaction will be triggered by a single glider coming from the construction site at the intersection of the two arms. It's easy enough to come up with a collection of still lifes that will do this; the trick is to find a set that's reasonably close to minimal. My current goal is to find SODs (Seeds Of Destruction) that no more than double the original population.<br />
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The other item that needs special explanation is the encoding of four channels into one, and the special limitations placed on the construction-arm salvos by that architecture.<br />
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The original Gemini had twelve parallel channels corresponding to the four glider lanes that were used to construct the various salvo combinations that acted on the elbow to produce INC and DEC movements and fire EVEN and ODD gliders. The four-glider-lane shoulder architecture was taken from Paul Chapman's prototype universal constructor -- but the prototype was "the first thing that worked" and pretty far from optimal.<br />
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It turns out to be very easy to find sets of three lanes where combination salvos (one or more sets of one, two, or three synchronized gliders) will produce all the necessary INC/DEC/ODD/EVEN operations. Once you allow multiple "cycles" -- two or three sets of synchronized gliders, not just one set -- it's even possible to cut the number of lanes down to two, or even <a href="http://cranemtn.com/life/files/RLE-1-lane.txt">just one</a> (!) These construction-elbow manipulation salvos are all the work of Paul Chapman and a custom search utility he wrote in the summer of 2010.<br />
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It seems amazing that there's a universal set of operations at all using a single glider lane. But with <a href="http://cranemtn.com/life/files/Geminoid-1lane-operations.rle">pairs of synchronized gliders on a the same lane</a> there are dozens of operations available. Many of them need five cycles instead of three or four, but considering the minimal highway width that's not much of a handicap.<br />
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The <a href="http://cranemtn.com/life/files/Geminoid-9fd-operations.rle">lane set I chose</a> for a redesigned Geminoid spaceship -- pairs of gliders on lanes -5 and 4, separated by 9 cells -- has the advantage of being completely symmetrical, meaning that LEFT and RIGHT gliders can be fired equally well just by using a mirror-image salvo. This will come in handy when it's time to trigger the destruction of the old copy of the Geminoid... Also, glider inserters are available that leave the lane nine cells away completely unaffected when placing a glider, so all possible glider sets are trivially constructible.<br />
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Run the pattern in the "<a href="http://cranemtn.com/life/files/Geminoid-with-660-tick-cycles.rle">Geminoid replicator unit</a>" link, and advance or delay some of the gliders in the first cycle (set of four). The corresponding output gliders will be advanced or delayed by the same amount with no ill effects -- unless the distance between any two adjacent gliders drops below 497 ticks.<br />
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The unusual feature of this operation set is that gliders are <i>required</i> on both lanes for each cycle of each operation. The single channel is decoded into four channels with a simple set of parallel period quadruplers, which allows the decoder to be completely asynchronous -- but it means that leaving out a glider would have disastrous consequences for the decoding process. Thus there will have to be extensive use of NOP operations (in this case, four pairs of gliders that have no net effect on the construction-arm elbow). It's also quite likely that all the operations the Geminoid uses will be exactly four cycles in length, but this isn't quite necessary for all cases.Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-50078026281945366772009-02-07T07:06:00.004-05:002009-02-07T09:39:43.184-05:00First complete glider-to-Cordership converter<p>For years now I've been fruitlessly plotting to put together a Herschel layout utility for <a href="http://golly.sourceforge.net">Golly</a>, to help design multi-glider shotguns and other large-scale Herschel signal circuitry. One of my first uses for the utility will be to design a (relatively) compact Cordership gun that can be triggered by a single input glider.</p><br /><p style="clear:both;">It seems Calcyman has finally gotten tired of waiting for this wondrous device to appear, so he has built one himself: the world's very first complete <a href="http://cranemtn.com/life/weblog/H-to-C.rle">glider-to-Cordership converter</a>! (The link goes to the RLE pattern file; here's the <a href="http://cranemtn.com/life/weblog/H-to-C.mcl">MCell version</a>.)<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJRW1Ucyg0aME2A2cQquk6dkDpDjcp3ZKUgLsKdRjaqe1rQtv9pCohYBkXmBGUwAr-vygNq1OQUvpX6RySE4AQaZQ_KcP2mPX94VuB7u0jd2xVuUGADHVKkroUST84Y0p8V_sW9A/s1600-h/H-to-C.PNG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 389px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgJRW1Ucyg0aME2A2cQquk6dkDpDjcp3ZKUgLsKdRjaqe1rQtv9pCohYBkXmBGUwAr-vygNq1OQUvpX6RySE4AQaZQ_KcP2mPX94VuB7u0jd2xVuUGADHVKkroUST84Y0p8V_sW9A/s400/H-to-C.PNG" border="0" alt=""id="BLOGGER_PHOTO_ID_5300047579364082498" /></a><br /><p>Input gliders at the lower left are converted into clean 3-engine Paul Tooke Corderships in 13,311 ticks -- as long as no two gliders are closer together than 708 ticks. The signal is split into three main parts. The one in the center triggers an improved Herschel-to-swimmer converter using a new 5-glider recipe (see <a href="http://b3s23life.blogspot.com/2007/06/new-kind-of-signal-though-not-useful.html">my last post</a> for the old 6-glider solution.)</p><br /><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEIaxoNVNC2Kee93DtpTtRp5Kd88ljPEf5z4ydmc57TAJN2XG_z8p29wAr4HnEv9m5feHGCXy4e2XP5LxSd_VFzPV5KNTbFXj1pF5-oF7UePatws_Njv3Q0592IENvqc5KwdAb5w/s1600-h/H-to-S-5G.PNG"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;width: 386px; height: 400px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiEIaxoNVNC2Kee93DtpTtRp5Kd88ljPEf5z4ydmc57TAJN2XG_z8p29wAr4HnEv9m5feHGCXy4e2XP5LxSd_VFzPV5KNTbFXj1pF5-oF7UePatws_Njv3Q0592IENvqc5KwdAb5w/s400/H-to-S-5G.PNG" border="0" alt=""id="BLOGGER_PHOTO_ID_5300062706704438674" /></a>The new reaction [<a href="http://cranemtn.com/life/weblog/H-to-S-5G.rle">RLE</a> / <a href="http://cranemtn.com/life/weblog/H-to-S-5G.mcl">MCL</a>] uses the usual four gliders to create a switch engine, but a modified Fx119 Herschel circuit allows a single glider to suppress all the extra junk the switch engine creates, until it has moved far enough forward to pick up the swimmer track.</p><br /><p style="clear:both;">The other two signals trigger two mirror-symmetric Cordership-wing constructors. Each of these builds a new switch engine next to the original swimmer, which then replaces the swimmer-lane support structure on that side. Once both wings are in place, the swimmer becomes the central engine of a free-flying Cordership.</p><br /><p>I'm working on tightening up this pattern somewhat; Calcyman's new suppression reaction disposes of glider #1 from the old H-to-S, but the embarrassing #6b is still in there. The wing constructors use parts from an old universal shotgun-building toolkit, which tends to produce fairly large and sprawling patterns -- so it may make sense to adjust these at the same time.</p><br /><p>[Further bulletins as events warrant.]</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-70768752261632215722007-06-17T15:02:00.000-05:002007-08-23T15:58:56.163-05:00A New Kind of Signal (though not a useful one yet)This is a speculative project that has been in the works for a long time: an odd-period Herschel loop that includes a switch-engine stage. I wanted to see what <a href="http://pentadecathlon.com/lifeNews/2005/09/bobsled_run_update.html">David Bell's "swimmers"</a> looked like when incorporated into a stable Herschel track. The current version isn't exactly pretty, but it does work. Here's the <a href=" http://cranemtn.com/life/files/2007-06-17-H-to-S-to-H.rle">RLE pattern file</a>.<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3HfR05HvJv7u7XffAkwJtOjhPBl6ZgNGZM298cScFGNR1G3BgZAaHxeQiXjWZxIwtvuQ7K3g2mOuLDIOIWkCFPBuqf7eV9lsnDlsCucmPjkINznlrDDkFQVfM1-tSfc6BBkbnIw/s1600-h/HtoStoH-p9995.GIF"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3HfR05HvJv7u7XffAkwJtOjhPBl6ZgNGZM298cScFGNR1G3BgZAaHxeQiXjWZxIwtvuQ7K3g2mOuLDIOIWkCFPBuqf7eV9lsnDlsCucmPjkINznlrDDkFQVfM1-tSfc6BBkbnIw/s400/HtoStoH-p9995.GIF" border="0" alt=""id="BLOGGER_PHOTO_ID_5077145183506860098" /></a><br /><h3>What Went Wrong This Time?</h3><br />The center of this circuit is an extensible Herschel fanout device based on paired F171 conduits. Theoretically adding another synchronized signal is simply a matter of adding another pair of F171s to the beginning of the series, and running a Hersrch search to produce an appropriately-timed output. F171 is a relatively slow conduit, so you do get a little extra time for adjustments with each new pair.<br /><br />But it turned out not to be enough; it gets increasingly hard to reach around the edges of the conduits that have already been placed. After using the last four outputs (circuits 6, 5, 4, and 3, working backwards -- the two ends of the F171 chains, and the two extensible tandem-glider outputs) it was impossible to route the previous tandem-glider signal around to get it where I wanted it fast enough. The signal could be hurried into the general neighborhood, but it didn't quite hit any of the spacetime locations I needed. I tried most if not all of the likely Herschel-to-glider converters that could produce either of the two gliders coming in from the southwest.<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-KZFtutX-oFxVyDmkCAr7hibMjT4DOOkJEHEXkDBa1LfHyFZbhp1IjksYXOX6FfGRrwMKBwhlShmG1RtEpVPTYEjeyGbA7Q4BfCKx_7csbGFOh-18mYHAVYU78aC0ZefLh7-s0Q/s1600-h/Annotated-H-to-S-Envelope.GIF"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-KZFtutX-oFxVyDmkCAr7hibMjT4DOOkJEHEXkDBa1LfHyFZbhp1IjksYXOX6FfGRrwMKBwhlShmG1RtEpVPTYEjeyGbA7Q4BfCKx_7csbGFOh-18mYHAVYU78aC0ZefLh7-s0Q/s400/Annotated-H-to-S-Envelope.GIF" border="0" alt=""id="BLOGGER_PHOTO_ID_5078923776708774002" /></a><br />I should probably have tried simply skipping the output of one F171-pair and checking to see if 342 ticks was enough extra time to allow a connection from one link further back. Something to try next time around --<br /><br />In this case, the failure of the extensible fanout meant that other types of Herschel fanout devices (circuits 1 and 2 in the labeled MCell "envelope" diagram at right) had to be bolted on instead, before the split that feeds the two F171 chains. This allowed plenty of time to route two signals around to feed the SW shotgun, though the design uses up a lot more space and the conversion takes longer.<br /><br />As usual, the layout was done from the inside out, so to speak, with the H-to-G converters in the deepest part of the fanout tree "solved" first. Also as usual, toward the outer edges expert Herschel plumbers may detect hints of increasing impatience with high-level architectural issues...<br /><h3>Not Good Enough Yet</h3><br />Unfortunately I'm going to have to rebuild the whole thing eventually, because of a mistake I made in the layout very early on. Basically I thought I had a clean way to get a Herschel to the northeasternmost H-to-G converter (circuit #6) in the right number of ticks, but there was a flaw in the only conduit that fit there: it worked only half the time (i.e., it needed a blinker as one of its suppressing catalysts, to keep the Herschel signal from interfering with other catalysts later on; otherwise it produced an extra blinker).<br /><br />So to make this odd-period loop work, there's a huge extra Herschel conduit bolted on to the top of the converter (circuit 6b) to suppress the extra blinker. 6b is a large slow glider-to-Herschel converter -- this was the easiest way to get a spare Herschel out without changing the rest of the circuits.<br /><br />The repeat rate of the full circuit was going to be up in the 600-tick range in any case, because of the boojum-transmitter adjustment I used in circuit #2... and because the swimmer-to-Herschel stage at the other end of the channel uses basically the same slow glider-to-Herschel mechanism, except it reflects an extra glider back to clean up a junk block.<br /><br />In any case, two Herschels are doing the job of delivering the last glider to the northeast in the switch-engine recipe, where one Herschel should really be plenty... kind of spoils the whole construction. I'm not sure the idea of "elegance" really applies to these extended Herschel-track experiments -- but anyway it isn't quite up to my arbitrary standards for these things.<br /><br /><h3>General notes on multi-Herschel constructions</h3><br />Laying out these things is a balancing act between ridiculously large solutions and ridiculous amounts of time spent working out the bugs in more compact circuitry. It's easy to produce any glider timings you want, for example, if you leave enough space for a boojum-reflector timing adjustment on every signal path; known Herschel conduits can give you output gliders with any timing mod 8, relatively quickly (usually three or four conduits, sometimes two -- assuming the output lane is an reasonable distance ahead of the input Herschel.)<br /><br />But when adjustments are necessary, it tends to affect the compression of the circuitry: if the adjusted boojum-reflected glider is sent into a tandem-glider transceiver, the repeat time will get worse the more the reflector is moved back. If the glider goes into a standard G-to-H, then you're immediately stuck with the repeat time of the G-to-H (currently I think this is still at least 497 ticks). Thus a "good" circuit design should probably try to avoid adjustable components -- ideally the signal-splitter outputs should be routed fairly directly toward their goals. Too bad it never actually seems to work that way...<br /><br /><h3>Another Approach (that doesn't seem to work)</h3><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxNGQM6qGeG3KEGxR6Cl2OGxa7Rgo46kywyxf9w9j92kcXDtF8UXNFlOzb-kpxS6JN2DOKpXJXGNHZ1K3V4LjJQnuJ-LSidJSUfVLmj8jdFHsMlfx7f4O9rWEA0Jb4oFpnCcrKzA/s1600-h/Swimmer-alt-recipe.GIF"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxNGQM6qGeG3KEGxR6Cl2OGxa7Rgo46kywyxf9w9j92kcXDtF8UXNFlOzb-kpxS6JN2DOKpXJXGNHZ1K3V4LjJQnuJ-LSidJSUfVLmj8jdFHsMlfx7f4O9rWEA0Jb4oFpnCcrKzA/s400/Swimmer-alt-recipe.GIF" border="0" alt=""id="BLOGGER_PHOTO_ID_5077145187801827410" /></a><br />I'd also like to have one more look at the idea of using junk still-lifes or oscillators to keep the switch engine going in its early cycles, on the way from the construction site into the diagonal track. Currently two of the six gliders in the recipe just suppress the switch engine's exhaust, doing the same job that the boats do in the permanent track. A simple block, blinker, or beehive can do the same job, and get cleanly destroyed in the process; they can be placed any time after the initial construction gliders go by but before the switch engine hits the key spot with its exhaust.<br /><br />#C Four gliders plus two blocks produce a 'swimmer'<br />#C -- the blocks must be placed after the gliders go past.<br />#C Theoretically Herschel-to-block converters might make this<br />#C as efficient as the six-glider version, but Herschel tracks<br />#C close to the swimmer lane tend to get in the way of<br />#C the incoming gliders; an all-glider solution was much easier.<br />x = 69, y = 71, rule = B3/S23<br />19bo$17b3o$16bo5boo$16boo4boo3$25bobo$25boo$26bo$$15bobo$16boo$16bo$oo<br />$oo3$29bo5boo$28bo6boo$28b3o$5boo$5boo$$20boo21boo$19bobo20bobo$21bo<br />21bo4$15boo$15boo$51boo$50bobo$51bo3$22bo$21bobo$21boo$59boo$58bobo$<br />59bo3$30bo$29bobo$29boo$67boo$66bobo$67bo3$38bo$37bobo$37boo6$46bo$45b<br />obo$45boo$$67boo$67boo3$54bo$53bobo$53boo!<br /><br />I spent a lot of time fiddling around with Herschel-to-junk converters a few months back, but discovered as usual that being able to adjust the timing of the suppressing signal -- i.e., building the suppressing junk at any of a moderate range of times during the construction -- wasn't worth losing the wider range of adjustability in the delivery location: when you're placing stationary junk you have to hit the right location exactly and you have to worry about the converter catalysts getting in the way, where with a glider you can place the H-to-G converter anywhere along the input diagonal.<br /><br /><h3>Five Types of Interchangeable Signals</h3><br />It seems a little odd that there aren't more kinds of asynchronous signal tracks by now. For tracks where converters to and from other signal types have been explictly constructed, we've got gliders, *WSSes, Herschels, 2c/3 diagonal wires, and now switch engines. How many have I left out? Even if we say that the tracks can contain low-period oscillators, I don't think there are very many more types (?) <br /><br />I'd say that things like Caterpillar blinker trails and telegraph wires don't count (yet) because they move each time they're used, and nobody has bothered to set up a way to send a signal through only when an input comes in. Theoretically a telegraph could transmit information asynchronously, but not if it's being powered by high-period guns as in the current model (a signal is sent every cycle, but it's modified slightly depending on the input.)<br /><br />I do have a rough design for an asynchronous telegraph that avoids sending ten pulses per signal (or a reverse signal) to reset the wire. But it would end up similar in size and latency to the current model, and at this rate it will be several years to never before that sees the light of day. Converters using Corderships or 2c/5 spaceships as signals would be at a similar order of size and level of effort.<br /><br />Maybe someone can supply p15 converters to get a signal out of an orthogonal pi-heptomino track made of pentadecathlons --<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbQz7via3X6JhzuGrS_O13MJD0mIbI7375PETAkh4OIVnH-ZDv_HUwTF7xUF2VHFTDdl6jCWh4AYNlABzjZpJVWIsbdD64Sk9DSw9mRzKoc4F0pQY5Hfx8-NPDHuqg4f1WFbZd2g/s1600-h/Pi-tracks-DRH-17Feb1997.GIF"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgbQz7via3X6JhzuGrS_O13MJD0mIbI7375PETAkh4OIVnH-ZDv_HUwTF7xUF2VHFTDdl6jCWh4AYNlABzjZpJVWIsbdD64Sk9DSw9mRzKoc4F0pQY5Hfx8-NPDHuqg4f1WFbZd2g/s400/Pi-tracks-DRH-17Feb1997.GIF" border="0" alt=""id="BLOGGER_PHOTO_ID_5077365412249929826" /></a><br />#C pi-heptomino conduits: Dean Hickerson, 17 February 1997<br />#C Herschel-to-pi stage by Paul Callahan (part of Fx176)<br />x = 151, y = 75, rule = B3/S23<br />124bo3bo$123boo3boo6$104boo6boo25boo6boo$103bobbo4bobbo23bobbo4bobbo$<br />102b6obb6o21b6obb6o$103bobbo4bobbo23bobbo4bobbo$104boo6boo25boo6boo6$<br />107b4o$106b6o$105b8o$104boo6boo$105b8o$35bo17bo17bo17bo16b6o$34bobo15b<br />obo15bobo15bobo16b4o$135b3o$134bo3bo$34b3o15b3o15b3o15b3o43bo3bo$34b3o<br />15b3o15b3o15b3o44b3o$35bo17bo17bo17bo$95boo$95boo$35bo17bo17bo17bo$34b<br />3o15b3o15b3o15b3o44b3o$34b3o15b3o15b3o15b3o43bo3bo$134bo3bo$135b3o$34b<br />obo15bobo15bobo15bobo$11boo8boo12bo17bo17bo17bo$12bo8boo$12bobo$13boo<br />$$126boo$7boo117boo$8bo$8bobo$9boo$$116bobboboobobbo$116b4oboob4o$116b<br />obboboobobbo3$9bo$9bobo$9b3o$11bo$$21boo$21boobboo8bo17bo17bo17bo$25bo<br />bo6bobo15bobo15bobo15bobo17boo$bboo23bo80boo$3bo23boo$3o31b3o15b3o15b<br />3o15b3o$o33b3o15b3o15b3o15b3o$35bo17bo17bo17bo3$35bo17bo17bo17bo$34b3o<br />15b3o15b3o15b3o$34b3o15b3o15b3o15b3o3$34bobo15bobo15bobo15bobo$35bo17b<br />o17bo17bo!<br /><br />Getting the signal started is no problem, using a stable Herschel-to-pi stage, but I don't think anyone has found a good converter for the end yet. Should be possible to engineer a multi-stage one, at least, where some useful junk is destroyed and re-created. Obviously it would be p15 or p30, not stable, but it would still be fun to see a really big pi orbital working.<br /><br /><h3>A Small Direct Converter (if wishes were horses)</h3><br /><br />When Brice Due was working on a revision of ptbsearch last year, I held out some hopes that a compact H-to-S (Herschel-to-swimmer) converter might happen show up, once the search code started keeping an eye out for "tamable" switch engines along with other more likely transients (Herschels, B-heptominos, R-pentominoes, and so forth.)<br /><br />Come to think of it, one could also keep an eye out for transient patterns that could trigger a 2c/3 signal -- a direct H-to-2c/3 would save even more spaghetti wiring than an H-to-S would... though a direct 2c/3-to-H is probably a harder problem, maybe more something for a 'dr'-type search on a new supercomputer, or a distributed computing system.<br /><h3>Distributed Searches?</h3><br />Periodically I try to work on finding a way to usefully distribute an exhaustive ptbsearch search (or dr or wls -- pick your poison). But so far I've more or less hit a wall and bounced off, every time. The most promising line of research seems to be finding a way to short-circuit repeated searches in one area, probably using hash tables and lots of RAM.<br /><br />To make this a little less vague: you often notice that a search problem splits into separate sub-searches, where you end up going through all the permutations of Solution A | B | C ..., say in one corner of the search area, and Solution Z | Y | X ... in another corner. Since the local conditions are identical and [A|B|C...][Z|Y|X...] works equally well in any combination, it might really only be necessary to go through A, B, C... once and Z, Y, X... once, and record the results of the search in a hash table somehow.<br /><br />Might work even better to short-circuit searches that _don't_ produce solutions; how much of a WLS search involves going over the same ground over and over, for example? My perception is that a majority of WLS's time is wasted chasing its tail in this way -- but quite possibly that's just an artifact of my relative inability to set up successful WLS searches!<br /><br />Anyway, maybe one of these days we'll get there. A non-engineered "Conway-space" H-to-S would go a long way toward allowing Herschel circuitry to be packed into tighter spaces: at the moment, the new F171 is the best diagonal conduit available. Oherwise, parallel circuits that run diagonally tend to have to travel Manhattan-style, with a lot of 90-degree turns and sharp corners that get in each others' way -- or they have to convert signals to tandem gliders and back, which is also fairly awkward (mostly because of chirality limitations in the standard transmitter).Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0tag:blogger.com,1999:blog-8285929.post-11700280594723351142007-04-27T08:56:00.000-05:002007-05-01T12:22:59.924-05:00Hex Counter and Cells Within Cells<p><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd9zbSWfx41l5mv6v88W9kKAQa4zegrQBKum_CeJvBmiSgjeXMqDPMIZ2z_ffFgY1rv8LFZwIU1-Gyd9wey6zNczMQBF3TiII94dniF5uMMBjmK2rO_AY7zl4m39F6qXhjYYYYpQ/s1600-h/counter-start.gif"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgd9zbSWfx41l5mv6v88W9kKAQa4zegrQBKum_CeJvBmiSgjeXMqDPMIZ2z_ffFgY1rv8LFZwIU1-Gyd9wey6zNczMQBF3TiII94dniF5uMMBjmK2rO_AY7zl4m39F6qXhjYYYYpQ/s400/counter-start.gif" border="0" alt=""id="BLOGGER_PHOTO_ID_5059577371133451970" /></a>Some incredible patterns have been included with the latest version of <a href="http://golly.sourceforge.net">Golly</a>, a cross-platform editor and player that can display huge CA patterns, and often run them at unheard-of speeds. <a href="http://sourceforge.net/project/showfiles.php?group_id=139354&package_id=152849&release_id=501321">Golly 1.2</a> came out in mid-April on SourceForge; one of the new patterns is a two-digit hexadecimal counter implemented as a <a href="http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life">Conway's Life</a> pattern. It's a modernization of sorts of Alan Hensel's 1994 "<a href="http://www.math.ucdavis.edu/~dean/RLE/dec.counter.html">Decimal Counter</a>" pattern -- an animated Java version of which is now <a href="http://www.collidoscope.com/cgolve/patternbigobjects.html#Decimal%20counter">available on the Web</a> [collidoscope.com].</p><br /><br />Another <a href="http://b3s23life.blogspot.com/2006/09/brice-dues-game-of-life-metapixel.html">set of patterns</a> by the same author, using some of the same components, are composed of huge grids of <a href="http://otcametapixel.blogspot.com">metapixels</a> -- regions thousands of cells square that are designed to mimic the behavior of the underlying cellular automaton, or that can be "reprogrammed" to simulate other rules.</p><br />The Golly engine is based on <a href="http://en.wikipedia.org/wiki/Hashlife">hashlife</a> (see the <a href="http://www.ddj.com/dept/ai/184406478">Dr. Dobb's Journal link</a> for details on how the algorithm works).</p><br /><p>The hex counter can be found in the Hashing-Examples folder in Golly's pattern collection, along with three metapixel samples. This series of screenshots shows the counter in action at various scales.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrXcJiDmULmVxBvOl97xmQ1TUX2UZXPqggqMLHkcb3NzScCR0suQQdNN3cVfNvh9tnE9tWh8sGHGhg0G_4vdje_gUk00LJsa6C1yS5brO8jKLt4lQy10O6R7vlgdxC6wMU_0AalQ/s1600-h/HexCounterZoom0.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrXcJiDmULmVxBvOl97xmQ1TUX2UZXPqggqMLHkcb3NzScCR0suQQdNN3cVfNvh9tnE9tWh8sGHGhg0G_4vdje_gUk00LJsa6C1yS5brO8jKLt4lQy10O6R7vlgdxC6wMU_0AalQ/s400/HexCounterZoom0.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059181345083989682" /></a>The first screenshot shows individual cells in the underlying grid, making up two <a href="http://www.argentum.freeserve.co.uk/lex_s.htm#stilllife">still lifes</a> (a block and a fishhook eater) and two <a href="http://www.argentum.freeserve.co.uk/lex_s.htm#spaceship">spaceships</a> (lightweight and middleweight).</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNIfLasjtBdUJSEq_7Ihf7BDUIEP9FIL4_wcsBCZk8X2sRZNmqILueGcKIxbXV55IYW-IQpTyKWPhQuiKHu5hpKxPqOcqK3IZqsHe3htx7S59q4Q_yaTz7o6kko309Z3uFiAhkSg/s1600-h/HexCounterZoom1.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjNIfLasjtBdUJSEq_7Ihf7BDUIEP9FIL4_wcsBCZk8X2sRZNmqILueGcKIxbXV55IYW-IQpTyKWPhQuiKHu5hpKxPqOcqK3IZqsHe3htx7S59q4Q_yaTz7o6kko309Z3uFiAhkSg/s400/HexCounterZoom1.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059181263479611042" /></a>The two spaceships are part of a high-period salvo that either creates a block or 'pulls' it along a row of memory bits that encode each pixel of the 'hex counter' movie.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqvYVry1bUYXxYzqn1TJUlk2U14D-wcQqHgfv04JHEshR3rxvBJH-q72EGUXDaaoWqel7OMX3Fm-Iinf5-hbQFSEJRwoAQ1SEmSYKUjX5dpjqgoKWjP6erXdqmq2UWd3pQn2CnPQ/s1600-h/HexCounterZoom2.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqvYVry1bUYXxYzqn1TJUlk2U14D-wcQqHgfv04JHEshR3rxvBJH-q72EGUXDaaoWqel7OMX3Fm-Iinf5-hbQFSEJRwoAQ1SEmSYKUjX5dpjqgoKWjP6erXdqmq2UWd3pQn2CnPQ/s400/HexCounterZoom2.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059181186170199698" /></a>The two blockers in the lower left corner both suppress the creation of blocks. The one on the left ends the block-pull cycle and allows the movie to cycle back to the beginning. The one on the right cleans up the extra block in an identical reaction triggered by the salvo-suppression glider coming in from the upper left, instead of by a block.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkX0V4JoF4yrGELC0ot3ALE-7v97vcA-GScoXwxC9StGO7ao9bCMO9kInsHnQWMPs7JlOzn7paRUqzBZo1wJ2GyX8lU3QIevAmE4DWnsbIvN4RlPbNRUnvuheE_5UTGFAUSXYF3g/s1600-h/HexCounterZoom3.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkX0V4JoF4yrGELC0ot3ALE-7v97vcA-GScoXwxC9StGO7ao9bCMO9kInsHnQWMPs7JlOzn7paRUqzBZo1wJ2GyX8lU3QIevAmE4DWnsbIvN4RlPbNRUnvuheE_5UTGFAUSXYF3g/s400/HexCounterZoom3.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059181104565821058" /></a>The suppressing glider is itself suppressed by a glider from a high-period <a href="http://www.argentum.freeserve.co.uk/lex_h.htm#herschel">Herschel</a>-based gun that ends just to the right of this image. It is made from a long series of Herschel period-doublers plus a Herschel-to-glider <a href="http://www.argentum.freeserve.co.uk/lex_c.htm#converter">converter</a>.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiImpGcy8Fu3u8JRxR4s1gszG9gHAjqev76PEwXBAPd-gI9aDY4ratK5JxVJBTX4DUp_-aZv564X3JUXyadi3Hn6Ee96FuKVPe7uVy0dZrz1cnZGckkCuYBAX0P1b18EsHVumbtlA/s1600-h/HexCounterZoom4.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiImpGcy8Fu3u8JRxR4s1gszG9gHAjqev76PEwXBAPd-gI9aDY4ratK5JxVJBTX4DUp_-aZv564X3JUXyadi3Hn6Ee96FuKVPe7uVy0dZrz1cnZGckkCuYBAX0P1b18EsHVumbtlA/s400/HexCounterZoom4.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059181027256409714" /></a>This is the first subpixel zoom in the series, so individual cells can no longer be seen and shapes may become somewhat distorted. For example, the two seven-bit eaters at center left, which are part of the row of 'memory bits' that tell the movie pixel when to toggle ON and OFF, are reduced to four-bit polyominoes in this view.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVN_hObtzWqwLDkHr3Rtc-eQCvDJmSWiDpMabYhgKK_2v2sTAMzegsl854Jm8UgU4DhiOKzpL_LflWgAJ5WREjrCLGEHz9gF7-moBFIBZkwNSVB_5ZA2joR7J0GhUhn4weiOe4QQ/s1600-h/HexCounterZoom5.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVN_hObtzWqwLDkHr3Rtc-eQCvDJmSWiDpMabYhgKK_2v2sTAMzegsl854Jm8UgU4DhiOKzpL_LflWgAJ5WREjrCLGEHz9gF7-moBFIBZkwNSVB_5ZA2joR7J0GhUhn4weiOe4QQ/s400/HexCounterZoom5.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059180425960988258" /></a>The rows of lightweight spaceships (LWSSs) that form the ON state of each movie pixel can now be seen clearly at the top. No LWSSs can be seen at the bottom edge because that pixel is currently turned OFF.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQBnlBnabI7ntAzJ3gmY0JYUwXCRJNPhW0R8yVZLq_-3YaolNsKA9GfnTIs5rcP0vPOzAxzjMsLT6TNIZwsmduIxuOG_OpXYmYxEXZTzJUpsv6JEtH3ZwLu92Iu3lIJ8Qw9MMz5Q/s1600-h/HexCounterZoom6.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQBnlBnabI7ntAzJ3gmY0JYUwXCRJNPhW0R8yVZLq_-3YaolNsKA9GfnTIs5rcP0vPOzAxzjMsLT6TNIZwsmduIxuOG_OpXYmYxEXZTzJUpsv6JEtH3ZwLu92Iu3lIJ8Qw9MMz5Q/s400/HexCounterZoom6.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059180271342165570" /></a>Here an entire edge of a single movie metapixel can be seen; in the center can be seen the row of memory bits that encode half of the metapixel's contribution to the movie. For compactness, the even and odd bits of the movie are stored along separate edges of the metapixels.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFDAfuUVj5_CY9Z6f5h7ErgJFURbBumqOZyu1cyjFOPA3MXN_qU_zcUb-pdNKaKNTOk2Og7AYxbEJ1msG-sF3OXW3wURsIBVJzU5N__z2fos_jjtr_ags8mBGsxPjOONi4P81opA/s1600-h/HexCounterZoom7.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFDAfuUVj5_CY9Z6f5h7ErgJFURbBumqOZyu1cyjFOPA3MXN_qU_zcUb-pdNKaKNTOk2Og7AYxbEJ1msG-sF3OXW3wURsIBVJzU5N__z2fos_jjtr_ags8mBGsxPjOONi4P81opA/s400/HexCounterZoom7.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059180142493146674" /></a>The other half of the movie's frames are encoded in a column along the left edge of the movie metapixel, on a diagonal mirror-image from the row along the bottom. At this zoom, two entire metapixels are visible, and the memory-bit columns are visible only as thin vertical lines at the far left. It can be seen that different metapixels contain different coded sequences.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRHel2mmv8LRnJWA2tCffJimXIIpZEnK_GCuTRF6aRdY9tj_ASEHrqSBc7Nv571zr5R7CFShnWyv1njxeBcz5cwEm-EndOxqUHrGaIpIS1IlK0n0n-97s2N0qESkVXDeFpPdgGag/s1600-h/HexCounterZoom8.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgRHel2mmv8LRnJWA2tCffJimXIIpZEnK_GCuTRF6aRdY9tj_ASEHrqSBc7Nv571zr5R7CFShnWyv1njxeBcz5cwEm-EndOxqUHrGaIpIS1IlK0n0n-97s2N0qESkVXDeFpPdgGag/s400/HexCounterZoom8.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059180069478702626" /></a>Here several metapixels can be seen at once. The differential shading between the two halves of the pixels at this scale is an artifact of the LWSSs' rectangular shape, and the fact that they are not spaced a power-of-two distance from each other.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWqKJiE36hc8OyWcuX_w-NfHRDxyTFVOLVX909mpAxKT_uoDCy-DNEZT6BtTxSthEFGYZOJ-u5ChJURWUjI7DUJVYBetd5Qro40Vpoe1tqn9jhi8Ja_ctRXqYyUKnwUzeQ_zAgaQ/s1600-h/HexCounterZoom9.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWqKJiE36hc8OyWcuX_w-NfHRDxyTFVOLVX909mpAxKT_uoDCy-DNEZT6BtTxSthEFGYZOJ-u5ChJURWUjI7DUJVYBetd5Qro40Vpoe1tqn9jhi8Ja_ctRXqYyUKnwUzeQ_zAgaQ/s400/HexCounterZoom9.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059179983579356690" /></a>At this scale the pixels appear solid and almost all of the details of the control mechanisms are too small to be seen.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8i2TkhyryjUguGOFWhGnTqV9lpZsR6bjlnQfjHw9M_AiPknf4megKgjf3LccRiogLCtuLuxmn83JYeL2YuF-GxKUMw8xyVuUG6nXnMmcsQlszhYhAZaUomUxbjqAeYEZwITMxZA/s1600-h/HexCounterZoomA.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8i2TkhyryjUguGOFWhGnTqV9lpZsR6bjlnQfjHw9M_AiPknf4megKgjf3LccRiogLCtuLuxmn83JYeL2YuF-GxKUMw8xyVuUG6nXnMmcsQlszhYhAZaUomUxbjqAeYEZwITMxZA/s400/HexCounterZoomA.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059179889090076162" /></a>At this scale the entire 'movie screen' can be seen. The movie's frame rate will vary widely depending on the memory and CPU speed, but with a step size of 8^4 or 8^5 it may reach several frames per second once Golly's hash tables have been populated.</p><br /><p style="clear:both;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdfFvG_4A48RwWMR5m9pC9lgqS1hGOQyntbt5FbcCr0rRGnwKPWTCNr8v97Cka9ghPBmF1g5URBFxDdlxDz7qg3Cs5xkCe4poo4OqztEzD7JIM5cOM6JhgcFEvV0J27yFUcYuuhA/s1600-h/HexCounterZoomB.png"><img style="float:right; margin:0 0 10px 10px;cursor:pointer; cursor:hand;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhdfFvG_4A48RwWMR5m9pC9lgqS1hGOQyntbt5FbcCr0rRGnwKPWTCNr8v97Cka9ghPBmF1g5URBFxDdlxDz7qg3Cs5xkCe4poo4OqztEzD7JIM5cOM6JhgcFEvV0J27yFUcYuuhA/s400/HexCounterZoomB.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059179798895762930" /></a>A final view of the movie screen with all the construction details lost in the distance.</p>Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com1tag:blogger.com,1999:blog-8285929.post-1169501034136098592007-01-22T16:23:00.000-05:002007-05-02T11:13:03.149-05:00Stable pseudo-Heisenburp device and other P1 wiring projectsI've been experimenting recently with what might be called "staged-recovery" <a href="http://www.argentum.freeserve.co.uk/lex_h.htm#herschelconduit">Herschel conduit</a> constructions. Reactions using only stable (P1) catalysts are often imperfect -- that is, there's no known way to accomplish many signal-processing tasks without either<br /><br /> (a) temporarily destroying some still life, and going back and replacing it later, or<br /><br /> (b) creating an unwanted still life as a byproduct of a useful reaction, and going back and removing it later.<br /><br />Generally (b) is easier than (a), since most simple still lifes can be annihilated by a single glider on the correct lane -- maybe with the help of a catalyst, but with few or no timing constraints. If a period-2 byproduct (most commonly a blinker) has to be modified or removed, this usually cuts in half the allowable spacetime locations for cleanup gliders, but still leaves a very wide search space.<br /><br />So this kind of repair just means routing a Herschel to any one of twenty-plus known <a href="http://cranemtn.com/life/files/HtoG26Oct2006.zip">Herschel-to-glider converters</a>, anywhere along the target glider lane, with a wide range of timings (usually the quicker the better). With this many degrees of freedom, a <a href="http://cranemtn.com/life/files/Hersrch23Jan2007.zip">Hersrch</a> search can generally find a fairly compact solution.<br /><br />-- Compact as these things go, that is! With a choice of 17 conduits in the basic set, a string of (say) three to five conduits will often be enough to put a glider on the correct lane, without having to wander off too far in the wrong direction -- unless the glider lane is too close to the input Herschel. A target area at least fifty cells away from the input Herschel should usually allow a clean connection to be made. I'll work on some rough coverage graphs for a separate posting.<br /><br />The basic idea behind a staged-recovery construction is that it's often possible to quickly make a repair, even a difficult repair -- say, rebuilding a loaf used to reflect an incoming glider, as shown below -- at the cost of some minor damage to the repairing circuitry. If the damage itself can be repaired relatively quickly and easily, the result is a somewhat more complex circuit that can recover more quickly overall -- if the initial part of the circuit is triggered again, the damaged area can often be repaired before the next signal reaches it.<br /><br /><p style="clear: both"><div class="figure"><a href="http://cranemtn.com/life/weblog/2007-01-22-highway-robber-no-stage.rle"><img class="life" alt="highway robber with no staged recovery" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXjCWuyWfS1ogqyPPFDwfCA3g5Tik5zVVfCtjlMrOU0Y3xHHEQhajRfUDX-DVcr0ajawpq79UmGZtJBbHEJOG68wvromP4rSJvh1JZkXBkibU1dbQTnCucNzF7Nx0BGkBW9B5FbQ/s400/2007-01-22-highway-robber-no-stage.png" border="0" alt="" id="BLOGGER_PHOTO_ID_5059927784630230738" /></a><div style="text-align: left">Highway robber without a staged-recovery mechanism -- recovery time is 2381 ticks.</div></div>As an example of a staged-recovery construction, here's a "highway robber" that absorbs gliders on a given lane and produces optional output gliders or Herschels, while letting gliders on all lanes beyond the key lane pass unharmed. This version takes the straightforward route of first producing Herschel signals from the initial glider, then using the Herschels to rebuild the original loaf. (The loaf is dangled in the key glider lane as "bait", and is destroyed while reflecting the input glider.)</p><br /><p style="clear: both"><div class="figure"><a href="http://cranemtn.com/life/weblog/2007-01-22-highway-robber-staged.rle"><img class="life" alt="highway robber with staged recovery" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEii56Y3jEcnn4g3PPqtFs-tcgSxeWZq8IYCj5a5XD1CGKHeFeicz-8-Ew6j8uTFo7NNcFLJZwjzosHgzf6UzT-ai9vZA-CbLK6LznUQ1jq02qWAngi9iUaA92Fdprh-zpnvyCIVZw/s400/2007-01-22-highway-robber-staged.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059928978631139042" /></a><div style="text-align: left">Highway robber with staged-recovery mechanism --<br />recovery time is 1696 ticks, but the pattern does not become<br />stable again for 2234 ticks.</div></div>Here's the same basic reaction using two stages, where the stage 2 circuit removes two extra beehives from the stage 1 circuit, and as a result allows the highway robber to recover more quickly overall, and also to produce an output signal much more quickly:</p><br /><br /><p style="clear: both"><div class="figure"><a href="http://cranemtn.com/life/weblog/2007-01-22-Heisenburp.rle"><img class="life" alt="complete pseudo-Heisenburp device" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8Iir8ngAwjD8QE-PDAT5wU6A9IICO1V1nB_2pfbo7_EQXYsN7YGALcoLHfd-uWDXHcwkNpqQgptGPxcnzs-DmxrjeUzMfYCvwQuraMr1A0_WXQ2ohwrp-z3j0e-SKU2TSd6iJDA/s400/2007-01-22-Heisenburp.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059929296458718962" /></a><br /><div style="text-align: left">stable pseudo-Heisenburp device -- recovery time is 1847 ticks.</div></div>And here's the same idea taken a little further -- attaching the highway robber to a revised 2c/3 transceiver produces a stable pseudo-Heisenburp device, which "borrows" a glider from the edge of a fleet of gliders, and later (thanks to the magic of stable 2c/3 signal wires) puts it back in exactly the right location relative to the other gliders in the fleet:</p><br /><br /><p>The primary use of the staged-recovery idea in the transmitter is in the northeast circuit, which asynchronously rebuilds a beehive and sends in a glider to reset the beginning of the 2c/3 wire after the signal is sent. The pattern could be rearranged to trigger this circuit considerably faster -- or even *before* the main trigger signal arrives (in which case the quiescent state of the transmitter would not include a beehive).</p><br /><br /><p style="clear: both">Here's a <a href="http://golly.cvs.sourceforge.net/*checkout*/golly/golly/src/Scripts/heisenburp.py">Python script</a> that builds a complete P1 Heisenburp device from its component parts. The above screenshot shows what it looks like in <a href="http://sf.net/projects/golly">Golly 1.1</a>. It can also take advantage of the new multi-layer functionality in <a href="golly.sourceforge.net">Golly 1.2</a>. In multi-layer mode, the script produces a screen something like this:</p><br /><p style="clear: both"><div class="figure"><a href="http://cranemtn.com/life/weblog/2007-01-22-Heisenburp.rle"><img alt="screenshot of multiple tiled layers in Golly" class="life" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTXhZvIQR_OBlECFERg1rQbf8LWDmgJ8_oejNl6esiSL3MycdU7QxX9OxwgYA5bGbRULWW9UB-mIwZUWGE6O8EDlhEdoZ-tmiCL5p-xJ0rl2KniniEuql05uEJwwRAjIKt59zqEg/s400/2007-01-22-Heisenburp-layers.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5059930353020673794" /></a><br /><div style="text-align: left">tiled views of the Heisenburp device: screenshot from Golly 1.2 beta</div></div></p><br /><br /><p style="clear: both"><b>Update:</b> The latest version of this script is now included as Scripts/heisenburp.py in the Golly 1.2 release distribution.Dave Greenehttp://www.blogger.com/profile/13093546924554276281noreply@blogger.com0