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 RCT16 ("Reverse Caber Tosser", 16 gliders) demonstration pattern.
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 "RCT15" demo pattern 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!
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 seed pattern for Alan Hensel's decimal counter -- a pattern over 1200 cells wide and 600 cells high. In the final stages, the patterns evolve into this:
x = 1383, y = 627, rule = B3/S23
388b2o169b2o$389bo169bo$389bobo165bobo$390b2o165b2o8$386b2o173b2o$385b
obo173bobo$385b2o175b2o5$384b2o177b2o$383bo2bo175bo2bo$384bobo175bobo$
385bo177bo6$364bo219bo$363bobo217bobo$363b2o219b2o4$370b2o205b2o$369bo
bo205bobo$369b2o207b2o6$403b3o137b3o2$417bo113bo$416bobo111bobo$366b2o
48b2o113b2o48b2o$366b2o42b2o125b2o42b2o$409bobo125bobo$383b2o24b2o127b
2o24b2o$382bo2bo177bo2bo$352bo30b2o179b2o30bo$276bo74bobo241bobo$275bo
bo74b2o241b2o$276b2o100b2o38b2o109b2o38b2o$378b2o38b2o109b2o38b2o2$
385bo15b2o143b2o15bo$384bobo13bo2bo42bo55bo42bo2bo13bobo$385bobo13b2o
42bobo53bobo42b2o13bobo$386b2o40bo16b2o55b2o16bo40b2o$428bo91bo$428bo
91bo2$381b2o183b2o$381b2o23b2o133b2o23b2o$405bo2bo25b2o77b2o25bo2bo$
405bo2bo24bobo77bobo24bo2bo$406b2o25b2o79b2o25b2o$377b2o191b2o$376bobo
191bobo$377bo193bo$403b2o139b2o$403b2o37b2o61b2o37b2o$442b2o61b2o2$
413b2o10b2o95b2o10b2o$244b2o167b2o9bo2bo93bo2bo9b2o$243bobo179b2o95b2o
$244bo5$430b2o85b2o$429bo2bo83bo2bo$429bo2bo83bo2bo$430b2o85b2o4$427b
2o91b2o$427b2o91b2o$293b2o$292bobo$293bo4$153b2o$152bobo$151bobo$152bo
131b2o$149bo135bo$148bobo131b3o$149b2o131bo16bo$200b2o96bobo$199bobo
96b2o$132bo57b2o6bobo$131bobo55bobo7bo83b2o$127b2o3bo55bobo11b2o78bo2b
o20bo$127bobo42bo16bo12bobo77bo2bo19bobo$128bo42bobo12bo16bo16bo62b2o
21bo$144bo25bobo12bobo31bobo$143bobo24b2o14b2o27b2o3bo$142bobo29b2o39b
obo82b2o$121bo20b2o30bobo39bo82bobo104b2o$120bobo52bo124bo106bo$119bob
o285bobo$119b2o287b2o$2b2o119b2o$2bobo42b2o74bobo$3bo42bobo75bo$37b2o
6bobo$bo34bobo7bo43b2o249bo380bo$obo32bobo11b2o39bobo247bobo80b2o99b2o
195bobo$bo17bo16bo12bobo39bo248b2o81b2o99b2o161b2o33b2o$18bobo12bo16bo
74b2o158b2o117b2o281bobo$17bobo12bobo54bo34bobo157bobo116bobo34b2o65b
2o179bo$17b2o14b2o53bobo32bobo157bobo117b2o34bo2bo63bo2bo$21b2o61b2o3b
o17bo16bo159bo155b2o65b2o$21bobo59bobo20bobo12bo$22bo51b2o6bobo20bobo
12bobo$73bobo7bo21b2o14b2o312b2o75b2o$72bobo11b2o21b2o291b2o31b2o75b2o
$73bo12bobo20bobo289bo2bo47b2o41b2o511bo$70bo16bo22bo291bobo37bo9b2o
41b2o9bo500bobo$69bobo331bo37bobo61bobo470b2o27b2o$70b2o208bo161bobo
59bobo222bo247bobo31bo$279bobo161b2o59b2o222bobo247bo31bobo$275b2o3bo
260b2o185b2o281bobo$275bobo263bo438bo31b2o$276bo22bo123b2o114bobo437bo
bo$298bobo81bo39bobo13b2o69b2o28b2o439bo$297bobo81bobo39bo14b2o69b2o$
297b2o82b2o144b2o461bo$527bobo411b2o46bobo$528bo367b2o24b2o16bobo47bob
o$291bo12bo591bobo23bobo16bo49b2o$290bobo10bobo82b2o507bobo6b2o15bobo
84b2o$269bo19bobo11b2o82bobo508bo7bobo15bo18bo66bobo$268bobo18b2o96b2o
154b2o349b2o11bobo32bobo66bobo$267bobo273bobo347bobo12bo34bo3b2o63bo$
267b2o275b2o331bo16bo16bo35bobo$271b2o23bo579bobo31bobo35bobo$271bobo
21bobo579bo3b2o27b2o37bo$272bo8bo13b2o583bobo62b2o$280bobo25b2o111b3o
457bo62bobo$279bobo25bobo235b2o318bo79bo$279b2o27bo126bo108bo2bo316bob
o$434bobo107bobo318bobo$384b2o48b2o109bo320b2o$286bo97b2o42b2o$272bo
12bobo139bobo$271bobo11b2o14b2o98b2o24b2o$270bobo27bobo97bo2bo418b2o$
270b2o29bo68bo30b2o419bobo$369bobo194bo256bobo$370b2o193bobo256bo$264b
o12bo118b2o38b2o128b2o252b2o$263bobo10bobo117b2o38b2o381bobo$262bobo
11b2o87b2o436bo16bo$262b2o100bobo36bo15b2o381bobo$292b2o71bo36bobo13bo
2bo42bo94b2o242bo3b2o21b2o$291bobo109bobo13b2o42bobo93bobo244bobo20bob
o$256bo12bo22bo111b2o40bo16b2o95b2o210bo34bo22bo$255bobo10bobo175bo
324bobo17bo$254bobo11b2o176bo324b2o17bobo39bo$254b2o467b2o50bo15bobo
37bobo$399b2o322bobo48bobo15b2o38bo$399b2o23b2o298bobo48bobo$248bo12bo
22b2o137bo2bo25b2o71b3o197bo50b2o$247bobo10bobo20bobo137bo2bo24bobo
230bo$246bobo11b2o22bo139b2o25b2o60bo169bobo$246b2o147b2o115bobo169b2o
$394bobo116b2o48b2o$395bo123b2o42b2o$240bo12bo167b2o54b2o40bobo$239bob
o10bobo22b2o142b2o37b2o15bobo40b2o24b2o$238bobo11b2o22bobo181b2o16bo
66bo2bo180bo$238b2o37bo268b2o30bo149bobo$431b2o10b2o132bobo149bo3b2o$
431b2o9bo2bo131b2o153bobo$232bo12bo197b2o66b2o38b2o180bo$231bobo10bobo
264b2o38b2o$230bobo11b2o24b2o$230b2o37bobo256b2o15bo$270bo213bo42bo2bo
13bobo159bo33bo$483bobo42b2o13bobo159bobo31bobo$224bo12bo210b2o34b2o
16bo40b2o161bobo31bobo$223bobo10bobo208bo2bo51bo101b2o101b2o32b2o$222b
obo11b2o209bo2bo51bo101bobo130b2o$222b2o39b2o183b2o155bo130bobo$262bob
o283b2o151bo12bo22bo$263bo196b2o61b2o23b2o150bobo10bobo$216bo12bo229bo
2bo32b2o25bo2bo175b2o11bobo$215bobo10bobo214b2o13b2o33bobo24bo2bo189b
2o$214bobo11b2o215b2o49b2o25b2o$214b2o336b2o$256b2o294bobo154bo12bo$
255bobo295bo154bobo10bobo$208bo12bo34bo200b2o67b2o181b2o11bobo$207bobo
10bobo233bo2bo27b2o37b2o195b2o$206bobo11b2o234bobo28b2o206b2o$206b2o
249bo237bobo$445b2o57b2o10b2o178bo20bo12bo$249b2o194bobo55bo2bo9b2o
198bobo10bobo$200bo12bo34bobo195b2o56b2o211b2o11bobo$199bobo10bobo34bo
481b2o$198bobo11b2o235bo$198b2o248bobo251b2o$449b2o251bobo20bo12bo$
703bo20bobo10bobo$192bo12bo36b2o255b2o93b2o4b2o123b2o11bobo$191bobo10b
obo34bobo254bo2bo91bo2bo4bo137b2o$190bobo11b2o36bo255bo2bo91bo2bo4bobo
$190b2o307b2o93b2o6b2o$709b2o22bo12bo$709bobo20bobo10bobo$184bo12bo
512bo22b2o11bobo$183bobo10bobo36b2o265b2o243b2o$182bobo11b2o36bobo265b
2o$182b2o51bo$741bo12bo$716b2o22bobo10bobo$176bo12bo526bobo22b2o11bobo
$175bobo10bobo526bo37b2o$174bobo11b2o38b2o$174b2o51bobo$228bo520bo12bo
$472b2o274bobo10bobo$168bo12bo290b2o249b2o24b2o11bobo$167bobo10bobo
540bobo37b2o$166bobo11b2o273b2o267bo$166b2o53b2o231bo2bo$220bobo232b2o
300bo12bo$221bo534bobo10bobo$160bo12bo583b2o11bobo$159bobo10bobo285b2o
268b2o39b2o$158bobo11b2o286b2o268bobo$158b2o283b2o286bo$214b2o227b2o9b
o310bo12bo$213bobo237bobo308bobo10bobo$152bo12bo48bo237bobo310b2o11bob
o$151bobo10bobo285b2o325b2o$150bobo11b2o304b2o265b2o$150b2o318bobo264b
obo$471bo266bo34bo12bo$207b2o248b2o313bobo10bobo$144bo12bo48bobo248b2o
314b2o11bobo$143bobo10bobo48bo579b2o$142bobo11b2o$142b2o600b2o$453b2o
68b2o219bobo34bo12bo$452bobo20b2o46bobo219bo34bobo10bobo$149bo50b2o
251bo21b2o47bo256b2o11bobo$148bobo48bobo593b2o$148b2o50bo291b2o$491bo
2bo$492b2o257b2o36bo12bo$454b2o295bobo34bobo10bobo$454bobo295bo36b2o
11bobo$193b2o260bo31b2o314b2o$192bobo292b2o42b2o$193bo310b2o24bo2bo$
494bo9b2o25b2o264bo12bo$141b2o350bobo262b2o36bobo10bobo$141b2o351bobo
261bobo36b2o11bobo$495b2o262bo51b2o$186b2o$185bobo340b2o$186bo340bo2bo
274bo12bo$473b2o15b2o35bobo274bobo10bobo$466bo5bo2bo14b2o36bo236b2o38b
2o11bobo$465bobo5b2o290bobo51b2o$465bo2bo297bo$179b2o285b2o$178bobo
279b2o351bo12bo$179bo279bobo35b2o313bobo10bobo$460bo36bo315b2o11bobo$
498b3o271b2o53b2o$482b2o16bo95bo175bobo$481bobo111bobo175bo$172b2o308b
o55b2o56b2o223bo12bo$171bobo256bo107bobo279bobo10bobo$172bo256bobo107b
o281b2o11bobo$429b2o67b2o335b2o$497bo2bo278b2o$497bobo279bobo$320bo73b
o103bo281bo48bo12bo$319bobo71bobo46b2o161bo222bobo10bobo$319b2o72b2o
47bobo159bobo222b2o11bobo$443bo57b2o102b2o236b2o$501bobo$502bo283b2o$
786bobo48bo$313bo473bo48bobo$312bobo297bo224b2o$312b2o297bobo239bo$
612b2o238bobo$853bobo$793b2o59b2o$477b2o314bobo$306bo170bobo314bo$305b
obo170bo140bo228bo$305b2o311bobo226bobo$619b2o227b2o2$800b2o$800bobo$
801bo$298bo55b2o270bo$297bobo54b2o198b2o69bobo$297b2o255b2o70b2o2$807b
2o46b2o$807bobo45b2o$808bo$633bo$290bo341bobo$289bobo341b2o$289b2o56b
2o211b2o$346bobo211bobo251b2o$347bo213bo252bobo$815bo$640bo$283bo69b2o
199b2o83bobo$282bobo54b2o11bobo199bobo83b2o$282b2o54bobo10bobo201bobo$
339bo12bo203bo13b2o$472b2o96bobo$471bobo97bo$345b2o125bo174bo176b2o$
276bo54b2o11bobo299bobo175bobo$275bobo52bobo10bobo218b2o81b2o176bo$
275b2o54bo12bo219bobo11b2o$565bobo10bobo$566bo12bo$337b2o$336bobo315bo
$269bo52b2o11bobo234b2o79bobo$268bobo50bobo12bo235bobo11b2o66b2o$268b
2o52bo250bobo10bobo$574bo12bo2$328b2o$327bobo250b2o79bo$313b2o11bobo
251bobo11b2o64bobo$261bo50bobo12bo253bobo10bobo64b2o$260bobo50bo268bo
12bo$260b2o2$319b2o267b2o$305b2o11bobo159bo107bobo11b2o$304bobo10bobo
159bobo107bobo10bobo64bo$254bo50bo12bo161bobo107bo12bo64bobo$253bobo
225b2o186b2o$253b2o263bo$311b2o204bobo76b2o$297b2o11bobo162bo42bo77bob
o11b2o$296bobo10bobo162bobo120bobo10bobo$297bo12bo164b2o43bo77bo12bo$
247bo271bobo$246bobo270b2o157bo$246b2o55b2o299b2o71bobo$289b2o11bobo
299bobo11b2o58b2o$288bobo10bobo301bobo10bobo$289bo12bo303bo12bo$382bo$
240bo140bobo$239bobo53b2o85b2o136b2o90b2o71bo$239b2o53bobo223bobo89bob
o11b2o56bobo$280b2o11bobo225bobo89bobo10bobo56b2o$279bobo12bo227bo91bo
12bo$42bo237bo625bo$41bobo488bo372bobo$42b2o16b2o171bo297bobo86b2o265b
2o16b2o$60b2o170bobo51b2o244bo87bobo11b2o251b2o$232b2o38b2o11bobo57b2o
274bobo10bobo$271bobo10bobo57bobo187bo87bo12bo$272bo12bo59bo187bobo47b
o$533b2o47bobo111bo$583bo44b2o65bobo$226bo51b2o264bo83bobo65b2o$225bob
o36b2o11bobo263bobo6bo32bo43bobo11b2o$225b2o36bobo10bobo264b2o7b3o29bo
bo43bo12bobo$23b2o239bo12bo262bo14bo28b2o58bo279b2o$22bobo514bobo12b2o
368bobo$23bo28b2o486bobo7b2o43bo107bo191b2o28bo$52b2o216b2o269b2o7bobo
41bobo6bo33b2o63bobo190b2o$219bo36b2o11bobo280bo41b2o7b3o31bobo63b2o$
42b2o174bobo34bobo10bobo281b2o11bo25bo14bo31bobo264b2o$42b2o13bo160b2o
36bo12bo294bobo23bobo12b2o32bo13b2o236bo13b2o$56bobo506bobo23bobo7b2o
50bobo234bobo$49bo6bobo507b2o24b2o7bobo50bo235bobo6bo$48bobo6bo204b2o
339bo287bo6bobo$47bobo198b2o11bobo339b2o11bo282bobo$47b2o163bo34bobo
10bobo352bobo29b2o63bo187b2o$211bobo34bo12bo354bobo28bobo11b2o48bobo$
211b2o404b2o29bobo10bobo48b2o$622bo26bo12bo$254b2o261b2o102bobo$240b2o
11bobo260bo2bo101b2o3bo$239bobo10bobo261bo2bo105bobo27b2o$205bo34bo12b
o263b2o107bo28bobo61bo$50b2o8b2o142bobo449bobo59bobo166b2o8b2o$50b2o8b
2o142b2o451bo61b2o166b2o8b2o$246b2o$77b2o10b2o141b2o11bobo271bo112bo
40b2o183b2o10b2o$76bo2bo9b2o140bobo10bobo270b3o111bobo39bobo182b2o9bo
2bo$77b2o153bo12bo164bo105bo114b2o41bo195b2o$198bo210bobo104b2o109b2o
97bo$197bobo208bo2bo215bobo13b2o80bobo$72b2o123b2o39b2o169b2o217bobo
12bobo21b2o57b2o147b2o$72b2o150b2o11bobo389bo9bo5bo21bobo11b2o192b2o$
223bobo10bobo193bo206b3o3b2o21bobo10bobo$79bo144bo12bo179b2o12bobo208b
o26bo12bo186bo$78bobo336b2o13b2o207b2o225bobo$71b2o6bobo651bo133bobo6b
2o$70bobo7b2o148b2o443b2o55bobo132b2o7bobo$70b2o144b2o11bobo443bobo55b
2o142b2o$215bobo10bobo214b2o229bobo$187bo28bo12bo214bobo203b2o25bo13b
2o$75b2o109bobo256bo204bobo38bobo178b2o$75b2o109b2o463bobo38bo179b2o$
65b2o155b2o428bo229b2o$64bobo141b2o11bobo517bo140bobo$64b2o141bobo10bo
bo439bo22b2o53bobo140b2o$208bo12bo439bobo21bobo11b2o40b2o$180bo481bo
23bobo10bobo$179bobo505bo12bo$179b2o33b2o448bo$213bobo447bobo$212bobo
245bo202b2o28b2o53bo$213bo179b2o57bo6bobo231bobo11b2o38bobo$393bobo54b
3o7b2o232bobo10bobo38b2o$173bo22b2o196bo54bo14bo230bo12bo$172bobo20bob
o251b2o12bobo$172b2o22bo256b2o7bobo$452bobo7b2o237b2o$452bo211b2o35bob
o11b2o$202b2o235bo11b2o211bobo35bobo10bobo$188b2o11bobo234bobo224bobo
35bo12bo$166bo20bobo10bobo234bobo226bo$165bobo20bo12bo235b2o320bo$165b
2o266bo275b2o47bobo$432bobo274bobo47b2o$194b2o233bo3b2o275bobo11b2o$
180b2o11bobo232bobo280bo12bobo$179bobo10bobo234bo295bo$159bo20bo12bo$
158bobo262bo342bo$158b2o222bo39bobo246b2o45b2o45bobo80b2o$186b2o193bob
o39b2o246bobo44bobo11b2o32b2o81bo$172b2o11bobo190bo3b2o43b2o238bo5bo
45bobo10bobo111b3o$171bobo10bobo190bobo31b2o13bobo238b3o3b2o45bo12bo
112bo$172bo12bo192bo16bo14bobo12bobo242bo$152bo241bobo13bo5bo9bo242b2o
$151bobo218bo22b2o12b2o3b3o309b2o45bo$151b2o25b2o191bobo25bo13bo312bob
o43bobo$164b2o11bobo192b2o24bobo12b2o312bobo43b2o$163bobo10bobo197b2o
19bobo328bo$164bo12bo182b2o13bobo19b2o275bo$359bobo12bobo296bobo68b2o$
145bo213bo5bo9bo297b2o69bobo$144bobo23b2o186b2o3b3o303b2o74bo34bo$144b
2o10b2o11bobo190bo306bobo107bobo$155bobo10bobo191b2o306bobo107b2o$156b
o12bo501bo66b2o$342bo395bobo11b2o$341bobo395bobo10bobo$162b2o178bo397b
o12bo$148b2o11bobo69b2o23b2o98bo319bo108bo$147bobo10bobo69bobo22bobo
80bo16bobo317bobo106bobo$148bo12bo71bo23bo5bo75bobo16b2o317b2o3bo63b2o
39b2o$256b2o3b3o76b2o20b2o317bobo62bobo11b2o$260bo100bobo318bo64bobo
10bobo$154b2o104b2o45bo22bo29bobo385bo12bo$153bobo150bobo13bo6bobo29bo
326bo$152bobo152b2o11b3o7b2o355bobo$153bo157b2o6bo14bo352b2o65b2o$295b
2o13bobo6b2o12bobo347b2o69bobo11b2o26bo$125b2o124b2o26bo14bobo12bobo
11b2o7bobo348bobo13b2o54bobo10bobo24bobo$124bobo123bobo25bobo13bo5bo9b
o11bobo7b2o350bobo12bobo54bo12bo26b2o$125bo123bobo27b2o12b2o3b3o21bo
362bo9bo5bo$238b2o10bo32bo13bo23b2o372b3o3b2o$168bo69bobo41bobo12b2o
399bo63b2o$167bobo69bo41bobo413b2o63bobo11b2o$168b2o111b2o480bobo10bob
o24bo87b2o$60bo111b2o590bo12bo24bobo86bo$59bobo109bobo629b2o87b3o$60b
2o16b2o90bobo721bo$78b2o91bo17bo468bo47b2o62b2o$188bobo466bobo46bobo
61bobo$189bo54b2o411b2o48bobo61bobo$149b2o54bo22bo14bobo462bo63bo13b2o
22bo$149bobo35bo16bobo13bo6bobo13bo5bo536bobo20bobo$150bo35bobo16b2o
11b3o7b2o12b2o3b3o468bo68bo22b2o$187b2o20b2o6bo14bo13bo470bobo$208bobo
6b2o12bobo12b2o470bo$207bobo11b2o7bobo547b2o$41b2o165bo11bobo7b2o488bo
59bobo11b2o$40bobo177bo498bobo59bobo10bobo$41bo28b2o147b2o498b2o61bo
12bo$70b2o84b2o661bo$156bobo571bo87bobo$60b2o95bo493bo77bobo6bo49b2o
29b2o$60b2o13bo574bobo76b2o7b3o47bobo11b2o$74bobo574b2o73bo14bo47bobo
10bobo$67bo6bobo648bobo12b2o48bo12bo$66bobo6bo650bobo7b2o$65bobo659b2o
7bobo87bo$65b2o671bo57b2o27bobo$738b2o11bo44bobo27b2o60bo$750bobo44bob
o87bobo$751bobo44bo13b2o55b2o16b2o$752b2o58bobo54b2o$673b2o138bo$672bo
2bo157bo$672bo2bo156bobo$68b2o8b2o593b2o131b2o25b2o$68b2o8b2o726bobo
11b2o$121bo15bo669bobo10bobo$95b2o10b2o11bobo13bobo669bo12bo$94bo2bo9b
2o12bo15bo537bo76bo$95b2o576b3o76b3o151b2o$672bo82bo58b2o90bobo$672b2o
80b2o44bo13bobo11b2o47b2o28bo$90b2o658b2o47bobo13bobo10bobo46b2o$90b2o
24bo15bo617bobo47b2o14bo12bo$115bobo13bobo566b2o50bo134b2o$97bo18b2o
14b2o566b2o50b2o119bo13b2o$96bobo723b2o48bobo$89b2o6bobo722bobo22b2o
23bobo6bo$88bobo7b2o592b2o129bobo21bobo23bo6bobo$88b2o601bo2bo129bo23b
o32bobo$692bobo187b2o$117b2o574bo64bo$93b2o22bobo637bobo$93b2o23bo638b
2o$83b2o669bo$82bobo668bobo$82b2o670bobo$755b2o3bo$759bobo107b2o8b2o$
760bo108b2o8b2o$819b2o$762bo55bobo19b2o10b2o$144b2o615bobo55bo20b2o9bo
2bo$89b2o53bobo614b2o89b2o$89bobo53bo$90bo$857b2o$857b2o2$795bo55bo$
762b2o30bobo53bobo$762bobo29b2o53bobo6b2o$763bobo24b2o57b2o7bobo$764bo
25bobo66b2o$791bobo$681b2o91bo17bo$680bobo90bobo78b2o$681bo92bo79b2o$
864b2o$776bo50b2o6b2o27bobo$775bobo48bo2bo4bobo28b2o$775b2o49bo2bo4bo$
827b2o4b2o17$752b2o$751bobo$752bo$843b2o$842bobo$843bo11$1380bo$1378bo
3bo$142b2o1233bo$142b2o1233bo4bo$1377b5o2$141b2o$141b2o4$135b2o$135b2o
$774b2o$773bobo$141b2o631bo$141b2o!
#C [[ X -52 Y -143 ZOOM -2 STEP 5 AUTOSTART LOOP 12000 THUMBNAIL THUMBSIZE 2 ]]What Is This All About?
A glance through the LifeWiki 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.
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 what exactly can we build by crashing gliders together? -- and an obvious corollary, for any given Life pattern, is how few gliders can we use?
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.
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 Life textbook). They're all puzzles that nobody has ever solved before, and there's an unbounded number of them. A recent set of extra-hard problems was posted on November 10th, for example -- and they were all solved in well under a week.
Conversely, we can ask what can we build with a fixed number of gliders? 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
how many gliders does it take to construct...
... a block? (Two.)
... a lightweight spaceship? (Three.)
... a glider-producing switch engine? (Four.)
... a unix oscillator? (Five.)
... a queen bee shuttle? (Six.)
... a Coe ship? (Seven.)
... a Gosper glider gun? (Eight.)
... a 2-engine Cordership? (Nine.)
... a blinker puffer? (Ten.)
x = 998, y = 822, rule = B3/S23
991bobo$991b2o$992bo5$195bo$178bo17b2o$176bobo16b2o$177b2o$992bo$991bo
$991b3o9$997bo$995b2o$996b2o23$851bo$851bobo$851b2o34$183bo$184bo$182b
3o26$221bo$222bo$220b3o5$202bo$200bobo$201b2o31$677bo$677bobo16bo$677b
2o17bobo$161bobo10bo521b2o$162b2o11b2o$162bo11b2o32$145bo436bo$146b2o
433bo$145b2o434b3o4$581bo$149bo431bobo$150bo430b2o$148b3o3bo$155bo$
153b3o34$117bobo355bo$118b2o355bobo$118bo356b2o34$92bo$93bo$91b3o7$
358bo$357bo$357b3o$107bo$108bo$106b3o2$350bo$349bo$349b3o17$237bo$237b
obo$237b2o27$83bo$81bobo$82b2o$222bo$221bo$221b3o24$127bo$125b2o$41bo
84b2o$39bobo$40b2o21$27bo$27bobo$27b2o$2bo$obo$b2o55$126b2o$126bobo$
126bo31$225bo$224b2o$224bobo65$376b2o$375b2o$377bo29$121bo356b2o$108b
2o11b2o355bobo$109b2o9bobo355bo$108bo$464b3o$464bo$465bo36$145b3o$147b
o$146bo$142b2o$141bobo$143bo34$171b2o520b2o$172b2o519bobo9b3o$171bo
521bo11bo$188bo517bo$188b2o$187bobo31$224b2o$223bobo$225bo$812b2o$811b
2o$813bo15$204b3o$206bo$205bo600bo$805b2o$805bobo5$183b3o$185bo$184bo
68$186b2o782b2o$187b2o781bobo$186bo783bo14$193b2o$194b2o$193bo4$995b3o
$995bo$996bo$204b3o$206bo$205bo!
#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 ]]
#C [[ T 50 ]] # block
#C [[ T 150 X -413 Y 0 ]]
#C [[ T 200 ]] # LWSS
#C [[ T 300 X -340 Y 0 ]]
#C [[ T 360 ]] # GPSE
#C [[ T 450 X -270 Y 0 ]]
#C [[ T 575 ]] # unix
#C [[ T 650 X -200 Y 0 ]]
#C [[ T 700 ]] # queen bee shuttle
#C [[ T 820 X -130 Y 0 ]]
#C [[ T 880 ]] # Coe ship
#C [[ T 950 X -60 Y 0 ]]
#C [[ T 1100 ]] # 2-engine Cordership
#C [[ T 1150 X 20 Y 0 Z 8 ]]
#C [[ T 1250 ]] # blinker puffer
#C [[ T 1550 X 96 Y 0 Z 10 ]]
#C [[ T 1700 ]]
#C [[ T 1775 X -483 Y -10 ]]
#C [[ LABEL 13 413 10 "block\n(2 gliders)" ]]
#C [[ LABEL 85 423 10 "LWSS\n(3 gliders)" ]]
#C [[ LABEL 150 423 10 "GPSE\n(4 gliders)" ]]
#C [[ LABEL 223 423 10 "unix\n(5 gliders)" ]]
#C [[ LABEL 292 423 10 "queen bee shuttle\n(6 gliders)" ]]
#C [[ LABEL 368 423 10 "Coe ship\n(7 gliders)" ]]
#C [[ LABEL 435 423 10 "Gosper glider gun\n(8 gliders)" ]]
#C [[ LABEL 512 428 10 "2-engine Cordership\n(9 gliders)" ]]
#C [[ LABEL 595 423 10 "blinker puffer\n(10 gliders)" ]]
... 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
... a pattern that can compute the digits of pi and print them out in the Life universe? (Fifteen.)
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 spaceship that travels by making reflected copies of itself, 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.
That doesn't seem to make a lot of sense, to put it mildly. So... what exactly is going on here?
The Full-Sized RCT15
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.
Completely counterintuitively, any pattern that can be constructed by colliding any 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 lot farther apart.
For example, moving those groups of gliders to exactly the correct distances from each other would build a complete Gemini spaceship -- 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 173,449 colliding gliders (at least that's the current known recipe).
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 factors of two bigger and slower than the RCT demo pattern that builds the decimal counter pattern shown above.
Storing Data in Empty Space: How Does It Work?
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 this LifeViewer animation to get a closer look at the details. The mechanism is also described in detail in previous posts on this blog, and elsewhere. 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 Brett Berger's November 16 blog post on these subjects.
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 ending up with a remainder of either 0 or 1 after each division.
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.
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.
Getting Something for (Almost) Nothing
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.
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 2028-bit sequence for building an 8-cell object called a shillelagh.
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.
Ours Not To Reason Why...
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 329 gliders instead of 15, with only relatively minor cleanup problems. Here again, see Brett Berger's blog post for more details.
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: what is the absolute smallest total number of gliders that we can do this with? As of November 15th, the RCT15 patterns represent our collective best effort to answer this question: "Fifteen!"
Yet More Obsessive Optimizing
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.
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 "decoder and better construction arm" (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.
That isn't the end of the bootstrap process, though! The DBCA is efficient enough to build an even more complicated mechanism, the "extreme compression construction arm" (ECCA), which takes over construction work from the DBCA. The ECCA is 30% more efficient than the DBCA, and it can fire gliders in multiple directions, and 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.
Remember, the point of this whole exercise is not to build a DBCA or an ECCA. The point is to build whatever pattern we want to build, 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.
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.
The RCT Demo Pattern
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.
Neither of the full patterns can be simulated effectively on any software that we currently have available. Golly, 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.
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 smaller RCT pattern 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.
These extra gliders are constructed with sparse streams of MWSSes, 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.
The RCT Viewer script
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. This Lua script 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.
To use the script, start by opening the rct15.mc.gz file in Golly. Then navigate to the forum page where the RCT viewer Lua script is published, click "Select All" in the code box, hit Ctrl+C to copy, and then in Golly choose File > Run Clipboard. 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.
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.
... Anything* ?
In Conway's Life, the claim of universal construction -- the ability of a mechanism to build "anything" -- is inevitably limited by the existence of Gardens of Eden, grandparentless patterns, and other patterns that provably can not be constructed by any number of colliding gliders -- including some recently discovered still lifes and oscillators.
To summarize: all Conway's Life universal constructors can construct anything that can be constructed, so they can all build any structure that any other universal constructor can build.
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.
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 glider-producing switch engines 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:
x = 2611, y = 1354, rule = LifeHistory
542.14D114.7D1365.14D$456.29D53.22D15.56D37.11D32.38D1207.29D53.22D
15.56D39.7D53.16D$455.33D47.28D12.57D34.13D31.40D1205.33D47.28D12.57D
36.10D49.23D$455.36D42.32D10.57D33.14D31.40D1205.36D42.32D10.57D34.
13D45.28D$455.38D39.35D8.57D31.16D31.40D1205.38D39.35D8.57D33.14D43.
31D$455.39D36.38D7.57D30.17D31.40D1205.39D36.38D7.57D31.16D42.32D$
455.40D34.40D6.57D28.19D31.40D1205.40D34.40D6.57D30.17D40.34D$455.42D
31.42D5.57D27.20D31.40D1205.42D31.42D5.57D28.19D39.35D$455.42D30.44D
4.57D25.22D31.40D1205.42D30.44D4.57D26.21D38.36D$455.43D28.45D4.56D
24.24D31.39D1206.43D28.45D4.56D26.22D37.37D$455.11D14.19D26.18D13.15D
27.11D45.25D31.11D1234.11D14.19D26.18D13.15D27.11D46.24D36.17D13.8D$
455.11D18.15D25.16D19.12D27.11D43.27D31.11D1234.11D18.15D25.16D19.12D
27.11D45.25D35.15D19.5D$455.11D20.14D23.15D23.10D27.11D42.16D.11D31.
11D1234.11D20.14D23.15D23.10D27.11D43.27D35.13D$455.11D21.13D23.14D
26.8D27.11D41.15D3.11D31.11D1234.11D21.13D23.14D26.8D27.11D42.28D34.
13D$455.11D22.13D21.14D29.6D27.11D41.14D4.11D31.11D1234.11D22.13D21.
14D29.6D27.11D41.15D2.12D33.13D$455.11D22.13D20.14D31.5D27.11D41.12D
6.11D31.11D1234.11D22.13D20.14D31.5D27.11D40.14D4.12D33.12D$455.11D
23.12D20.13D34.2D28.11D40.11D8.11D31.11D1234.11D23.12D20.13D34.2D28.
11D40.13D5.12D32.12D$455.11D23.12D19.13D65.11D40.10D9.11D31.11D1234.
11D23.12D19.13D65.11D40.11D7.12D32.11D$455.11D24.11D19.12D66.11D41.7D
11.11D31.11D1234.11D24.11D19.12D66.11D40.9D9.12D31.12D$455.11D24.12D
17.13D66.11D41.5D13.11D31.11D1234.11D24.12D17.13D66.11D40.8D10.12D31.
11D$455.11D24.12D17.12D67.11D41.4D14.11D31.11D1234.11D24.12D17.12D67.
11D40.6D12.12D31.11D$455.11D24.12D16.13D67.11D59.11D31.11D1234.11D24.
12D16.13D67.11D41.3D14.12D30.11D$455.11D24.12D16.12D68.11D59.11D31.
11D1234.11D24.12D16.12D68.11D58.12D30.11D$455.11D24.11D17.12D68.11D
59.11D31.11D1234.11D24.11D17.12D68.11D58.12D29.11D$455.11D24.11D16.
12D69.11D59.11D31.11D1234.11D24.11D16.12D69.11D58.12D29.11D$455.11D
24.11D16.12D69.11D59.11D31.11D1234.11D24.11D16.12D69.11D58.12D29.11D$
455.11D23.12D16.12D69.11D59.11D31.11D1234.11D23.12D16.12D69.11D58.12D
29.10D$455.11D23.12D16.11D70.11D59.11D31.11D1234.11D23.12D16.11D70.
11D58.12D29.10D$455.11D22.12D16.12D70.11D59.11D31.11D1234.11D22.12D
16.12D70.11D58.12D28.11D$455.11D22.12D16.12D70.11D59.11D31.11D1234.
11D22.12D16.12D70.11D58.12D28.11D$455.11D21.13D16.12D70.11D59.11D31.
11D2.9D1223.11D21.13D16.12D70.11D58.12D28.11D$455.11D20.13D17.12D70.
11D59.11D31.29D1216.11D20.13D17.12D70.11D58.12D28.11D11.11D$455.11D
18.14D18.11D71.11D59.11D31.32D1213.11D18.14D18.11D71.11D58.12D28.10D
7.20D$455.11D16.16D18.11D71.11D59.11D31.34D1211.11D16.16D18.11D71.11D
58.12D28.10D5.25D$455.11D10.21D19.11D71.11D59.11D31.36D1209.11D10.21D
19.11D71.11D58.12D28.10D2.29D$455.41D20.11D71.11D59.11D31.37D1208.41D
20.11D71.11D58.12D27.44D$455.39D21.12D71.11D59.11D31.38D1207.39D21.
12D71.11D58.12D27.45D$455.38D22.12D71.11D59.11D31.39D1206.38D22.12D
71.11D58.12D27.46D$455.36D24.12D71.11D59.11D31.40D1205.36D24.12D71.
11D58.12D27.47D$455.34D26.12D71.11D59.11D32.10D6.24D1204.34D26.12D71.
11D58.12D27.47D$455.33D27.12D71.11D59.11D55.18D1203.33D27.12D71.11D
58.12D27.22D9.17D$455.35D25.12D71.11D59.11D57.16D1203.35D25.12D71.11D
58.12D27.18D16.15D$455.36D25.11D71.11D59.11D59.15D1202.36D25.11D71.
11D58.12D27.15D20.14D$455.37D24.11D71.11D59.11D60.14D1202.37D24.11D
71.11D58.12D27.13D24.12D$455.11D11.16D23.11D71.11D59.11D61.14D1201.
11D11.16D23.11D71.11D58.12D27.12D25.13D$455.11D13.14D23.11D71.11D59.
11D62.13D1201.11D13.14D23.11D71.11D58.12D27.11D27.12D$455.11D15.13D
22.11D71.11D59.11D63.12D1201.11D15.13D22.11D71.11D58.12D27.11D27.12D$
455.11D16.13D21.12D70.11D59.11D63.12D1201.11D16.13D21.12D70.11D58.12D
27.11D28.11D$455.11D17.12D21.12D70.11D59.11D63.13D1200.11D17.12D21.
12D70.11D58.12D27.11D28.12D$455.11D17.13D20.12D70.11D59.11D64.12D
1200.11D17.13D20.12D70.11D58.12D27.11D28.12D$455.11D18.12D20.12D70.
11D59.11D64.12D1200.11D18.12D20.12D70.11D58.12D27.11D28.12D$455.11D
19.12D20.11D70.11D59.11D64.12D1200.11D19.12D20.11D70.11D58.12D27.12D
28.11D$455.11D19.12D20.12D69.11D59.11D64.12D1200.11D19.12D20.12D69.
11D58.12D28.11D28.11D$455.11D20.12D19.12D69.11D59.11D64.12D1200.11D
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334.A.A2$59.2A$60.2A$59.A!
#C [[ WIDTH 800 HEIGHT 500 ZOOM -4 ]]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.
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.)
