Conway's Life: Work in Progress

Miscellaneous topics in Conway's Game of Life -- unfinished projects of all kinds and conditions

29 August 2020

Self-constructing diagonal spaceships, now with limit speed c/4!

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 construction arm. 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.

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 ash, which was then converted into a new copy of the spaceship's circuitry by a slow salvo.

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 seed 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.

Here is the incredibly large and complex seed used by the new Demonoid spaceship:

Code: Select all
x = 1296, y = 1352, rule = B3/S23
939bo$938bobo$938b2o16$925bo$924bobo$923bobo$923b2o3$925b2o$925bobo$
926bo6$922bo$921bobo$922b2o$622bo$621bobo283bo$622b2o282bobo$905bobo$
905b2o23b2o$929bobo$928bobo$907b2o20bo$907bobo$908bo7$903bo$902bobo$
902bo2bo55bo$903bobo54bobo$638bo249bo15bo56b2o$637bobo247bobo$638bobo
245bobo12b2o51b2o$639b2o245b2o12bo2bo49bo2bo$900bobo50bo2bo$901bo52b2o
$637b2o249b2o$636bobo249bobo$637bo251bo7$889bo$637b2o249bobo$636bo2bo
231bo11bo3bo2bo$637b2o231bobo9bobo3b2o$644b2o11bo211bobo10bobo$643bo2b
o9bobo210b2o12bo$644bobo10bobo$645bo12b2o$871b2o$871bobo$656b2o214bo$
655bobo$656bo3$870bo$869bobo$868bo2bo$869b2o$656bo197bo11bo$655bobo
195bobo9bobo$655bo2bo3bo11bo177bobo10bo2bo$656b2o3bobo9bobo176b2o12b2o
$661bobo10bobo$662bo12b2o$854b2o$854bobo$673b2o180bo$672bobo$673bo3$
997bo$996bobo$996b2o48bo$675b2o368bobo$674bo2bo159bo16b2o189bo2bo$675b
2o159bobo8b2o5bobo189b2o11bo$835bobo9b2o6bo202bobo$835b2o221b2o$876bo
105bo$875bobo103bobo$837b2o37b2o104b2o$837bobo$679bo158bo30b2o104b2o
59b2o$678bobo187bo2bo102bo2bo58bobo16bo$679b2o187bo2bo102bo2bo59bo16bo
bo$869b2o104b2o77b2o$535bo$534bobo165bo268bo$535b2o164bobo131b2o133bob
o59b2o$702bobo129bo2bo132b2o59bo2bo$703b2o130b2o156b2o36bo2bo$569bo
397b2o24b2o37b2o$568bobo396bobo$568b2o131b2o265b2o49b2o$700bobo114bo
170b2o29bobo$575b2o124bo114bobo169b2o30bo$574bo2bo237bobo144bo45bo$
533bo40bo2bo237b2o15bo128bobo43bobo$532bobo40b2o254bobo128b2o43b2o$
533bobo295b2o182b2o$534b2o167bo113b2o136b2o57bo2bo$702bobo112bobo113bo
20bo2bo56bo2bo$538bo163bo2bo112bo113bobo19bo2bo57b2o$537bobo163b2o228b
2o20b2o$538bo168bo$706bobo160bo56b2o$705bo2bo159bobo54bo2bo$706b2o14bo
93b2o51b2o54bo2bo$721bobo92bobo107b2o$722bobo92bo44b2o$723b2o76bo59bo
2bo137b2o$800bobo58bo2bo74bo13b2o47bobo$799bobo60b2o74bobo12b2o48bo$
721b2o76b2o137b2o$720bobo94b2o155b2o$721bo94bo2bo154b2o$801b2o13bo2bo
129b2o47b2o$801bobo13b2o130b2o46bo2bo$802bo166b2o26bo2bo$969b2o27b2o2$
667bo$666bobo57bo$666b2o57bobo$726b2o$673b2o65bo56bo$606bo65bo2bo63bob
o54bobo$605bobo64bo2bo64bobo53b2o$605b2o66b2o51b2o13b2o40bo36bo$726bob
o53bobo34bobo$612b2o113bo53bobo36b2o$567bo43bo2bo124b2o40b2o13b2o$566b
obo42bo2bo123bobo54bobo15b2o41bo$566b2o44b2o125bo56bo15bo2bo39bobo$
783b2o27bo2bo40b2o$573b2o118bo89bobo27b2o$572bo2bo116bobo83b2o4bo64b2o
$572bo2bo116b2o84b2o68bo2bo69bo$573b2o165b2o106bo2bo68bobo$699b2o38bob
o107b2o69b2o$698bo2bo38bo$698bo2bo54bo25b2o$529bo169b2o54bobo24bobo$
528bobo225bobo24bo$529b2o226b2o233b2o$739b2o251bobo$738bo2bo251bo$738b
o2bo13b2o198bo$501b2o236b2o13bobo26b2o169bobo$500bobo252bo26bo2bo168b
2o$501bo280bo2bo202b2o$783b2o202bo2bo$559bo192b2o233bo2bo$558bobo190bo
2bo233b2o139bo$505b2o52b2o189bo2bo374bobo$504bo2bo243b2o17bo357b2o$
504bo2bo54b2o205bobo$505b2o54bobo206bobo322b2o$531bo29b2o193bo14b2o
321bobo$530bobo222bobo335bobo$531b2o22b2o197bobo177bo159bo$555b2o197b
2o13b2o162bobo174bo$768bobo162b2o174bobo4bo$524b2o243bo142b2o196b2o3bo
bo$523bobo34b2o350b2o200bobo$524bo35b2o539b2o11b2o$1101bobo$907b2o193b
o$907b2o$528b2o$527bo2bo242b2o$527bo2bo222bo18bo2bo128b2o$528b2o51bo
170bobo17bobo129b2o$580bobo169b2o19bo55bo54bo$581b2o245bobo52bobo$759b
2o18bo49b2o52b2o201b2o8bo$758bo2bo16bobo119b2o183bo2bo6bobo4bo$758bo2b
o16b2o42b2o56b2o18b2o183bobo8b2o3bobo$759b2o60bo2bo55bobo203bo13bobo$
821bo2bo56b2o217b2o$822b2o$1084b2o$1083bo2bo$1084b2o2$800bo$799bobo63b
o44bo$800bobo61bobo42bobo$801b2o61b2o43b2o$905b2o$572b2o287b2o42bobo$
572b2o225b2o60bobo42b2o$798bobo61b2o215bo$799bo266bo11bobo4bo$1065bobo
11b2o3bobo$576b2o487bobo15bobo$576b2o488bo16b2o$581bo$580bobo$581b2o$
585b2o$584bobo$584b2o213b2o16bo27bo$798bobo5b2o8bobo25bobo215b2o$799bo
6b2o9bobo24b2o215bo2bo$818b2o241bobo$841b2o219bo$841bobo$816b2o24b2o
49bo$815bobo74bobo130b2o$816bo4b2o69b2o88b2o41bobo$821b2o65b2o92bobo
41bo$888bobo92bo$889b2o$598bo458bo$597bobo217b2o202b2o33bobo4bo$598b2o
216bobo159b2o40bo2bo33b2o3bobo$817bo159bo2bo39bo2bo18b2o5bo11bobo$977b
o2bo40b2o19bobo3bobo10b2o$978b2o63bo4bobo$644bo404bo$508b2o88bo44bobo$
418bo88bobo87bobo43b2o171b2o68b2o$417bobo88bo89b2o215bo2bo67bobo$418b
2o11bo13bo156b2o46b2o163bo2bo68bo72b2o$425bo4bobo11bobo93b2o59bobo45bo
2bo163b2o142bobo$424bobo3b2o12bo2bo91bobo59b2o46bo2bo308bo$425bobo17b
2o65b2o26bo109b2o$426b2o83bo2bo367b2o$511bo2bo152bo213bo2bo$512b2o152b
obo212bo2bo71b2o83bo$544b2o120b2o214b2o71bo2bo69bo11bobo4bo$443b2o98bo
2bo73bo24bo309bo2bo68bobo11b2o3bobo$443bobo97bo2bo72bobo22bobo26b2o
281b2o69bobo15bobo$444b2o98b2o74b2o23b2o25bo2bo352bo16b2o$604b2o66bo2b
o$603bobo42b2o23b2o$604bo42bobo219b2o$647b2o220b2o2$559b2o$558bobo47b
2o254b2o158b2o$559bo47bo2bo253b2o157bo2bo$450bo9bo146bo2bo412bobo$444b
o4bobo7bobo146b2o414bo$443bobo3b2o8bobo152bo48bo$444bobo13bo102b2o48bo
bo46bobo$445b2o115bo2bo48b2o47b2o$562bo2bo52b2o330b2o$563b2o52bobo46b
2o282bobo$463bo153b2o46bobo283bo$462bobo200b2o$462bo2bo542bo10bo$463b
2o542bobo8bobo4bo$946b2o60b2o9b2o3bobo$945bo2bo74bobo$945bo2bo74b2o$
946b2o3$1007b2o$1007b2o3$471bo10bo$465bo4bobo8bobo$464bobo3b2o9b2o$
465bobo174b2o32bo$466b2o174b2o31bobo72bo$676b2o71bobo$609b2o138b2o250b
o$608bobo36b2o351bobo4bo$482b2o125bo37b2o107b2o235b2o6b2o3bobo$482b2o
271bo2bo233bo2bo9bobo$755bo2bo123bo109bobo10b2o$756b2o123bobo105bo3bo$
613b2o93bo172bo2bo103bobo$612bo2bo91bobo172b2o104bo2bo$612bo2bo91b2o
280b2o$613b2o$714b2o$713bo2bo180b2o$489bo223bo2bo180b2o$483bo4bobo223b
2o$482bobo3b2o6b2o388bo16b2o$483bobo9bo2bo386bobo15bobo$484b2o10bobo
386bobo11b2o3bobo$497bo3bo384bo11bobo4bo68bo9bo$500bobo396bo73bobo7bob
o4bo$499bo2bo470bobo8b2o3bobo$500b2o205bo266bo13bobo$706bobo279b2o$
667bo39b2o$666bobo$667b2o41b2o259bo$709bobo258bobo$709b2o258bo2bo$970b
2o$671bo$506bo163bobo$500bo4bobo163b2o228b2o$499bobo3b2o7bo160b2o224bo
bo$500bobo10bobo158bobo225bo$501b2o10bobo158b2o235bo381b2o$514bo395bob
o10b2o368bobo$523bo386bobo10bobo368bo$522bobo386bo7b2o3bobo38bo$523b2o
393bobo4bo26bo11bobo4bo$919bo31bobo11b2o3bobo$951bobo15bobo$641b2o309b
o16b2o$640bobo$641bo321b2o$963b2o$727b2o$727b2o538b2o$645b2o278bo341bo
bo$644bo2bo276bobo21b2o318b2o$644bo2bo276b2o21bo2bo$526bo118b2o84b2o
214bobo$520bo4bobo203b2o215bo$519bobo3b2o7bo395bo$520bobo10bobo393bobo
353b2o$521b2o10bobo162b2o228bo2bo344b2o7bobo$534bo163b2o229b2o12b2o
330bobo8bo$543bo399bobo329b2o$542bobo394b2o3bobo$543b2o158b2o233bobo4b
o$703b2o234bo9$582b2o361b2o$581bobo360bo2bo$546bo35bo358bo3b2o$540bo4b
obo392bobo16b2o$539bobo3b2o7bo384bobo17bobo$540bobo10bobo384bo14b2o3bo
bo$541b2o10bobo30b2o366bobo4bo$554bo30bo2bo366bo$563bo21bo2bo$562bobo
21b2o$563b2o2$640b2o$639bobo$640bo$960bo$959bobo$825b2o132bo2bo$644b2o
178bo2bo132b2o$643bo2bo177bo2bo$643bo2bo178b2o107b2o$644b2o287bo2bo$
566bo13b2o351bo2bo$560bo4bobo5bo5bo2bo351b2o$559bobo3b2o5bobo4bo2bo
247bo$560bobo9b2o6b2o247bobo132bo16b2o$499bo61b2o266b2o132bobo15bobo$
498bobo438bo23bobo11b2o3bobo$497bo2bo437bobo23bo11bobo4bo$498b2o438b2o
37bo3$781b2o$483b2o296b2o$483b2o2$477b2o16bo290b2o$476bobo15bobo289b2o
$475bobo3b2o11bobo85bo9bo$476bo4bobo11bo80bo4bobo7bobo$482bo92bobo3b2o
8bobo145b2o$576bobo13bo145bobo140b2o$577b2o159b2o140bo2bo$880bo2bo115b
2o$741b2o138b2o71b2o28bo14bobo$595bo145bobo209bo2bo26bobo9b2o3bobo$
594bobo145bo210bo2bo25bobo9bobo4bo$594bo2bo356b2o26b2o6bo4bo$476bo118b
2o289bo102bobo$475bobo407bobo100bo2bo$463b2o11b2o407b2o101bobo$462bobo
271b2o221bo29bo$461bobo3b2o266bo2bo219bobo$462bo4bobo265bo2bo219b2o$
468bo267b2o19b2o$484bo271bobo$483bobo257b2o11b2o$482bobo116bo140bobo
38b2o25b2o191bo$482b2o111bo4bobo11bo128bo15b2o22bobo23bobo185bo4bobo$
594bobo3b2o11bobo143bobo22bo24b2o185bobo3bobo10b2o$595bobo15bobo144bo
52b2o181b2o5bo11bobo$596b2o16bo198bobo195b2o3bobo$462bo351bo5b2o188bob
o4bo$461bobo138b2o215bo2bo188bo$449b2o11b2o138b2o215bo2bo$448bobo369b
2o$447bobo3b2o$448bo4bobo$454bo162b2o$470bo145bo2bo205bo$469bobo145bob
o204bobo$468bobo147bo205b2o190bo$468b2o545bobo$1015bo2bo$1016b2o4$451b
o373b2o$445b2o3bobo371bobo$444bobo3b2o372b2o$445bo382b2o190bo16b2o$
431b2o395bobo188bobo15bobo$430bobo396bo189bobo11b2o3bobo$429bobo3b2o
583bo11bobo4bo$430bo4bobo595bo$436bo$798b2o$797bobo$797b2o2$800b2o$
800bobo$801bo237bo$1038bobo$939b2o97b2o11b2o$938bo2bo109bobo$938bo2bo
105b2o3bobo$433b2o504b2o105bobo4bo$432bobo612bo$433bo597bo$424bo605bob
o$411b2o10bobo33b2o356b2o125bo86bobo$410bobo10bobo32bo2bo354bobo124bob
o86b2o$409bobo3b2o7bo33bo2bo35b2o317b2o125b2o$410bo4bobo41b2o35bo2bo$
416bo79bo2bo319b2o$497b2o320bobo13b2o$820bo14bobo$455bo380bo213b2o$
454bobo592bo2bo$455b2o36bo38b2o516bobo3b2o$492bobo36bo2bo516bo3bo2bo$
493b2o36bo2bo300b2o217bo2bo$410bo121b2o300bobo218b2o13b2o$409bobo422b
2o234bobo$397b2o11b2o170b2o482b2o3bobo$396bobo35b2o146bobo117b2o133b2o
226bobo4bo$395bobo3b2o30bo2bo91bo54b2o116bo2bo132bobo226bo$396bo4bobo
29bo2bo90bobo49b2o77b2o41bo2bo133bo$402bo31b2o92b2o39b2o7bobo76bo2bo
41b2o67b2o$418bo149bo2bo7bo77bo2bo109bo2bo$417bobo148bo2bo86b2o49b2o
59bo2bo87b2o$416bobo150b2o137bobo60b2o88b2o$416b2o12bo278bo$429bobo
346b2o$430b2o345bobo70b2o$565bo92bo119bo71bobo12b2o205b2o$396bo167bobo
90bobo191bo13b2o204bo2bo$395bobo167b2o90b2o409bo3b2o$383b2o11b2o669bob
o16b2o$382bobo550b2o129bobo17bobo$381bobo3b2o545bo2bo129bo14b2o3bobo$
382bo4bobo263b2o279bo2bo143bobo4bo$388bo264b2o4bo275b2o145bo$404bo163b
2o88bobo13b2o$403bobo162bobo87b2o13bo2bo$402bobo164b2o70b2o30bo2bo$
402b2o161b2o74bobo30b2o264bo$564bobo75b2o12b2o281bobo$565bo90bobo280b
2o159b2o$639b2o16bobo440bobo$638bobo17bo309b2o131bo$639bo34bo292bo2bo$
673bobo291bo2bo$380bo292b2o107b2o184b2o$379bobo399bo2bo$378bo2bo399bo
2bo$379b2o401b2o$973bo$675bo27b2o84b2o181bobo$674bobo25bo2bo82bobo80b
2o99b2o$557b2o62b2o51b2o26bo2bo83bo81bobo$557bobo61bobo79b2o167bo$558b
2o62b2o$358b2o16bo177b2o116b2o36b2o$357bobo15bobo175bobo63b2o31b2o18bo
bo9b2o6bo16bobo$356bobo3b2o11bobo176bo63bobo30bo2bo18bobo8b2o5bobo16bo
$357bo4bobo11bo242bo31bo2bo19bo16b2o$363bo288b2o$795b2o$450b2o193b2o
147bo2bo$449bo2bo192bobo146bo2bo$449bo2bo193bo148b2o$450b2o$426b2o374b
2o$425bo2bo372bobo$425bo2bo263bo109bo$426b2o18bo152b2o90bobo$445bobo
151bobo89b2o$359bo86b2o152b2o$353b2o3bobo349bo$352bobo3b2o62bo153b2o
19b2o90b2o18bobo$353bo67bobo114b2o35bobo18bobo90bobo10b2o5bo2bo$339b2o
81b2o114bobo35bo20bo92bobo9bobo5b2o252b2o$338bobo198b2o150bo11b2o258bo
2bo$337bobo3b2o190b2o426bo2bo$338bo4bobo188bobo342b2o83b2o$344bo190bo
343bobo$880bo28b2o$909bobo$558b2o350bo58bo$558b2o408bobo$890b2o76b2o$
889bobo$889b2o$554b2o155bo203b2o$554b2o154bobo179b2o21bobo$710b2o180bo
bo21bo$723bo169bo$323b2o397bobo$322bobo9b2o6b2o299b2o63b2o13b2o219b2o$
321bobo3b2o5bobo4bo2bo297bo2bo62bobo233bobo$322bo4bobo5bo5bo2bo297bo2b
o63bobo233bo$328bo13b2o299b2o65bo$723b2o$636b2o85bobo$636bobo85bo$637b
o2$803b2o$802bo2bo$802bo2bo$530b2o271b2o$325bo204b2o9b2o186bo$319b2o3b
obo213bobo185bobo79b2o$318bobo3b2o215bo186b2o13b2o64bobo63b2o38b2o38b
2o$319bo422bobo65bo63bo2bo37bobo36bobo$305b2o219b2o213bobo130bo2bo38bo
37b2o$304bobo219b2o198b2o14bo132b2o81b2o$303bobo3b2o415bobo229bobo$
304bo4bobo415bobo152b2o75bo$310bo417bo17b2o133bobo$500b2o243bo2bo133bo
64b2o14b2o$499bobo136b2o104bo2bo199b2o13bo2bo$500bo136bo2bo104b2o215bo
2bo$529b2o106bo2bo322b2o$529b2o107b2o$743bo207b2o$631b2o109bobo206b2o
36b2o$524b2o105bobo108b2o224bo19bo2bo$304b2o218b2o106bo334bobo18bo2bo$
303bo2bo660b2o20b2o$303bobo128b2o304b2o$304bo60b2o66bo2bo303bobo$364bo
2bo65bo2bo304bobo$364bo2bo66b2o306bo251bo$286b2o77b2o394bo231bobo$285b
obo13bo99b2o357bobo230b2o$284bobo3b2o8bobo97bo2bo80b2o275b2o$285bo4bob
o7bobo97bo2bo26bo53b2o250b2o145b2o$291bo9bo59bo39b2o26bobo303bo2bo143b
o2bo$360bobo67b2o303bo2bo143bo2bo$361b2o373b2o23b2o120b2o90b2o$480b2o
279bobo211bobo$340b2o55bo77b2o3b2o280bo127b2o84bo33b2o$339bo2bo53bobo
76b2o412bobo117bo2bo$339bo2bo54b2o491bo118bobo$340b2o395bo265bo6bo$
470b2o264bobo263bobo$285b2o183b2o265b2o263bobo$284bo2bo715bo$284bobo
49bo430bo135b2o$285bo49bobo428bobo133bo2bo$336b2o184b2o217b2o23b2o134b
o2bo$521bobo212bo4b2o160b2o46b2o$267b2o253bo212bobo213bobo$266bobo13bo
453b2o26b2o144b2o40bo53b2o$265bobo3b2o8bobo480bobo142bobo94bobo$266bo
4bobo7bobo357b2o122bobo142bo96bo$272bo9bo357bo2bo81b2o11b2o26bo$640bo
2bo80bo2bo9bobo$641b2o81bobo9bobo$725bo11bo$634b2o79b2o$634bobo77bo2bo
216b2o$635bo79b2o216bo2bo$933bo2bo$934b2o$266b2o$265bo2bo672b2o$266b2o
672bobo$941bo$250b2o204b2o$249bobo13bo190b2o$248bobo3b2o8bobo$249bo4bo
bo6bo2bo$255bo8b2o185b2o261bo$451b2o39b2o219bobo$492b2o205b2o13b2o84bo
$699bobo97bobo149b2o$700bobo96bobo3b2o143bo2bo$701bo14b2o82bo3bo2bo
142bo2bo$488b2o225bobo87bobo143b2o$488b2o224bobo89bo$2o633b2o59b2o17bo
242b2o$2o632bo2bo57bo2bo258bobo$5b2o245bo381bo2bo58bo2bo258bo$6bo239b
2o3bobo381b2o60b2o$3b3o239bobo3b2o$3bo242bo100b2o115b2o162b2o$232b2o
112bo2bo113bobo162bobo69bo105bo$231bobo112bo2bo114bo164bo56bo12bobo
103bobo12bo$230bobo3b2o109b2o336bobo12b2o103b2o12bobo$231bo4bobo447bob
o129bobo$237bo449bo131bo$702b2o99b2o$343bo345bo11bobo99bobo11bo$342bob
o251b2o90bobo9bobo101bobo9bobo$23b2o318b2o250bo2bo89bobo10bo103bo10bob
o$22bobo419b2o149bo2bo90bo127bo$23bo419bobo150b2o$444bo$589b2o$28b2o
559bobo$28b2o204bo355bo$228b2o3bobo$227bobo3b2o449bo137bo$228bo454bobo
135bobo$214b2o454b2o12b2o135b2o12b2o$213bobo454bobo161bobo$212bobo3b2o
193b2o256bo163bo$213bo4bobo191bobo271b2o131b2o$219bo193bo271bobo131bob
o$684bobo133bobo$671b2o12bo135bo12b2o$442b2o226bo2bo159bo2bo$442bobo
226b2o161b2o$443b2o2$440b2o$439bobo$213b2o225bo$212bo2bo452bo169bo$
212bo2bo216b2o233bobo167bobo$213b2o216bobo234b2o167b2o$432bo2$208b2o
460b2o163b2o11b2o$194b2o11bobo459bobo163bobo9bo2bo$193bobo11b2o459bobo
165bobo9bobo$192bobo3b2o5b2o314b2o146bo167bo11bo$193bo4bobo3bobo313bo
2bo334b2o$199bo4b2o314bo2bo333bo2bo$521b2o335b2o2$514b2o38b2o$514bobo
36bo2bo84b2o$357b2o156bo37bo2bo84bobo$356bo2bo194b2o86bobo$356bo2bo12b
2o269bo$193bo163b2o13bobo172b2o$192bobo178b2o172bobo$193b2o174b2o42b2o
133bo89b2o$368bobo42bobo221bo2bo$353bo15bo44b2o222bo2bo218bo$188bo163b
obo55b2o227b2o218bobo13b2o$187bobo163b2o54bobo447b2o13bo2bo$187bo2bo
219bo463bo2bo$174b2o12b2o417b2o33bo232b2o$173bobo430bo2bo31bobo213b2o$
172bobo3b2o426bo2bo32b2o213bobo$173bo4bobo120b2o304b2o249bobo$179bo
120bo2bo555bo$300bo2bo35b2o259b2o28b2o12b2o229bo$301b2o35bo2bo258bobo
26bo2bo10bobo228bobo$338bo2bo259bo27bo2bo9bobo229b2o$339b2o289b2o11bo
2$297bo$296bobo326b2o$297b2o36bo87b2o199bobo249bo$334bobo86bobo198b2o
249bobo$171bo163b2o19b2o66b2o87b2o107b2o251b2o$170bobo4bo178bobo40b2o
111bo2bo105bobo$158b2o10bobo3bobo178b2o39bobo20b2o89bo2bo105b2o$157bob
o11bo5b2o174b2o44bo20bobo90b2o358b2o$156bobo3b2o188bobo66bo451bobo$
157bo4bobo188bo152b2o366bobo$163bo342bobo113bo252bo$507bo113bobo$622b
2o$285b2o139b2o180b2o$284bo2bo137bo2bo178bobo$284bo2bo137bo2bo179bo15b
2o251b2o$285b2o139b2o195bobo251bobo$622bobo253bo$419b2o202bo$378b2o39b
obo46b2o26b2o$281bo95bobo40bo46bo2bo24bo2bo$280bobo95bo88bo2bo24bo2bo$
281b2o185b2o26b2o106b2o$603bo2bo$461b2o26b2o113b2o$461bobo25bobo$341b
2o119bo27bo$340bobo$341bo243bo$584bobo$583bobo16bo$129b2o221b2o229b2o
16bobo$128bobo220bobo248b2o$129bo222bo2$604b2o$591b2o10bobo$591bobo8bo
bo$592bo10bo2$272b2o$271bo2bo$271bo2bo$272b2o46b2o$319bobo266bo$320bo
266bobo$588b2o$268bo$267bobo$268b2o320b2o$577b2o10bobo$577bobo8bobo$
578bo10bo2$435b2o135bo$434bo2bo133bobo$434bo2bo133bo2bo$435b2o135b2o2$
428b2o$409b2o17bobo$408bo2bo17bo$408bo2bo$409b2o$349b2o217bo$348bobo
51b2o148b2o13bobo$349bo52bobo146bo2bo13b2o$403bo147bo2bo$552b2o$261b2o
307b2o$260bo2bo305bobo$260bo2bo304bobo$261b2o306bo$553bo$552bobo$553b
2o$257bo$256bobo$257b2o$302b2o$302b2o81b2o165bo$384bo2bo163bobo$384bo
2bo149b2o13b2o$243b2o52b2o86b2o150bobo$242bo2bo51b2o36b2o201bobo$242bo
2bo88bobo41b2o159bo14b2o$243b2o90bo42bobo172bobo$379bo172bobo$534b2o
17bo$533bo2bo$239bo48b2o244bo2bo$238bobo46bobo245b2o$239b2o47bo35b2o$
324bobo$325b2o211bo$537bobo$322b2o214b2o$321bobo202bo$322bo202bobo$
525b2o13b2o$539bobo$538bobo$359b2o178bo$358bo2bo163b2o$358bo2bo162bobo
$359b2o164bo2$352b2o$352bobo$353bo$275b2o52b2o$275bobo50bo2bo$276b2o
50bo2bo188bo$272b2o55b2o173b2o13bobo$271bobo229bo2bo13b2o$272bo49b2o
179bo2bo$322bobo179b2o$323bo198b2o$521bobo$520bobo16b2o$273b2o246bo16b
o2bo$272bobo230bo32bobo$273bo230bobo32bo$505b2o$540bo$539bobo$539b2o2$
504bo$503bobo$490b2o12b2o$490bobo$491bo$318b2o186b2o$317bo2bo184bobo$
317bo2bo183bobo$318b2o171b2o12bo$490bo2bo$311b2o178b2o$311bobo$312bo4$
488bo$487bobo$488b2o3$490b2o$489bobo$488bobo$468b2o19bo$468bobo$469bo
4$291b2o176b2o$290bo2bo174bo2bo$290bo2bo175b2o$291b2o2$276bo7b2o$275bo
bo6bobo$276bo8bo$466bo$272b2o191bobo$271bobo192b2o$270bobo$271bo$468b
2o$467bobo$448b2o16bobo$447bobo17bo$448bo2$266b2o$265bobo$266bo3$444b
2o$443bo2bo$444b2o6$442bo$441bobo$442b2o3$431bo12b2o$430bobo10bobo$
429bo2bo9bobo$430b2o11bo$423b2o$422bo2bo$423b2o8$423bo$422bobo$423b2o
3$412bo12b2o$411bobo10bobo$406b2o3bobo9bobo$405bo2bo3bo11bo$405bobo$
406bo7$406bo$405bobo$406b2o3$408b2o$407bobo$406bobo$407bo$386b2o$385bo
bo$386bo7$382b2o$381bo2bo$382b2o6$380bo$379bobo$380b2o288bo$669bobo$
670bobo$382b2o287b2o$381bobo$380bobo$381bo5$378b2o$377bobo$378bo25$
360b2o$360bobo$361bo337$30b3o$32bo$31bo!
[[ 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 ]]

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 crab. Crab spaceships are glide symmetric and have two attachment points for long barge/boat wicks. These wicks can burn cleanly, faster than the wickstretcher can travel.

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.

Code: Select all
x = 511, y = 511, rule = LifeSuper
67.pA.pA$68.2pA$68.pA47$116.S$117.S$115.3S118$277.M$276.M.M$277.2M35.
3N$316.N$315.N$312.2N$312.N2$310.N3.2N$309.N.N2.2N5.3N$258.2M48.N.N3.
N.N6.N$257.M2.M46.N.N6.2N4.N$257.M.M33.3N10.N.N6.N.4N$258.M36.N9.N.N
10.2N$280.2M5.2M5.N9.N.N8.N$279.M2.M3.M.M14.N.N8.N.N$265.2M13.M.M3.M
15.N.N8.N.N$265.2M14.M3.2M14.N.N8.N.N$300.N.N8.N.N$299.N.N8.N.N$252.
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
.N8.N.N3.3N$250.2M15.2M3.2M7.M11.N.N8.N.N6.N$249.M.M15.2M3.M.M4.3M10.
N.N8.N.N6.N$248.M.M22.M4.M12.N.N8.N.N$249.M28.2M10.N.N8.N.N$289.N.N8.
N.N$266.2M20.N.N8.N.N$266.2M19.N.N8.N.N$287.2N8.N.N8.2M$243.2M51.N.N
10.M$242.M.M50.N.N8.3M$242.2M15.2M34.2N9.M$259.M.M$261.M10.N$243.M17.
2M8.N.N33.2M$242.M.M27.2N32.M2.M$242.M.M25.2M35.M.M$243.M19.2M5.2M29.
2M5.M$264.M10.2M24.M$264.M.M3.2M2.M.M22.M.M$234.2M29.2M2.M2.M2.M23.2M
$234.2M33.M.M$231.M38.M45.2M6.M$230.M.M7.M65.2M8.M.M4.M.M$230.M.M5.3M
33.M26.M4.M.M8.M.M4.2M$231.M5.M6.M28.M.M5.2M5.2N10.M.M4.2M9.M$237.2M
4.M.M23.M3.M2.M3.M.M5.N.N10.2M$242.M.M18.2M4.M4.M.M4.M7.N$242.2M19.M.
M3.M5.M31.M$265.M14.M25.M.M5.2M$265.2M12.M.M.2M20.M2.M5.2M$272.3M3.M
2.M.2M21.2M$279.2M2$293.2M$257.2M8.2M11.2M11.2M$257.2M7.M2.M10.M$261.
M4.M2.M11.3M$260.M.M4.2M14.M$260.2M24.M$286.3M$289.M$266.M21.2M14.M$
265.M.M36.3M$264.M2.M32.M6.M$242.2M21.2M22.2M8.M.M4.2M$241.M.M16.2M
27.M10.M.M$242.M16.M2.M24.M.M11.2M$260.2M21.M3.2M$282.M.M$281.M.M$
281.2M$242.2M28.M$241.M2.M26.M.M$241.M2.M5.2M18.M.M$242.2M5.M2.M17.2M
$249.M2.M31.M$250.2M22.2M7.M.M$274.M9.M$272.M.M$272.2M5.2M$279.2M3$
265.M$264.M.M$255.2M7.2M$255.M.M20.2M$256.M20.M.M$278.M$233.3M$235.M$
234.M87$125.3W$127.W$126.W5$111.3W$113.W$112.W3$427.2S$426.2S$428.S
12$96.3S$98.S$97.S$132.3W$134.W$133.W21$71.2S$72.2S$71.S31$508.2pA$
508.pA.pA$508.pA44$27.2pA$26.pA.pA$28.pA23$.pA$.2pA$pA.pA!
#C [[ X 22 Y -37 Z 5 ]]

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.

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.

Here is a 21-glider slow salvo 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.

Code: Select all
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 ]]

26 July 2020

Spaceship Construction For Fun and Profit

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.

The full list of spaceships with known glider recipes can be found on the LifeWiki Glider Synthesis page. Considering that only one spaceship in the above list (60P5H2V0) had a known synthesis at the beginning of 2013, this is a lot of progress!

Here's a showcase animation created by Saka a few months ago to document the construction of 58P5H1V1, a 58-bit c/5 spaceship:

Code: Select all
x = 536, y = 536, rule = B3/S23
504bobo$504b2o$505bo2$503bo$501b2o$502b2o5bobo$17bo491b2o$18bo491bo$
16b3o$492bo20bobo$491bo21b2o8bobo$491b3o20bo8b2o$20bo503bo$5bobo13b2o$
6b2o12b2o$6bo2$4bo510bo$2bobo509bo$3b2o10bobo496b3o8bo$9bo6b2o505b2o$
10b2o4bo507b2o$9b2o$529bo$527b2o$493bobo32b2o$481bobo9b2o$481b2o11bo$
482bo52bo$533b2o$56bo430bobo44b2o$54bobo430b2o40bobo$55b2o431bo40b2o$
530bo$62bo$63bo$61b3o$487bo$486bo$486b3o20bo$463bobo41b2o$463b2o43b2o
13bo$464bo58bobo$523b2o$67bo$68bo435bo$66b3o426bo6b2o$470bo24bobo5b2o$
31bo438bobo22b2o$32b2o436b2o$31b2o$508bo$506b2o$74bo432b2o$75bo$73b3o$
461bo$461bobo$461b2o4$81bo404bo$82bo402bo$80b3o402b3o$452bo$452bobo$
436bo15b2o$434b2o$426bobo6b2o57bo$426b2o64b2o$427bo49bo15b2o$73bo402bo
$74bo401b3o$72b3o351bo$425bo$425b3o2$61bo$59bobo$60b2o406bo$467bo$65bo
bo399b3o$66b2o3bo$66bo5bo6bo$70b3o7b2o$79b2o9$408bo$407bo$400bobo4b3o$
114bo285b2o63bobo$115bo285bo63b2o$113b3o350bo6$465bo$458bo4b2o$458bobo
3b2o$458b2o5$394bobo$123bo270b2o$124b2o269bo$123b2o$136bo$137bo$135b3o
$398bo$397bo$397b3o$134bobo$135b2o300bo$135bo301bobo$437b2o$134bo$135b
o$133b3o$385bo$384bo52bo$384b3o48b2o$436b2o$380bo30bo$373bo4b2o31bobo$
371b2o6b2o30b2o$141bo230b2o46bo$139bobo276b2o$140b2o277b2o$372bo$129bo
bo240bobo$130b2o240b2o$130bo4$363bo37bo$140bo222bobo35bobo$141b2o27bo
192b2o36b2o$140b2o29b2o$170b2o6$382bo$382bobo$382b2o11$196bo$197b2o$
196b2o4$364bo$348bo15bobo$348bobo13b2o$348b2o10$195bo$196b2o134bobo25b
o$195b2o135b2o26bobo$333bo26b2o2$196bo$194bobo$195b2o$178bo21bobo151bo
bo2bo$176bobo22b2o151b2o3bobo$177b2o22bo141bo11bo3b2o$341b2o$342b2o10$
205bo$203bobo$204b2o2$212bo$213b2o$212b2o103$214bo$197b2o15b2o$198b2o
7b3o3bobo$197bo11bo136b3o$208bo137bo$320b2o25bo$319b2o$321bo3$320b3o$
320bo14b2o$182bo138bo12b2o$182b2o152bo$181bobo27bo$211b2o$210bobo130bo
$337b3o2b2o$337bo4bobo$338bo15$346b2o10bo$185b3o158bobo8b2o$187bo158bo
10bobo$186bo$181b2o$180bobo195bo$182bo7b2o185b2o$189bobo185bobo$191bo
2$178b3o203b3o$180bo172b3o23bo4bo$179bo173bo24b2o5bo$354bo23bobo12$
134b2o$135b2o$134bo2$140bo$140b2o$139bobo3$136b2o$137b2o$98b2o31bo4bo$
97bobo31b2o$99bo30bobo239b2o$371b2o$373bo2$414b2o$409b2o3bobo$404b2o2b
2o4bo$404bobo3bo$404bo8$418bo$417b2o$417bobo8$434b2o$434bobo$434bo14$
141b3o$143bo$142bo$78b3o$80bo$79bo2$75bo$75b2o$65b2o7bobo$64bobo$66bo
3$69bo$69b2o$68bobo$470b2o$449bo20bobo$95b2o351b2o20bo$94bobo351bobo$
96bo2$90b2o$91b2o386b2o$90bo369b2o17bobo$460bobo16bo$449b2o9bo$449bobo
$83b2o364bo$84b2o$83bo404b2o$451b2o35bobo$88b3o359b2o36bo$90bo361bo$
89bo$498b2o$498bobo$454b3o41bo$454bo$455bo3$502b3o$502bo$503bo2$28b2o$
27bobo$29bo7$15b2o$bo12bobo$b2o13bo$obo8bo$11b2o$10bobo4$2b2o$3b2o480b
o$2bo481b2o$484bobo2$8b2o40b3o$9b2o41bo$8bo42bo5$12b3o506bo$14bo505b2o
$13bo4b2o500bobo$17bobo$19bo506b2o$514b2o10bobo$41b3o469b2o11bo$43bo
471bo$21b2o19bo$20bobo$22bo15b2o$39b2o472bo$28bo9bo473b2o$28b2o482bobo
$27bobo$520b2o$519b2o$521bo$515b3o$515bo$40b2o474bo$41b2o$40bo!
[[
WIDTH 720
AUTOSTART
GPS 20
PAUSE 2 "58P5H1V1 Synthesis"
PAUSE 2 "By Kazyan (Tanner Jacobi)\nand Goldtiger997"
PAUSE 2 "The synthesis was posted \non the forums on April 3, 2020."
T 60 "At the time this animation was made,\nit cost 161 gliders."
T 139 "It has since been reduced to 100 gliders."
GPS 30 T 202 "Let's zoom in."
ZOOM 12 GPS 60
T 203 PAUSE 3 "First glider collision."
T 216 PAUSE 3 "Beehive at beehive made."
PAUSE 2 "This will become the 'centerpiece'\nof the consttruction."
T 455 "A complex seed constellation is gradually\nbuilt up around the beehive at beehive."
T 456 PAUSE 3 "OK, that last part was cool.\nIt will happen again on the other side."
X -12
PAUSE 2 "11 cells are added all at once."
T 485 "\n"
GPS 30 "Magic..."
T 550 X 0
COLOR POLY Red
POLYT 550 650 50
POLYLINE 266 252 269 255 264 260 261 257 266 252 12
POLYLINE 280 266 283 269 278 274 275 271 280 266 12
T 599 X 10 Y -10 "More of the superstructure is\nincrementally constructed."
T 600 PAUSE 3 "See those 2 long barges? \n They're going to get extended 4 times."
T 872 "\n"
T 873 PAUSE 3 "...And now they're boats, I guess. \n (Barges are a type of boat, right?)"
PAUSE 1 X 0 Y 0
T 936 PAUSE 3 "Here comes the really fun part!" ZOOM 5.5
PAUSE 2 "Hope you don't mind some SFX..."
PAUSE 0.5 LAYERS 10 DEPTH 2 THEME Fire
PAUSE 0.5 ZOOM 1 ANGLE 45 T 945
PAUSE 1 T 960 ZOOM 7.7 ANGLE 0 THEME Poison LAYERS 1
T 1000 "And the ship is done!"
T 1094 "Wait, don't forget cleanup!" THEME Blues X -6 Y 3
T 1100 PAUSE 3 X 25 Y -25 "The construction is complete!" ZOOM 15
LOOP 1500
]]
#C By: Saka

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.

Code: Select all
x = 425, y = 162, rule = B3/S23
241bo159bo$240bo159bo$240b3o157b3o3$172bo234bo$173bo12bo218b2o$171b3o
12bobo213bo3b2o$186b2o212b2o$401b2o$130bo280bo$131bo278bo$71bo13b2o42b
3o104bo44bo53bo54bo19b3o$71b2o12bobo147bobo42bobo51bobo52bobo$70bobo
12bo148bobo37b2o3bobo46b2o3bobo47b2o3bobo$6bo120b2o10bo38b2o54bo39bo4b
o16bo31bo4bo49bo4bo$7bo118bobo11bo36bobo51b2obo40b3obo15bo33b3obo21bo
28b3obo$5b3o117bobo10b3o35bobo51bo2bo44bo16b3o34bo22bobo29bo$125b2o49b
2o53b2o44bo53bo23b2o29bo$79b2o48b2o49b2o53b2o39bo3b2o48bo3b2o49bo3b2o$
78bo2bo46bo2bo47bo2bo51bo2bo37bo3bo2bo39bo6bo3bo2bo47bo3bo2bo13bo$79b
2obo7b2o37b2obo47b2obo51b2obo36b2o3b2obo39b2o4b2o3b2obo6bo39b2o3b2obo
6bo4b2o$81bobo6bobo38bobo48bobo29b3o20bobo42bobo37b2o12bobo4bobo45bobo
4bobo3bobo$81bobo6bo40bobo48bobo31bo20bobo42bobo51bobo5bo46bobo5bo$82b
o49bo50bo3b2o26bo22bo3b2o39bo3b2o48bo3b3o48bo3b3o$186bobo52bobo42bobo
51bo54bo$185bobo52bobo42bobo51bobo52bobo$185b2o29bo23b2o43b2o52bobo49b
obo2bo$216b2o122bo50b2o3bobo$215bobo179b2o$7b2o129b2o83b2o71b2o114b3o$
bo4bobo130b2o81bobo71bobo113bo$b2o5bo129bo85bo71bo116bo$obo234bo$236b
2o87b3o$22b3o195bo15bobo88bo$22bo23bo173b2o104bo$23bo22b2o171bobo98b2o
$45bobo273b2o$320bo2$328b2o$329b2o3b2o$328bo4bobo$335bo11$114b2o$115b
2o$114bo26$356bo$357b2o$356b2o$364bo$362bobo$363b2o$356bo$357b2o49bo$
356b2o48b2o$400bobo4b2o$64bobo333b2o$65b2o334bo$65bo58bo235bo$125bo
235bo$77bo45b3o233b3o29bo$75b2o314bobo$76b2o128bo141bo27bobo12b2o22bob
o$134bobo70b2o137bobo28b2o27bo8b2o$135b2o69b2o139b2o28bo26b2o10bo$135b
o75bobo191b2o$212b2o$212bo$415bo$413b2o$414b2o$208bo$209b2o$208b2o$
218bobo$17bobo132bo66b2o15bo68bo74bo$18b2o36bo94bobo65bo10bo4bobo61bo
4bobo67bo4bobo$18bo37b2o79b2o11bobo76bobo2bobo58b2obobo2bobo64b2obobo
2bobo28bo$55bobo78bobo12bo77bo2bo2bo53bo6bobo2bo2bo66bobo2bo2bo28bo$
138bo75b2o14b2o58bo5bo2b2o70bo2b2o32b3o$16bo50bo27bobo54bo60bobo20bo
51b3o6b2o6bo51bo14b2o6bo$10b2o3bobo43b2o3bobo5b2o19b2o49b2o3bobo5b2o
54bo14b2o3bobo5b2o54b2o3bobo5b2o43b2o15b2o3bobo5b2o$10bo4bo2bo42bo4bo
2bo3bo2bo19bo49bo4bo2bo3bo2bo68bo4bo2bo3bo2bo53bo4bo2bo3bo2bo41bobo15b
o4bo2bo3bo2bo$11b3obo3bo42b3obo3bo3bobo70b3obo3bo3bobo69b3obo3bo3bobo
54b3obo3bo3bobo60b3obo3bo3bobo$14bo5bo44bo5bo3bo58b2o14bo5bo3bo73bo5bo
3bo58bo5bo3bo58bo5bo5bo3bo$13bo7bo42bo7bo62b2o12bo7bo75bo7bo60bo7bo59b
3o4bo7bo$12bo3b2o4bo40bo3b2o4bo60bo13bo3b2o4bo73bo3b2o4bo58bo3b2o4bo
57bo6bo3b2o4bo$11bo3bo2bo4bo8b2o28bo3bo2bo4bo72bo3bo2bo4bo71bo3bo2bo4b
o56bo3bo2bo4bo56b2o4bo3bo2bo4bo25bobo$11b2o3b2obo4bo6b2o29b2o3b2obo4bo
71b2o3b2obo4bo70b2o3b2obo4bo55b2o3b2obo4bo61b2o3b2obo4bo24b2o$18bobo4b
o7bo35bobo4bo77bobo4bo4bo71bobo4bo4bo56bobo4bo4bo62bobo4bo4bo19bo$18bo
bo5bo42bobo5bo76bobo5bo2bobo50b2o18bobo5bo2bobo55bobo5bo2bobo61bobo5bo
2bobo$19bo3b3o44bo3b3o23b2o53bo3b3o2bobo50bobo19bo3b3o2bobo57bo3b3o2bo
bo63bo3b3o2bobo$22bo50bo25b2o57bo6bo53bo22bo6bo61bo6bo67bo6bo13b2o$21b
obo48bobo26bo55bobo81bobo42b2o22bobo35b3o34bobo18b2o$18bobo2bo45bobo2b
o79bobo2bo78bobo2bo4bo38b2o18bobo2bo4bo32bo31bobo2bo4bo15bo$18b2o3bobo
43b2o3bobo77b2o3bobo76b2o3bobobobo36bo20b2o3bobobobo30bo32b2o3bobobobo
$24b2o49b2o83b2o82b2obo2bo62b2obo2bo32b2o34b2obo2bo$212b3o33b2o65bob2o
34b2o35bob2o$214bo100bo36bo32b2o3bo$213bo102b3o66bo5b3o$79b2o237bo64bo
bo7bo$80b2o301b2o$79bo268b3o$350bo$163b3o183bo3bo$165bo149b2o36b2o$
157bo6bo13b2o71b2o62bobo34bobo4bo59b3o$157b2o18b2o55b3o13b2o49bo13bo
43b2o58bo$156bobo20bo56bo15bo48b2o55bobo24b2o33bo$235bo64bobo82bobo22b
3o$385bo24bo$245b3o163bo$228b2o17bo169bo5bo$227bobo16bo13b2o154b2o4b2o
$229bo29b2o155bobo3bobo$261bo96b3o$254bo105bo3b2o7bo$182b2o69b2o104bo
5b2o6b2o$182bobo68bobo7bo100bo7bobo$182bo79b2o$262bobo102b2o7b2o$366bo
bo6bobo$368bo8bo28b3o$406bo$407bo!
#C [[ THEME Fire LOOP 150 ]]
#C [[ POI X -196 Y -60 Z 11 ]]
#C [[ POI X -130 Y -60 Z 11 ]]
#C [[ POI X -80 Y -60 Z 11 ]]
#C [[ POI X -29 Y -60 Z 11 ]]
#C [[ POI X 26 Y -60 Z 11 ]]
#C [[ POI X 71 Y -60 Z 11 ]]
#C [[ POI X 125 Y -60 Z 11 ]]
#C [[ POI X 180 Y -60 Z 11 ]]
#C [[ POI X -193 Y 44 Z 11 ]]
#C [[ POI X -142 Y 44 Z 11 ]]
#C [[ POI X -57 Y 44 Z 11 ]]
#C [[ POI X 27 Y 44 Z 8 ]]
#C [[ POI X 96 Y 44 Z 8 ]]
#C [[ POI X 171 Y 44 Z 7 ]]

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 documented in a LifeWiki article.

02 July 2020

Newer Better Faster Smaller Stable Signal Circuits

In 2020 so far there's been a major surge in interest in stable circuitry. For example, on January 26 Entity Valkyrie constructed a period-11040 spider gun, and on May 22 a 58P5H1V1 gun -- 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.

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 Bandersnatch, so named because of its association with Snarks and Boojums in Lewis Carroll's poem The Hunting of the Snark (appropriately subtitled "an agony in eight fits".)

Code: Select all
#N Bandersnatch #O Entity Valkyrie and Martin Grant, 5 June 2020
#C Spartan 0-degree color-changing glider shifter
x = 50, y = 46, rule = B3/S23
o$b2o$2o16$45bo$44bobo$44bobo$43b2ob3o$31b2o16bo$31b2o10b2ob3o$43b2ob
o7$46b2o$37bo8b2o$36bobo$36bo2bo$37b2o$20b2o$19bobo$19bo24b2o$18b2o24b
2o5$35b2o$35b2o!
#C [[ THUMBNAIL THUMBSIZE 3 AUTOSTART WIDTH 640 HEIGHT 540 X 7 Y 10 THUMBSIZE 2 ZOOM 16 GPS 40 LOOP 200 ]]
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 863-tick recovery time. (The current record is a larger staged-recovery design with 742-tick recovery time.) The Bandersnatch consists of just seven well-separated still lifes, which is Spartan by the modern definition, so it is bound to become very useful in self-constructing circuitry as well.

In April, Louis-François Handfield constructed a much more compact universal regulator than the previous best known mechanism.

The following month Handfield also adapted Martin Grant's new HL161H conduit to make a useful color-changing edge shooter, HSW47T214. Its output lane is transparent, so it can serve as a merge circuit in a fairly compact glider adjustment toolkit.

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.

Code: Select all
#C universal *WSS-to-glider converter, repeat time 588 ticks
x = 679, y = 92, rule = B3/S23
591bo$591b3o$594bo$593b2o8b2o$603bo$601bobo18bo11b2o$601b2o18bobo10b2o
$587b2o32bobo$587b2o26b2o2b3ob2o$615bo2bo$613bobo3b3ob2o$613b2o6bob2o$
587b2o$587b2o5$611b2o13b2o$611b2o13b2o16b2o4bob2o$641b2o2bo4b2obo$640b
o2b2o3b2o$641bo5bo3b2o$642b3o2bob2obo$644bo3bobobob2obo$629b2o20b2obob
2o$630bo$627b3o$627bo$634b2o$616b2o17bo$617bo17bobo$616bo19b2o16b2o$
616b2o36b2o$607b2o$2b2o334bo268bobo$o4bo330bo3bo249bo2bo14bo$6bo334bo
252bo3b2o54b2o$o5bo329bo4bo248bo3bo2bo2bo53b2o$b6o330b5o249b4o3b2o19b
2o$619b2o$603b2o$603bobo$604bo$654bo$653bobo$654bo$629b2o$630bo$627b3o
$591b2o34bo16b2o$586b2o2bo2bo17b2o30bobo$583bo2bo4bobo17bobo29bo$582bo
bobo5bo20bo28b2o25bo$583bo2bob2o23b2o52b3o$586bo2bo76bo$587bo4bo73b2o$
588b5o2$590bo83b2o$589bobo2b2o29bo49bo$590b2o3bo27b3o49bob2o$592b3o27b
o44b2o4b3o2bo$592bo29b2o43b2o3bo3b2o$672b4o$642bo15b2o15bo$640b3o10b2o
2bobo12b3o$639bo14bo2bo13bo$626b2o11b2o11bo2b3o14b5o$626b2o24b3o21bo$
655bo18bo$654b2o18b2o$669bo$667b3o$666bo$595b2o68bo2b2o$595b2o69b2o2bo
$601b2o48b2o16b2o$601b2o48b2o3$599b2o$599b2o5b2o$606b2o31b2o3bo$639bo
3bobo$640bo3bobob2o$641bo4bob2o$627b2o10bob5o$627b2o9bobo4bob2obob2o$
639bo2b2obo2bob2obo$640b2obob2o12b2o$659b2o!
#C [[ X 285 Y 0 Z 5 AUTOSTART PAUSE 2 STEP 5 LOOP 2000 ]]

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.

Toward the end of June the stable-circuitry construction binge continued with a number of new stable eaters and spaceship-to-X converters, including a much smaller HWSS Heisenburp -- but these will probably fit much better in a future post.

17 January 2020

A Gentleman and a Scholar

On 30 December 2019, almost a decade after constructing the Gemini spaceship, Andrew J. Wade made a sudden reappearance in a very different corner of the Life spaceship construction field. This time the new discovery was the "scholar", the second known elementary 2c/7 spaceship (after the weekender, which was found by David Eppstein very nearly two decades ago).

The new spaceship was discovered using a depth-first search program called life_slice_ship_search. Details can be found on this conwaylife.com forum thread.

Code: Select all
#C 2c/7 elementary spaceship #2, "scholar",
#C found by Andrew J. Wade with life_slice_ship_search, 30 Dec 2019.
x = 23, y = 82, rule = B3/S23
11bo$10b3o$10b3o2$6b3o5b3o2$6bobo5bobo$6bobo5bobo$7bo7bo$6bo2bo3bo2bo$
7bob2ob2obo$4bo4bo3bo4bo$4b6o3b6o$4bo4bo3bo4bo$5b2obo5bob2o$9bo3bo$5bo
11bo$5bo3bo3bo3bo$6bo2bo3bo2bo$6bo2bo3bo2bo$b3o3bobo3bobo3b3o$o2bo3b9o
3bo2bo$o2bo2b2ob5ob2o2bo2bo$7b2o2bo2b2o$6b2o3bo3b2o$6b2o7b2o$9b2ob2o$
6bo3bobo3bo$6bo3bobo3bo$6b2o2bobo2b2o$8b3ob3o$4b2ob2o5b2ob2o$3bo2b2o7b
2o2bo$2bo17bo$3bob3o7b3obo$6bo2bo3bo2bo$7b3o3b3o$4b2o4bobo4b2o$9bo3bo$
5bo4bobo4bo$2bo6b2ob2o6bo$b2o2b3obo3bob3o2b2o$o5b4o3b4o5bo$bo3b2o2bo3b
o2b2o3bo$2b3o2bobo3bobo2b3o2$7b3o3b3o$6b2o7b2o$5b2o9b2o$5bobo7bobo$6bo
9bo$7bobo3bobo$7bobo3bobo$6bo9bo$6bo9bo$6bo3bobo3bo$7bo2bobo2bo$7bo2bo
bo2bo2$8b3ob3o$8bobobobo$9b5o$3b3o11b3o$3b3o11b3o$bo3bo11bo3bo$5bo11bo
$6bo9bo$bo3bo3bobobo3bo3bo$2b2o4bo5bo4b2o$3bo15bo$4b3o9b3o$5bo5bo5bo$
10b3o$9b2ob2o$9b5o$6b3o2bo2b3o$4bo13bo$4bobo9bobo$6bo9bo$3bobo11bobo$
2bo2bo11bo2bo$3b2o13b2o!
#C [[ GRID THEME 7 TRACKLOOP 7 0 -2/7 THUMBSIZE 2 HEIGHT 680 ZOOM 7 GPS 7 AUTOSTART ]]

11 July 2019

Less Than Two Gliders Per Cell, For All Constructible Still Lifes

On 19 June 2019 a surprising milestone was reached. Goldtiger997 made a final improvement to a 17-bit still-life synthesis -- ID xs17_03p6413z39c -- 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 "17-in-16" project.)

This made it possible to announce a surprising result: there's a strict upper bound for the cost in gliders for any strict still life, assuming it can be constructed by colliding gliders at all. If a glider-constructible still life contains N ON cells, then it can be constructed with less than 2N gliders.

A Mix of Theory and Practice

For still lifes larger than 17 bits, this result is supplied by the strange and wonderful RCT method. The RCT (reverse caber tosser) 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 construction arm. 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.

The situation is much more straightforward for still lifes with up to 17 ON cells. Extensive soup searches recorded by Catagolue, 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.

We've Come a Long Way, Conway

For example, just a few years ago the best known recipe for an 8x6 17-bit still life with ID xs17_gbaikoz1252 was around 73 gliders:

Code: Select all
#C Incremental 73-glider synthesis of xs17_gbaikoz1252.
#C Adapted from Mark Niemiec's database,
#C http://conwaylife.com/ref/mniemiec/17/17-1202.rle
x = 185, y = 236, rule = B3/S23
143bo$143bobo$143b2o$140bo$138bobo$139b2o2$143bo$141b2o$142b2o2$133bob
o15bo$133b2o15bo$96bo33bo3bo15b3o$91bo3bo15b2o15bobo10b2o$92b2ob3o12bo
2bo15b2o9bo2bo$91b2o17bo2bo26bo2bo9bo$10bo100b2o17bo10b2o9b2o$11b2obo
115b2o20bobo$10b2o2bobo112bobo34b2ob2o$14b2o12b2o18b2o18b2o18b2o18b2o
28b2o27bobobobo$27bo2bob2o13bo2bob2o13bo2bob2o13bo2bob2o13bo2bob2o23bo
2bob2o5b3o15bo2bob2o$23bo4bobobo15bobobo15bobobo15bobobo15bobobo25bobo
bo6bo18bobo$22b2o5b2obobo14b2obobo14b2obo16b2obo16b2obo26b2obo7bo18b2o
$22bobo8b2o18b2o17bob2o16bob2o16bob2o26bob2o$2b2o68bo2bo16bo2bo16bo2bo
26bo2bo$3b2o68b2o18b2o18b2o28b2o$2bo2$151b2o$151bobo$53bo97bo$50bo2bob
o$48bobo2b2o$49b2o6$50b3o$50bo$51bo11$19bo42bo$19bobo38b2o$19b2o40b2o$
94bo$95bo4bo$93b3o3bo$6b2ob2o15b2ob2o15b2ob2o15b2ob2o15b2ob2o8b3o4b2ob
2o4b2o9b2ob2o4b2o19b2ob2o4b2o$7bobobobo13bobobo15bobobo15bobobo15bobob
o15bobobo3bo11bobobo3bo21bobobo3bo$7bo2bob2o13bo2bobobo12bo2bobobo12bo
2bobo14bo2bobo14bo2bobo3bo10bo2bobo3bo20bo2bobo3bo$8bobo17bobo2b2o13bo
bo2b2o13bobobo15bobobo15bobobo4bo10bobobo4bo20bobobo4bo$9b2o12bo5b2o
18b2o18b2ob2o15b2ob2o5bo9b2ob2o2b2o11b2ob2o2b2o3bo17b2ob2o4bo$21b2o75b
2o40bo28bo$22b2o74bobo39b3o27bo$56bobo77b2o33bo$15b2o39b2o37b3o37bobo
32b2o$16b2ob3o35bo39bo39bo3b2o$15bo3bo76bo45b2o$20bo34b3o83bo$55bo$56b
o2$58b3o$58bo$59bo13$6b2ob2o4b2o29b2ob2o4b2o29b2ob2o4b2o29b2ob2o4b2o$
7bobobo3bo31bobobo3bo31bobobo3bo31bobobo3bo$7bo2bobo3bo30bo2bobo3bo30b
o2bobo3bo30bo2bobo3bo$8bobobo4bo30bobobo4bo30bobobo4bo30bobobo4bo$9b2o
b2o4bo30b2ob2o4bo30b2ob2o4bo30b2ob2o4bo$19bo39bo39bo39bo$20bo39bo39bo
39bo$21bo39bo39bo39bo$20b2o3bo36bo39bo39bo$24bo38bo39bo39bo$24b3o35b2o
38b2o3bo34b2o$20b2o84bo$19bobo84b3o$21bo3b2o75b2o$26b2o73bobo$25bo77bo
3b2o$108b2o$107bo10$59bo$59bobo$59b2o$54bo$54bobo$54b2o5bobo$61b2o$53b
o8bo55bo$54b2o60bobo$53b2o62b2o$120bo$61bo25bo19bo11bo17bo$60b2o23b3o
17b3o11b3o13b3o$6b2ob2o4b2o9b2ob2o4b2o9b2ob2o4b2o3bobo13b2ob2o3bo11b2o
b2o3bo21b2ob2o3bo$7bobobo3bo11bobobo3bo11bobobo3bo21bobobo3bo11bobobo
3bo10bobo8bobobo3bo6b3o$7bo2bobo3bo10bo2bobo3bo10bo2bobo3bo20bo2bobo3b
o10bo2bobo3bo10b2o8bo2bobo3bo4b3o$8bobobo4bo10bobobo4bo10bobobo4bo20bo
bobo4bo10bobobo4bo9bo10bobobo4bo$9b2ob2o4bo10b2ob2o4bo10b2ob2o4bo20b2o
b2o4bo10b2ob2o4bo20b2ob2o4bo$19bo19bo19bo29bo19bo29bo$20bo19bo19bo29bo
19bo29bo$21bo10b2o7bo10b2o7bo20b2o7bo10b2o7bo20b2o7bo$22bo9b2o8bo9b2o
8bo19b2o8bo9b2o8bo19b2o8bo$9b2o12bo19bo19bo29bo19bo29bo$6bo2bobo3b2o5b
2o8b2o8b2o8b2o8b2o18b2o8b2o8b2o8b2o18b2o8b2o$4bobo2bo4b2o16b2o18b2o28b
2o18b2o28b2o$5b2o9bo3$160bo$158b2o$159b2o4$143bobo$143b2o$144bo2$66bo$
67bo29bo29bo$65b3o28bobo27bobo$96bobo27bobo$62b3o32bo29bo$64bo$13bo49b
o$6bo5bo$7bo4b3o$5b3o$b3o$3bo126bo$2bo128bo$129b3o2$42bo29bo29bo29bo$
41bobo27bobo27bobo27bobo$42b2o28b2o28b2o28b2o3$169b2o$169bo$170b3o$17b
o29bo29bo29bo29bo34bo4bo$15b3o27b3o27b3o27b3o27b3o37b3o$6b2ob2o3bo21b
2ob2o3bo21b2ob2o3bo21b2ob2o3bo21b2ob2o3bo31b2ob2o3bo$7bobobo3bo6b3o12b
obobo3bo6b3o12bobobo3bo6b3o12bobobo3bo6b3o12bobobo3bo6b3o22bobobo3bo6b
3o$7bo2bobo3bo4b3o13bo2bobo3bo4b3o13bo2bobo3bo4b3o13bo2bobo3bo4b3o13bo
2bobo3bo4b3o23bo2bobo3bo4b3o$8bobobo4bo20bobobo4bo20bobobo4bo20bobobo
4bo20bobobo4bo30bobobo4bo$9b2ob2o4bo20b2ob2o4bo20b2ob2o4bo20b2ob2o4bo
20b2ob2o4bo30b2ob2o4bo$19bo29bo29bo29bo29bo39bo$20bo29bo29bo29bo29bo
39bo$12b2o7bo20b2o7bo20b2o7bo20b2o7bo20b2o7bo30b2o7bo$12b2o8bo19b2o8bo
19b2o8bo19b2o8bo19b2o8bo29b2o8bo$23bo29bo29bo29bo29bo39bo$12b2o8b2o18b
2o8b2o18b2o8b2o18b2o8b2o18b2o8b2o28b2o8b2o$12b2o28b2o28b2o28b2o28b2o
38b2o6$102bo$101bo$101b3o9$79bo$77b2o10bo$78b2o7b2o$88b2o$92bo$92bobo$
92b2o$5bo3b2o28b2o38b2o65bo$3bobo3bo25b2o2bo28b3o4b2o2bo15bo49bo$4b2o
4b3o22b2o3b3o27bo4b2o3b3o12bobo47b3o$b2o9bo4bo24bo4bo21bo12bo4bo7b2o$o
bo12b3o27b3o37b3o32b2o18b2o6b2o10b2o$2bo3b2ob2o3bo21b2ob2o3bo31b2ob2o
3bo31b2obo2bo13b2obo2bo5bobo5b2obo2bo$7bobobo3bo6b3o12bobobo3bo6b3o11b
3o8bobobo3bo6b3o22bobobobo13bobobobo4bo8bobobobo$7bo2bobo3bo4b3o13bo2b
obo3bo4b3o14bo8bo2bobo3bo4b3o23bo2bob2o13bo2bob2o13bo2bobo$8bobobo4bo
20bobobo4bo19bo10bobobo4bo30bobo17bobo17bobo$9b2ob2o4bo20b2ob2o4bo30b
2ob2o4bo30b2o18b2o18b2o$19bo29bo39bo$20bo29bo39bo$12b2o7bo20b2o7bo30b
2o7bo7bo$12b2o8bo19b2o8bo29b2o8bo6bobo$23bo29bo39bo5b2o$12b2o8b2o18b2o
8b2o28b2o8b2o$12b2o28b2o38b2o$97b2o3bo$88bo9b2obo$77bo10b2o7bo3b3o$77b
2o8bobo$76bobo!

#C [[ AUTOSTART X 137 Y 3 Z 2 PAUSE 2 GPS 25 LOOP 150 ]]

Thanks to soup search data from Catagolue, that same still life can now be constructed with just 10 gliders:

Code: Select all
#C 10-glider continuous synthesis of xs17_gbaikoz1252
#C http://catagolue.appspot.com/object?apgcode=xs17_gbaikoz1252&rule=b3s23
x = 30, y = 37, rule = B3/S23
3bo$4bo$2b3o4$13bo$12bo$12b3o3$2bo24bo$obo24bobo$b2o24b2o11$15bo$14bo
$4bo5bo3b3o8bo$4b2o4b2o12b2o$3bobo3bobo12bobo6$11bo8b2o$11b2o6b2o$10b
obo8bo!
#C [[ AUTOSTART PAUSE 2 GPS 25 T 150 X -5 Y 10 Z 12 PAUSE 2 LOOP 151 ]]

At the time of writing (mid-July 2019), there are still several dozen 17-bit still lifes 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 here.

UPDATE 9/9/2019: Construction recipes with 16 gliders or fewer have now been found for all 17-bit still lifes.

Some Related Open Questions

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.

Notice for example that quad pseudo 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.

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.

10 November 2018

New Tools for Self-Construction

Time for a new post on self-constructing circuitry! I've been updating the same old post since 2014, but I think there's now some news that warrants a new article.

Self-Construction Just Got A Lot Easier

For the last several years Adam P. Goucher has been incrementally working out the construction details for a "0E0P metacell". A metacell 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.

"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.

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.

Automatically Generated Construction Recipes

A key breakthrough enabling the construction of the 0E0P metacell was a publicly available search program written by Goucher, capable of finding a single-channel 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).

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.

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.

Fast HashLife-friendly Orthogonoid

Older version with slow elbow push:

Lower-population version with Cordership elbow push:

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.
  • 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.
  • 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.
  • The green arrows show the direction the recipe travels.
  • 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.

Features of slsparse used to build the new Orthognoid include

  • automatic compilation of very widely separated metaclusters

    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.

  • automatically compiled elbow push and hand push, with different Corderships

    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.

  • automatically compiled non-Spartan objects

    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 Spartan, but with slsparse the state of the art has moved well past that artificial limitation.

Hashlife-friendly Demonoid


(The image at right is not exactly to scale, but it's close enough that it should be recognizable.)

Features of slsparse that appear in the new Demonoid include

  • long-distance elbow pull

    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.

  • Snarkbreaker

    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.

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.

Challenge: Install the latest slsparse and use it to build a lower-population Demonoid than the current model, 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 this walkthrough on the LifeWiki.

------------------------------------------------

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.

Another trick used in the Demonoid that slsparse doesn't know about yet is

  • destruction of old circuitry by *WSS produced directly from construction elbow

  • 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.

Loopship

Features of slsparse used in building the loopship:

  • automatically compiled on-lane construction

    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.

A new feature of slsparse that could be used to build a somewhat smaller loopship:

  • automatically compiled 0-degree construction for sufficiently narrow on-lane constellations

    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.

Other mechanisms used in the loopship

  • destruction by GoL-destroy search result

    A separate search program called GoL-destroy 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.

  • one-time turners

    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.
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.

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.

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.

An accurate diagram would show all these paths stacked exactly on top of each other, like the illustration at left.

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.


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:

The actual loopship has significantly different shapes at different times in its construction cycle. Here's a snapshot diagram where

  • 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.

  • the remainder of the recipe traveling northeast will construct a new splitter-plus-Snarks constellation (a future blue dot halfway between the two Corderships).
  • a copy of the full recipe is heading southwest around the left-hand loop (green arrows).

  • 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.

The Switching System

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.

Final Challenges

The loopship is considerably bigger than it needs to be... 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 loopship forum thread.