This is the best construction I could come up with for cluster -> frozen anything.
Code: Select all
x = 922, y = 2226, rule = B3/S23
919bo$919bobo$897bobo19b2o$897b2o$898bo18$825bobo$825b2o$826bo25bo$
851bo$839bo11b3o$838bo$838b3o17$900bo$900bobo$878bobo19b2o$878b2o$879b
o18$806bobo$806b2o$807bo25bo$832bo$820bo11b3o$819bo$819b3o17$881bo$
881bobo$859bobo19b2o$859b2o$860bo18$787bobo$787b2o$788bo25bo$813bo$
801bo11b3o$800bo$800b3o17$862bo$862bobo$840bobo19b2o$840b2o$841bo18$
768bobo$768b2o$769bo25bo$794bo$782bo11b3o$781bo$781b3o17$843bo$843bobo
$821bobo19b2o$821b2o$822bo18$749bobo$749b2o$750bo25bo$775bo$763bo11b3o
$762bo$762b3o17$824bo$824bobo$802bobo19b2o$802b2o$803bo18$730bobo$730b
2o$731bo25bo$756bo$744bo11b3o$743bo$743b3o17$805bo$805bobo$783bobo19b
2o$783b2o$784bo18$711bobo$711b2o$712bo25bo$737bo$725bo11b3o$724bo$724b
3o17$786bo$786bobo$764bobo19b2o$764b2o$765bo18$692bobo$692b2o$693bo25b
o$718bo$706bo11b3o$705bo$705b3o17$767bo$767bobo$745bobo19b2o$745b2o$
746bo18$673bobo$673b2o$674bo25bo$699bo$687bo11b3o$686bo$686b3o17$748bo
$748bobo$726bobo19b2o$726b2o$727bo18$654bobo$654b2o$655bo25bo$680bo$
668bo11b3o$667bo$667b3o17$729bo$729bobo$707bobo19b2o$707b2o$708bo18$
635bobo$635b2o$636bo25bo$661bo$649bo11b3o$648bo$648b3o13$627bo31b2o$
627b2o30bob2o$626bo2bo31b2o$627bobo15bo13b2o$626bo2bo15b2o10b2o51bo$
626bo2bo17bo62bobo$626bobo16b2o10bobo28bobo19b2o$627b3o14bobo11bo29b2o
$645bo43bo$643bobo$641bo$641bobo5$626b2o$626b2o$668bo$628bo39b2o$627b
3o8bo4bo10b3o13bo$626bob2o6b4o3bo11b2obo10b3o$625b2obo7b2obob2obo9bob
2obo7bob3o$626b2o8b2o15b2o4b2o4bo5bo$627bo2b2o10bobo9bo3b2o6bo4bo$631b
3o7b2obo10b4o21bo$632b2o5bob3o12bo12bo10b2o$633bo5bo12b2o25bo2bo$652b
2o26bobo$679bo2bo$679bo2bo$679bobo$680b3o$697b3o$697bobo$659b3o35bo2bo
$661bo36b3o$660bo37b3o$696bo2bo$699bo$696bo$679b2o$679b2o17bo$697bo$
676b3o2bo15b2o$680b3o21bo$612bobo66b2o6b3o11bobo$612b2o67bo7b3o11bobo$
613bo25bo39b2o8bo2bo11bo$638bo41bo2b2o5bobo$626bo11b3o43b3o3b2o9bo6b3o
$625bo59b2o12b3o$625b3o58bo16b2o6bo$704bo2bo$704b2o4bo$706bo2bo$702b2o
b2o$703bo12$687bo$675b2o10bobo$665bobo7b2o10b2o$665b2o$666bo18$593bobo
$593b2o$594bo25bo$619bo$607bo11b3o$606bo$606b3o65b2o$674b2o14$612bo$
610b6o$610b2o2b2o52bo$668bobo$582b3o12b3o14bo31bobo19b2o$583bo16bo9b2o
2bo31b2o$583b3o11bo2bo9b2o3bo31bo$598b2o14bo$598b2o12bobo$597bo2bo12bo
$597bo$599b2o$673b2o$673b2o3$582b2o28bo$582b2o28bo$589bo22b2o$588bobo
6b2o12bobo$587b2obo6b2o11bo2bo7b3o$585b2o2bo19bo4bo5bo3bo18b2o$585b5o
4bo14bo2b3o10bo17b2o$584bo4bo3bobo2b3o15bo8bo19bo$584bob3o4bob3obo12b
2o10b2o17b3o$585b3o2bo3bo2bo9bo4bobo2bo2b4o18bobo$586bo10b3o2bo2bo10bo
5bo20b2o13bo$587bo4bo8bo6bobo6b2o23bo14b3o$587bo4bo9bo5b2o32bo17bo$
591bo11b3o34bo17b2o$659bo7$613b3o23bobo$615bo23bobo$614bo27bo7b2o5b2o
13b2o$652bo4b2o13b2o$636bo14bo12bo$635bob2o10bo3b2o7b2obo$634bo3b2o8bo
3bo2bo5b3obo$570bobo62bo2b2o2b2o5b2ob5o3bo4bo$570b2o64b2o4b2o7b2o2bo3b
o2bob2o3bo$571bo25bo32b3o20b2o4bo4bo3bobo$596bo35bo26bo3b2o3bobo$584bo
11bo34bo31bo5bo$583bo13bo3bo58bo$583b3o15bo59b2o$597b2o3bo63b2o$597bo
3b2o$597bo3bo$570b3o12b3o10bo2bo$570bo2bo10bo2bo11b3o$569bo3bo9bo4bo
11bobo$574bo10bo15b2o$570b3ob2o$574bo11b2o$569bo3b2o10bobo$573bo11bobo
15b2o$603b2o$591bo71bo$566bobo20bo72bobo$566b2o21b2o71bo2bo$567bo25bo
69b2o$592bo52bo$580bo11b3o29b2o19bobo23b2o$579bo43bo2b2o17b2o19b2o3b2o
$579b3o41b2ob2o34bo3b2o$624bo2bo33bobo$624b5o32bobo$626b3o33bo10bo$
629bo42bobo$672b2o$629b2o15bo$580bo48b2o14b3o$578b3o50bo12b2o2bo$577bo
bo7b3o39b2o17b2o$559bo4bo4bo6b2o11bo7bo2b3o42b3ob2o$558bo2bo2bo3bobo
17bo8b2o4b2o41bo2b2o$558bo2b2o5bobo7b3o12b4o4b2o28b2o12b3o$561b2o29b4o
2bo32b2o15b2o$562b2o27b3o2bo51b2o$563b2o25b2o2b2o$591b3ob3o$592b2o3bo
43bo$593bo10b3o34bobo$606bo12bobo19b2o$605bo13b2o41bo$620bo40bobo$661b
o2bo$662b2o2$670b2o$665b2o3b2o$660b2o3b2o$658b3obo$658bo3bo$659b2o11bo
$655bo2bo12bobo$642bo15bo12b2o$641b2o12bobo$622bobo16b3o3bo$622bobo17b
obo2bo$623bo19bo2bo$645bo$647bo$547bobo97bo$547b2o$548bo25bo$573bo$
561bo11b3o$560bo$560b3o$664bo$663bobo$663bo2bo$664b2o$655bo$655bo$655b
o13b2o$669b2o4$671bo$670bobo$670b2o3$622bo$622bobo$600bobo19b2o$600b2o
$601bo7$663bo$662bobo$662bo2bo$663b2o$654bo$654bo$654bo13b2o$668b2o4$
528bobo139bo$528b2o139bobo$529bo25bo113b2o$554bo$542bo11b3o$541bo$541b
3o10$662bo$661bobo$661bo2bo$662b2o$653bo$653bo$653bo13b2o$603bo63b2o$
603bobo$581bobo19b2o$581b2o$582bo86bo$668bobo$668b2o14$661bo$660bobo$
509bobo148bo2bo$509b2o150b2o$510bo25bo115bo$535bo116bo$523bo11b3o114bo
13b2o$522bo143b2o$522b3o3$668bo$667bobo$667b2o12$584bo$584bobo$562bobo
19b2o74bo$562b2o95bobo$563bo95bo2bo$660b2o$651bo$651bo$651bo13b2o$665b
2o4$667bo$666bobo$666b2o7$490bobo$490b2o$491bo25bo$516bo$504bo11b3o$
503bo$503b3o$659bo$658bobo$658bo2bo$659b2o$650bo$650bo$650bo13b2o$664b
2o4$666bo$665bobo$665b2o3$565bo$565bobo$543bobo19b2o$543b2o$544bo7$
658bo$657bobo$657bo2bo$658b2o$649bo$649bo$649bo13b2o$663b2o4$471bobo
191bo$471b2o191bobo$472bo25bo165b2o$497bo$485bo11b3o$484bo$484b3o10$
657bo$656bobo$656bo2bo$657b2o$648bo$648bo$648bo13b2o$546bo115b2o$546bo
bo$524bobo19b2o$524b2o$525bo138bo$663bobo$663b2o14$656bo$655bobo$452bo
bo200bo2bo$452b2o202b2o$453bo25bo167bo$478bo168bo$466bo11b3o166bo13b2o
$465bo195b2o$465b3o3$663bo$662bobo$662b2o12$527bo$527bobo$505bobo19b2o
126bo$505b2o147bobo$506bo147bo2bo$655b2o$646bo$646bo$646bo13b2o$660b2o
4$662bo$661bobo$661b2o7$433bobo$433b2o$434bo25bo$459bo$447bo11b3o$446b
o$446b3o$654bo$653bobo$653bo2bo$654b2o$645bo$645bo$645bo13b2o$659b2o4$
661bo$660bobo$660b2o3$508bo$508bobo$486bobo19b2o$486b2o$487bo6$446b3o$
446bo2bo203bo$448b2o202bobo$652bo2bo$444bo2bo205b2o$418bo13b3o10b2o
197bo$417b3o12bo2bo12b2o194bo$416b2obo11bo3bo11b3o194bo13b2o$432bo2b2o
11bo209b2o$434bo10bo2bo$432b2o12b2o$418bo12b3o$417bo13b3o18bobo205bo$
416b2o33bobobo203bobo$659b2o$423b2o13b3o8bo7bo$422bo2b2o10bo3bo16bo$
422b2ob2o10bo3bo7b3o6bo16b3o$422b2o2bo8b2o5b2o5b2o8bo16bo$424b2o8bo4bo
4bo4b2o2bo4bo17b3o$434bo3bobo3bo5bob3o2b2o$434bo4bo4bo5b2ob4o$435b2o5b
2o8b2o$424b2o11b6o10bo$424b2o11b2o2b2o$440b3o50b3o$439bobo50bo2bo$439b
2o51bo3bo$491b2obobo155bo$475b2o14b2ob2o155bobo$475b2o15b3o156bo2bo$
482bo169b2o$410bobo68bobo159bo$410b2o68b2obo159bo$411bo25bo40b2o2bo
160bo13b2o$436bo6b3o32b5o4bo11b3o155b2o$424bo11b3o6bo31bo4bo3bobo9bo3b
o$423bo20bo32bob3o4bobo8bo5bo$423b3o52b3o2bo3bo8bo3bo3bo$479bo16bo2bob
o2bo154bo$480bo4bo10bo3bo3bo153bobo$480bo4bo11bo5bo154b2o$484bo13bo3bo
$499b3o$460b3o37b2o$462bo37b2o$461bo38b2o9$485bo165bo$485bobo162bobo$
463bobo19b2o163bo2bo$463b2o186b2o$464bo177bo$642bo$642bo13b2o$425bo
230b2o$423b2ob2o$423b2ob2o$424bob3o$423b3o232bo$396bo13b3o244bobo$395b
3o12bo2bo243b2o$394b2o2bo13b2o$394bo3bo$394bob2o10bo2bo$394b2o13b2o$
412b2o10b2o$411b3o10b2o34b2o19bo$395bo16bo18bo28b2o20bo$395bo13bo2bo
17bobo29bo17b3o$402bo7b2o18bobo27b3o$401b3o27bo27bobo$400b5o11bobo41b
2o13bo$399b2o3b2o9bobobo7b3o5b2o22bo14b3o$398b3o3b3o20bob2o5b2o21bo17b
o$399b2o3b2o7bo7bo5bob2o26bo17b2o173bo$400b5o17bo7bo45bo172bobo$401b3o
9b3o6bo8b3o215bo2bo$402bo10b2o8bo5bo4bo215b2o$413b2o2bo4bo10bo207bo$
402b2o10bob3o2b2o6bo211bo$402b2o10b2ob4o9bo210bo13b2o$416b2o237b2o$
417bo38bobo$456bobo$459bo7b2o5b2o$469bo4b2o181bo$453bo14bo12bo174bobo$
452bob2o10bo3b2o7b2obo173b2o$451bo3b2o8bo3bo2bo5b3obo$387bobo62bo2b2o
2b2o5b2ob5o3bo4bo$387b2o33b3o28b2o4b2o7b2o2bo3bo2bob2o3bo$388bo25bo9bo
45b2o4bo4bo3bobo$413bo9bo52bo3b2o3bobo$401bo11b3o64bo5bo$400bo76bo$
400b3o75b2o$483b2o3$439b3o$441bo$440bo208bo$648bobo$648bo2bo$649b2o$
640bo$640bo$640bo13b2o$456b3o195b2o$458bo$406bo50bo$404b6o88bo$404b2o
2b2o52bo36bo156bo$462bobo32b3o155bobo$376b3o12b3o14bo31bobo19b2o191b2o
$377bo16bo9b2o2bo31b2o$377b3o11bo2bo9b2o3bo31bo$392b2o14bo64b3o$392b2o
12bobo66bo$391bo2bo12bo66bo$391bo$393b2o46b3o$441bobo$439bo3bo$439bob
2o2bo$439bo3bo$376b2o28bo34b2o47b3o$376b2o28bo40bo44bo$383bo22b2o33bo
5bo43bo156bo$382bobo6b2o12bobo33bo4bo12b2o186bobo$381b2obo6b2o11bo2bo
7b3o26b3o12bobo185bo2bo$379b2o2bo19bo4bo5bo3bo42bo186b2o$379b5o4bo14bo
2b3o10bo39bobo177bo$378bo4bo3bobo2b3o15bo8bo38bo180bo$378bob3o4bob3obo
12b2o10b2o16bobo19bobo178bo13b2o$379b3o2bo3bo2bo9bo4bobo2bo2b4o18b2o
20bo48b3o143b2o$380bo10b3o2bo2bo10bo5bo20bo19bo51bo$381bo4bo8bo6bobo6b
2o95bo$381bo4bo9bo5b2o$385bo11b3o255bo$654bobo$654b2o3$524b3o$526bo$
525bo$407b3o57bo$409bo21bo34bobo$408bo22bobo32b2obo$430b2ob3o15bobo6bo
5bo2b2o$433b3o23bobo10bo$433b3o22b2obo10bo$433bobo23b3o5bo4bo68b3o$
364bobo65b2ob2o23bo8b2o72bo$364b2o67bobo106bo104bo$365bo25bo32b3o7bo
80bo130bobo$390bo35bo89bo129bo2bo$378bo11bo34bo88b3o130b2o$377bo13bo3b
o242bo$377b3o15bo242bo$391b2o3bo241bo13b2o$391bo3b2o161b3o91b2o$391bo
3bo164bo$364b3o12b3o10bo2bo163bo$364bo2bo10bo2bo11b3o45b3o$363bo3bo9bo
4bo11bobo46bo210bo$368bo10bo15b2o45bo210bobo$364b3ob2o283b2o$368bo11b
2o$363bo3b2o10bobo$367bo11bobo15b2o176b3o$397b2o178bo$385bo190bo$360bo
bo20bo74b3o$360b2o21b2o75bo$361bo25bo71bo$386bo52bo$374bo11b3o29b2o19b
obo$373bo43bo2b2o17b2o$373b3o41b2ob2o170b3o$418bo2bo172bo$418b5o170bo
52bo$420b3o52b3o167bobo$423bo53bo167bo2bo$476bo169b2o$423b2o15bo196bo$
374bo48b2o14b3o195bo$372b3o50bo12b2o2bo194bo13b2o$371bobo7b3o39b2o17b
2o165b3o39b2o$353bo4bo4bo6b2o11bo7bo2b3o42b3ob2o166bo$352bo2bo2bo3bobo
17bo8b2o4b2o41bo2b2o165bo$352bo2b2o5bobo7b3o12b4o4b2o28b2o12b3o50b3o$
355b2o29b4o2bo32b2o15b2o50bo158bo$356b2o27b3o2bo51b2o49bo158bobo$357b
2o25b2o2b2o262b2o$385b3ob3o$386b2o3bo43bo$387bo10b3o34bobo188b3o$400bo
12bobo19b2o191bo$399bo13b2o212bo$376bo37bo94b3o20bo$376bo134bo21bo$
375bobo132bo20b3o2$377b2o$347bo14bo$346b3o11b2ob2o12b2o$345b2o2bo10b2o
b2o$345b2ob2o11bob3o279bo$348b3o9b3o163b3o115bobo$346bob2o99bobo76bo
115bo2bo$345bo2bo87bo90bo117b2o$348bo86b2o12bobo$345bobo27b2o39bobo16b
3o3bo$346bo28b2o39bobo17bobo2bo208b2o$353bo28bo34bo19bo2bo209b2o$352b
3o6b2o18bobo55bo$351bobobo5b2o18bobo57bo$351bo3bo12bo10bo2bo58bo101b3o
$349b2o5b2o9bobo8b4o5bo157bo106bo$348bo4bo4bo8bobo7bo4bo3bobo15bo139bo
106bobo$347b3o2bobo2b3o8bo8bobob2o3bobo14b3o245b2o$348bo4bo4bo19b2o2b
2o3bo14b5o$349b3o4b2o6b3o5b2o8bo19b2ob3o$353b2o9bob2o5b2o5bob4o17b2ob
2o$351bo5bo6bob2o12b5o20bo$352b2o13bo14b2o$353bo2bo11b3o189b3o$353b2o
11bo4bo49b3o138bo$370bo49bo2bo137bo$366bo57bo$367bo52b2o$420b2o3bo$
425bo$403b2o18bo$403b2o16b3o220bo$410b2o9b2o154b3o63bobo$374b3o30b5o9b
o157bo63bo2bo$337bobo36bo28bo4bo16b3o148bo65b2o$337b2o36bo29bo3b3o$
338bo25bo39bo4b4o2bo10bobobo$363bo40bobo2bo2b3obo9b2ob2o218b2o$351bo
11b3o39bo3b3o2bobo7b2o5b2o216b2o$350bo59bo4bo6bo2bo2bo2bo2bo$350b3o54b
obo12bobo2bobo2bobo$407bobo12bo3b3o2bo2bo114bo44b3o$391b3o30b2ob3o2bo
117bo45bo54bo$393bo32b2o3b2o115b3o44bo54bobo$392bo36bo220b2o$427b2o2$
428b2o3$611b3o$613bo$612bo5$412bo$412bobo228bo$390bobo19b2o214b3o11bob
o$390b2o238bo11bo2bo$391bo237bo13b2o3$648b2o$648b2o2$350b3o$350bo2bo
291b3o$352b2o293bo2bo$646bob2obo$348bo2bo297b2o$322bo13b3o10b2o$321b3o
12bo2bo12b2o$320b2obo11bo3bo11b3o$336bo2b2o11bo$338bo10bo2bo$336b2o12b
2o31bobo$322bo12b3o43bo4bo$321bo13b3o18bobo22bo4bo$320b2o33bobobo25b2o
2$327b2o13b3o8bo7bo19b2o2b2o$326bo2b2o10bo3bo16bo18b2o2b2o14bo$326b2ob
2o10bo3bo7b3o6bo19bob3o13b3o$326b2o2bo8b2o5b2o5b2o8bo21bo14b3o239bo$
328b2o8bo4bo4bo4b2o2bo4bo21bo181bo74bobo$338bo3bobo3bo5bob3o2b2o37b4o
163bo73bo2bo$338bo4bo4bo5b2ob4o38b5o161b3o74b2o$339b2o5b2o8b2o41b2obo$
328b2o11b6o10bo$328b2o11b2o2b2o$344b3o$343bobo$343b2o37b2o$382bobo15b
2o$382bob2o7bo6b2o$381bob3o6b3o12bo$380b2obobo6b4o10bobo$314bobo62b2o
3b3o8b2o9bobo$314b2o64b2o3bo10b2o9bo$315bo25bo39b4o7b5o7b3o5bo$340bo6b
3o33b2o7b4o6b2obo5bobo$328bo11b3o6bo37bobo3b2o7b3obo4bobo$327bo20bo39b
o17b2o4bo$327b3o75bo3bo$405b2ob2o$407b3o4$364b3o$366bo274bo$365bo274bo
bo$640bo2bo$340bo300b2o$339b3o$307bobo28bo2b2o$305bo4bo27b3obo$305bo4b
o30b2o$309b2o14b2o54b3o$325bob2o8bo45bo$305b2o2b2o16b2o7bo45bo6bo$305b
2o2b2o14b2o9b3o50bobo$306bob3o12b2o42bobo19b2o$309bo57b2o$308bo14bobo
42bo$324bo2$398b3o$400bo$399bo183bo$584bo$582b3o$306b2o59b3o$306bobo
39bo18bo2bo$306bob2o9bob2o13b3o8bobo16bo3bo$305bob3o8bo5bo11b4o6b2o23b
o$304b2obobo7bo6bo11b5o5b4obo15b3ob2o42b3o$303b2o3b3o5bo7bo7b2o7bo5b3o
2bo18bo45bo222bo$304b2o3bo5bo3b2o3bo16b2o5bo3bo13bo3b2o44bo222bobo$
305b4o7bo4b4o13bob2o9bo18bo10bo2b2o253bo2bo$307b2o10bo4bo9bo2b4o44b2o
253b2o$311bobo6b2ob2o8b2ob2o46b2o$312bo21bobo26bobo$333bo29b2o15b2o2b
2o$364bo21bo$380b4o48b3o$382bo2bo48bo$433bo2$340b3o$342bo$341bo3$449b
3o$451bo$321b3o126bo$321bo2bo39bo26b3o$320bo3bo38bob2o8b2o17bo$320b4o
38bo4bo7b3obo4b2o5bo3bo$321bo44b2o10b3o6bo4bo3bo$292b2o13b3o52bobo13bo
6bobo4bo3bo$291bo2b2o11bo2bo51b2o24bo7bo$291b2ob2o11bo13bo63bobo7bo70b
3o$292bo2bo24bobo62bo8bo73bo170bo$292b5o14bo75b2o78bo170bobo$294b3o10b
obo17b3o308bo2bo$297bo9bo18bo3bo308b2o$306b2o17bo5bo$297b2o26bo5bo$
297b2o14b2o10bo5bo$299bo12bo2bo10bo3bo$297b2o13b2ob2o10b3o153b3o$313bo
2bo168bo$314b2o34bo133bo115bo$299b2o27b2o19b3o249bo$299b2o27b2o18b2o2b
o246b3o$348b2ob2o$314b2o35b3o$314b2o33bob2o$348bo2bo$351bo148b3o$287bo
bo58bobo151bo$287b2o60bo151bo$288bo25bo41bo10b3o$313bo41b3o8bo3bo$301b
o11b3o38bobobo7b2o3bo$300bo53bo3bo$300b3o49b2o5b2o6bo$316b3o32bo4bo4bo
10bo$318bo31b3o2bobo2b3o7b2o145b3o$317bo33bo4bo4bo10b2o145bo118bo$352b
3o4b2o11b2o144bo118bobo$356b2o14bobo262bo2bo$354bo5bo13bo263b2o$355b2o
16bo$356bo2bo$356b2o$333b3o38b2o$335bo38b2o158b3o$334bo201bo$535bo2$
306bo$304b6o$304b2o2b2o52bo$362bobo$276b3o12b3o14bo31bobo19b2o$277bo
16bo9b2o2bo31b2o209b3o$277b3o11bo2bo9b2o3bo31bo211bo$292b2o14bo243bo$
292b2o12bobo$291bo2bo12bo$291bo$293b2o46b3o$341bobo$339bo3bo$339bob2o
2bo222b3o$339bo3bo226bo66bo$276b2o28bo34b2o226bo47bo18bobo$276b2o28bo
40bo270bo17bo2bo$283bo22b2o33bo5bo268b3o18b2o$282bobo6b2o12bobo33bo4bo
12b2o$281b2obo6b2o11bo2bo7b3o26b3o12bobo$279b2o2bo19bo4bo5bo3bo42bo$
279b5o4bo14bo2b3o10bo39bobo$278bo4bo3bobo2b3o15bo8bo38bo226b3o$278bob
3o4bob3obo12b2o10b2o16bobo19bobo226bo$279b3o2bo3bo2bo9bo4bobo2bo2b4o
18b2o20bo227bo$280bo10b3o2bo2bo10bo5bo20bo19bo$281bo4bo8bo6bobo6b2o$
281bo4bo9bo5b2o$285bo11b3o3$602b3o$604bo$603bo3$307b3o57bo$309bo21bo
34bobo$308bo22bobo32b2obo$330b2ob3o15bobo6bo5bo2b2o$333b3o23bobo10bo
246b3o$333b3o22b2obo10bo248bo14bo$333bobo23b3o5bo4bo247bo14bobo$264bob
o65b2ob2o23bo8b2o264bo2bo$264b2o67bobo300b2o$265bo25bo32b3o7bo$290bo
35bo$278bo11bo34bo$277bo13bo3bo$277b3o15bo$291b2o3bo$291bo3b2o$291bo3b
o$264b3o12b3o10bo2bo$264bo2bo10bo2bo11b3o45b3o$263bo3bo9bo4bo11bobo26b
o19bo$268bo10bo15b2o25b3o17bo287b2o$264b3ob2o51b2o2bo304b2o$268bo11b2o
39b2ob2o$263bo3b2o10bobo42b3o$267bo11bobo15b2o23bob2o$297b2o22bo2bo$
285bo38bo$260bobo20bo37bobo34b3o$260b2o21b2o37bo37bo$261bo25bo41bo10b
3o16bo$286bo41b3o8bo3bo$274bo11b3o38bobobo7b2o3bo$273bo53bo3bo303bo$
273b3o49b2o5b2o6bo293bobo$324bo4bo4bo10bo288bo2bo$323b3o2bobo2b3o7b2o
290b2o$324bo4bo4bo10b2o28b3o$325b3o4b2o11b2o30bo$329b2o14bobo28bo$327b
o5bo13bo$274bo53b2o16bo$272b3o54bo2bo$271bobo7b3o45b2o$253bo4bo4bo6b2o
11bo7bo2b3o50b2o$252bo2bo2bo3bobo17bo8b2o4b2o48b2o$252bo2b2o5bobo7b3o
12b4o4b2o95b3o$255b2o29b4o2bo101bo$256b2o27b3o2bo102bo235b2o$257b2o25b
2o2b2o339b2o$285b3ob3o$286b2o3bo43bo$287bo10b3o34bobo$300bo12bobo19b2o
$299bo13b2o$276bo37bo94b3o$276bo134bo$275bobo132bo2$277b2o$247bo14bo
371bo$246b3o11b2ob2o12b2o36b3o315bobo$245b2o2bo10b2ob2o52bo315bo2bo$
245b2ob2o11bob3o50bo317b2o$248b3o9b3o163b3o$246bob2o178bo$245bo2bo178b
o$248bo$245bobo27b2o$246bo28b2o$253bo28bo49b3o$252b3o6b2o18bobo50bo$
251bobobo5b2o18bobo49bo$251bo3bo12bo10bo2bo160b3o$249b2o5b2o9bobo8b4o
5bo157bo$248bo4bo4bo8bobo7bo4bo3bobo15bo139bo183b2o$247b3o2bobo2b3o8bo
8bobob2o3bobo14b3o322b2o$248bo4bo4bo19b2o2b2o3bo14b5o$249b3o4b2o6b3o5b
2o8bo19b2ob3o$253b2o9bob2o5b2o5bob4o17b2ob2o41b3o$251bo5bo6bob2o12b5o
20bo45bo$252b2o13bo14b2o66bo$253bo2bo11b3o189b3o$253b2o11bo4bo49b3o
138bo$270bo49bo2bo137bo$266bo57bo$267bo52b2o$320b2o3bo307bo$325bo40b3o
263bobo$303b2o18bo44bo263bo2bo$303b2o16b3o43bo265b2o$310b2o9b2o154b3o$
274b3o30b5o9bo157bo$237bobo36bo28bo4bo16b3o148bo$237b2o36bo29bo3b3o$
238bo25bo39bo4b4o2bo10bobobo$263bo40bobo2bo2b3obo9b2ob2o$251bo11b3o39b
o3b3o2bobo7b2o5b2o50b3o$250bo59bo4bo6bo2bo2bo2bo2bo50bo$250b3o54bobo
12bobo2bobo2bobo49bo$307bobo12bo3b3o2bo2bo159b3o$291b3o30b2ob3o2bo163b
o$293bo32b2o3b2o162bo131b2o$265bo26bo36bo297b2o$264b3o60b2o$263bo2bo$
262b3o2b2o59b2o70b3o$263bo2b3o133bo$251bo12b2o2b2o131bo$235b3o12b3o14b
3o241b3o$235bo2bo10bo2b2o10b4obo243bo$235bo2bo10bob2o11b2o2b2o242bo$
234b4o13b2ob2o11b2o$234b2o12bo5bo$233bo15bo4bo377bo$234bo15bo2bo6bo
156b3o211bobo$234bo17bo6bo52bo106bo211bo2bo$247bo11b3o50bobo103bo213b
2o$246bo43bobo19b2o214b3o$246b3o41b2o238bo$291bo237bo2$293bo$292b3o$
291b2ob2o138b3o$291bo144bo$272bo162bo$259b2o10bobo19bo251b3o$258bo2bo
10bobo18b2o252bo$259b2o2b3o7bobo16bob2o250bo79b2o$225bobo15bob2o5bo9bo
2bo6bo3bo349b2o$225bo2b4o11bo3bo3b2o9bo5b2ob2o3bo34bo$225bo2bo5b2o7bo
3bo3bobo9b2obo4b2o2bo34b3o$227b2o5b2o11bo4bo9b3o4bobo2b2o20bo12b2o2bo
137b3o$228b3o13b2o11b2o4bo2bobo3b3o21b2o15bo139bo$260b3o4bo4b2o38bo
139bo$257bo2b2o46bo253b3o$258b3o47bobo253bo$286bobo19b2o253bo$286b2o$
287bo$267b3o361bo$269bo198b3o159bobo$268bo201bo159bo2bo$469bo161b2o$
579b3o$246b3o332bo$246bo2bo330bo$248b2o$318bo$244bo2bo68bo3bo$218bo13b
3o10b2o42bobo24bo3bo164b3o$217b3o12bo2bo12b2o38bo2bo18b2o3bo2b4o165bo$
216b2obo11bo3bo11b3o39b2o18b4o9b2o162bo$232bo2b2o11bo38bo20bo4bo5b2o
275b3o$234bo10bo2bo38bo19b2o4b2o4b2o277bo$232b2o12b2o39bo20b2o3bo6b4o
273bo27b2o$218bo12b3o79bo311b2o$217bo13b3o18bobo55bobo$216b2o33bobobo
55bo$502b3o$223b2o13b3o8bo7bo246bo$222bo2b2o10bo3bo16bo244bo$222b2ob2o
10bo3bo7b3o6bo354b3o$222b2o2bo8b2o5b2o5b2o8bo355bo$224b2o8bo4bo4bo4b2o
2bo4bo15b3o337bo$234bo3bobo3bo5bob3o2b2o14bo3bo$234bo4bo4bo5b2ob4o$
235b2o5b2o8b2o24bo351bo$224b2o11b6o10bo19b5o241b3o107bobo$224b2o11b2o
2b2o31bo246bo107bo2bo$240b3o277bo109b2o$239bobo$239b2o$292b3o$291bo2bo
$274b2o15b2obo$274b2o345bo$210bobo68bo254b3o81bobo$210b2o68bobo255bo
81bobo$211bo25bo42bobo254bo83bo$236bo6b3o35bo9b3o$224bo11b3o6bo32bo12b
2o323b2o7b2o$223bo20bo32bob2o4b3o327bo2bo5bo2bo$223b3o50b2o7b3o10b3o
315b2o7b2o$281bo15bo3bo$279b2obo13bo5bo318bo$280b4o13bo3bo251b3o64bobo
$284bo13b3o254bo64bobo$554bo66bo$260b3o$262bo$261bo37b2o$299b2o$236bo$
235b3o391bo$203bobo28bo2b2o331b3o55bobo$201bo4bo27b3obo333bo55bo2bo$
201bo4bo30b2o332bo57b2o$205b2o14b2o$221bob2o8bo$201b2o2b2o16b2o7bo52bo
$201b2o2b2o14b2o9b3o50bobo$202bob3o12b2o42bobo19b2o$205bo57b2o355bo$
204bo14bobo42bo322b3o29bobo$220bo368bo29bobo$588bo31bo2$615b2o7b2o$
614bo2bo5bo2bo$615b2o7b2o2$202b2o59b3o354bo$202bobo39bo18bo2bo337b3o
12bobo$202bob2o9bob2o13b3o8bobo16bo3bo339bo12bobo$201bob3o8bo5bo11b4o
6b2o23bo337bo14bo$200b2obobo7bo6bo11b5o5b4obo15b3ob2o$199b2o3b3o5bo7bo
7b2o7bo5b3o2bo18bo$200b2o3bo5bo3b2o3bo16b2o5bo3bo13bo3b2o$201b4o7bo4b
4o13bob2o9bo18bo10bo2b2o$203b2o10bo4bo9bo2b4o44b2o$207bobo6b2ob2o8b2ob
2o46b2o346bo$208bo21bobo26bobo365bobo$229bo29b2o15b2o2b2o345bo2bo$260b
o21bo345b2o$276b4o$278bo2bo3$236b3o$238bo$237bo5$217b3o405bo5bo$217bo
2bo39bo26b3o320bobo11bobo5bo$216bo3bo38bob2o8b2o17bo319bo2bo2b2o6b2o5b
3o$216b4o38bo4bo7b3obo4b2o5bo3bo322bo2bo6b3o4b2o$217bo44b2o10b3o6bo4bo
3bo317bo6bo8bo3b2o$188b2o13b3o52bobo13bo6bobo4bo3bo318bo5bo5b4o3bo$
187bo2b2o11bo2bo51b2o24bo7bo317bobo3b3o5b2o$187b2ob2o11bo13bo63bobo7bo
322b2ob3o3bo$188bo2bo24bobo62bo8bo327b2o$188b5o14bo75b2o$190b3o10bobo
17b3o$193bo9bo18bo3bo$202b2o17bo5bo399bo$193b2o26bo5bo398bobo$193b2o
14b2o10bo5bo398bo2bo$195bo12bo2bo10bo3bo400b2o$193b2o13b2ob2o10b3o$
209bo2bo$210b2o34bo$195b2o27b2o19b3o$195b2o27b2o18b2o2bo$244b2ob2o$
210b2o35b3o$210b2o33bob2o$244bo2bo$247bo$183bobo58bobo$183b2o60bo$184b
o25bo41bo10b3o$209bo41b3o8bo3bo$197bo11b3o38bobobo7b2o3bo$196bo53bo3bo
$196b3o49b2o5b2o6bo345b2o$212b3o32bo4bo4bo10bo340b2o$214bo31b3o2bobo2b
3o7b2o361b2o$213bo33bo4bo4bo10b2o359b2o$248b3o4b2o11b2o$252b2o14bobo$
250bo5bo13bo$251b2o16bo356bo$252bo2bo369bobo$252b2o371bo2bo$229b3o38b
2o354b2o$231bo38b2o$230bo2$206bo$206b2o$174bo33bo$173b3o13bo16b2o50bo$
172b5o10b6o12bobo50bobo$172b2ob3o9b2o2b2o13bo29bobo19b2o$173b2ob2o26bo
bo29b2o$175bo15bo10bo34bo$187b2o2bo10bobo$187b2o3bo$191bo$189bobo$190b
o$608b2o$608b2o$628b2o$173b2o27b2o424b2o$173b2o27b3o$180b2o23bo7b2o$
177b5o7bo14bo7bo2bo$175bo4bo9bo10b2o11b2o409bo$175bo3b3o6bo12b2o9bobob
2o16b3o387bobo$174bo4b4o2bo4bo11bobo7b2obo2bo15bo2bo386bo2bo$174bobo2b
o2b3ob5o11b4o6b2obo2bo15bo2bo387b2o$175bo3b3o2bobobobo11bo2bo9bo2bo14b
4o$180bo4b2o2bobo11b2o11b2o15b2o13b3o$177bobo7bo5bo38bo14bo3bo$177bobo
19b2o32bo18bo$194bo4b2o32bo$193bo53b2o3bo$194b2o53b3o6$205b3o$207bo$
206bo$243b2o3b2o$243b2o3b2o357b2o$243bo2bo6bo2bo350b2o$224bobo16bo9bo
373b2o$227b4o12b2o4bobo375b2o$227bo5b2o6bo4bo2bo7bo$160bobo25b3o31bo3b
2o5b2o13bobo2bo5b2o$160b2o26bo2bo32b2ob3o19b2o2bo5bobo$161bo25bo2b2o
31bo25b2o3bob2obobo362bo$186bo2bo63bo2bo3bo362bobo$163bo10b2o11b2o65b
2o367bo2bo$162b3o8bo2bo447b2o$161b2ob2o8bob2o15bo$161bo12bo$175bobo16b
2o$163bo10bo2b2o14bobo$163b2o15bo14b2o$162bob2o14bo13bo2$179b2o$179b2o
$166bo13bo14b2o$166b2o27b2o2$181b2o34bo$181b2o33b3o$156bobo56b2obo$
156b2o$157bo25bo422b2o$182bo52bo370b2o$170bo11b3o32bo17bobo388b2o$169b
o46bo18b2o389b2o$169b3o43b2o$237b3o$222b2o12bo3bo$221bo2b2o10bo2b2o
382bo$221b2ob2o10b2o384bobo$181b3o37b2o2bo396bo2bo$183bo39b2o13b2o383b
2o$182bo54bo2bo$152bo86b2o$151bobo$153bo69b2o$155b2o66b2o$152b6o83b2o$
152bobobobo23bo7bo50b2o$153b5o22b2o7bobo6b3o$154b3o24bo2bo6bo8bo$154b
3o25bobo5bo8bo$231bo$231bobo$173bo35bobo19b2o$172bobo34b2o$171bo3bo34b
o$172bo2bo$144bo14bo12bo2bo429b2o$143b3o13bo13bobo429b2o$143bo2bo11bob
o464b2o$145b2o478b2o$145bo14b2o$142b2o$142b4o14b2o$143bo2bo475bo$144bo
476bobo$208b3o410bo2bo$143bobo26b2o34bo2bo410b2o$143b2o27b2o33bo3bo$
179bo27b3o2bo$149b3o6b2o18bob2o26b4o11b2o$149b3o6b2o15b3o44b3o$165bo8b
5o43bo2bo$164bobo6bo2bo2b3o2bo20bobo14b2ob2o$146bo7b2o8bobo6bobo4bo2bo
bo19b2o15b2ob2o$146bobo6b2o5bo2bo8bo3b2o3bobo20bo14b2ob2o$145bo9b2o4b
4o5bo8bo4bo37bo$149b3o2b3o3bo4bo3bobo4b3o44b3o$153b3o4bobob2o3bobo4b2o
46bo$147bo4b3o6b2o2b2o3bo$148bo3bo12bo$149b2o12bob4o$163b5o$165b2o$
604b2o$604b2o$217bo406b2o$215b2o5bo401b2o$222bo$198bo4b2o$172b3o22bo4b
3o10bo2bo3b2o9bo$174bo22b2o2bo5b2o7b2o3bo2b2o6bobo386bo$173bo24bobo3bo
2b2o11bo3bobo4bo3bo384bobo$133bobo63b2o2bo17bo5bo4bo2bo384bo2bo$133b2o
65b3o19b4ob2o3b2obo385b2o$134bo25bo63bo2bobo3b2o$159bo70bo$147bo11b3o
66b2o$146bo$146b3o40b3o$191bo$190bo7$206b3o$208bo$207bo$603b2o$603b2o$
623b2o$623b2o2$208bo$208bobo12b3o$186bobo19b2o15bo394bo$186b2o36bo394b
obo$187bo431bo2bo$620b2o5$240b3o$242bo$241bo7$257b3o$259bo$258bo$114bo
bo485b2o$114b2o486b2o$115bo25bo480b2o$140bo481b2o$128bo11b3o$127bo$
127b3o144b3o$276bo342bo$275bo342bobo$618bo2bo$619b2o5$291b3o$293bo$
292bo6$189bo$189bobo116b3o$167bobo19b2o119bo$167b2o140bo$168bo432b2o$
601b2o$621b2o$621b2o3$325b3o$327bo290bo$326bo290bobo$617bo2bo$618b2o5$
342b3o$344bo$343bo$95bobo$95b2o$96bo25bo$121bo$109bo11b3o$108bo$108b3o
248b3o$361bo$360bo$600b2o$600b2o$620b2o$620b2o3$376b3o$378bo238bo$377b
o238bobo$616bo2bo$617b2o4$170bo$170bobo220b3o$148bobo19b2o223bo$148b2o
244bo$149bo6$410b3o$412bo$411bo$599b2o$599b2o$619b2o$619b2o3$427b3o$
429bo186bo$428bo186bobo$76bobo536bo2bo$76b2o538b2o$77bo25bo$102bo$90bo
11b3o$89bo$89b3o352b3o$446bo$445bo7$461b3o$463bo$462bo$598b2o$598b2o$
618b2o$618b2o2$151bo$151bobo324b3o$129bobo19b2o327bo134bo$129b2o348bo
134bobo$130bo483bo2bo$615b2o5$495b3o$497bo$496bo7$512b3o$514bo$513bo$
57bobo537b2o$57b2o538b2o$58bo25bo532b2o$83bo533b2o$71bo11b3o$70bo$70b
3o456b3o$531bo82bo$530bo82bobo$613bo2bo$614b2o5$546b3o$548bo$547bo6$
132bo$132bobo428b3o$110bobo19b2o431bo$110b2o452bo$111bo484b2o$596b2o$
616b2o$616b2o3$580b3o$582bo30bo$581bo30bobo$612bo2bo$613b2o5$597b3o$
599bo$598bo$38bobo$38b2o$39bo25bo$64bo$52bo11b3o$51bo$51b3o3$595b2o$
595b2o2$613b2o$613b2o3$612bo$611bobo$611bo2bo$612b2o4$113bo$113bobo$
91bobo19b2o$91b2o$92bo9$594b2o$594b2o2$612b2o$612b2o3$611bo$610bobo$
19bobo588bo2bo$19b2o590b2o$20bo25bo$45bo$33bo11b3o$32bo$32b3o12$593b2o
$593b2o2$611b2o$611b2o$94bo$94bobo$72bobo19b2o514bo$72b2o535bobo$73bo
535bo2bo$610b2o17$obo589b2o$2o590b2o$bo25bo$26bo583b2o$14bo11b3o581b2o
$13bo$13b3o$609bo$608bobo$608bo2bo$609b2o3$614bo$613b3o$612b2o2bo$616b
o$615bo$611bo$611bobo$611b2o3$75bo$75bobo$53bobo19b2o$53b2o$54bo536b2o
$591b2o!
If you follow what the left side is doing:
create a block
spark it twice, leaving a constellation with a loaf
use two forerakes to clean up everything but the loaf
use a backrake+forerake collision to produce a block near the loaf
use standard slow salvo techniques to move the block into position (3 forerakes)
A few complications come in because the track and the debris move away from one another. Notably, the backrake actually has to get sent earlier than its place in the recipe, and has to pass through the forerakes. In this case it works out, because the track needed a rephasing at that point anyway.
Because the lanes and phases are so constrained, we only actually get 9 distinct 2-glider collisions between forerake and backrake, making it difficult to produce desired debris. This block was the best suited for this task.
Lastly, the slow salvo recipes are a real pain because the rephasing reactions move the track 16 lanes forward every time, and we are sensitive to lane number mod 26. This means the final rake of the slow salvo recipe, which is 2 lanes behind the previous one, requires moving the track a whopping 128 lanes forward using 8 rephasings, because 128 - 26*5 = -2. This was still better than any other method I could find of placing that block, due to the restriction that all gliders be on even lanes.
The recipe also leaves a spare block. If no other modifications are made, the block just deletes one of the two output gliders of the climber. If the block is transformed it can be used to make other constellations that when thawed, give other outputs.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
A brief motivation of frozen tracks:
In Gabriel's caterpillar page, he writes "we have adjusted the vertical position of the blinker trails with
adjuster pies. We can always adjust a blinker trail to any desired vertical position in this way, because, luckily, 11 is relatively prime to 34."
His "adjuster pies" are what I have called a rephasing reaction in the Waterbear and here. However, we are not as lucky as he was. He had a generator of distance 11 in a 34-element cyclic group. In the Waterbear, the analogous two numbers were 95 and 342, which are 5*19 and 18*19. In this ship, the analogous two numbers are 160 and 360, which are 4*40 and 9*40. If we instead only consider forerakes as the construction elements, we get a different pair of numbers, 64 and 208, which are 4*16 and 13*16. All pairs listed are not relatively prime to each other. So in neither of the ships is it possible to reach every position in the group using only the rephasing reaction. I've tried to go into a bit of detail on where these numbers come from in previous posts, but even if you don't follow where they come from, understand that it means we are at a disadvantage relative to the caterpillar until we can reach other track positions.
Construction recipes have some degrees of freedom - first is where on the track they start. Say we had an eastbound LWSS recipe. In the caterpillar, if we wait 4 generations to start the recipe, the resulting LWSS is 2 cells further behind. In Waterbear/this ship, if we wait 4 generations to start, the track itself has moved, adding (1,1) and giving a net displacement of (3,1). Our list of naively reachable LWSS positions is then a line with slope 1/3. We also have the translational symmetry of the track to account for, so we can actually copy this line many times, giving the pattern below. The red lines, continued infinitely, give all the places the white cell of the LWSS could be at this generation.
Code: Select all
x = 83, y = 96, rule = LifeHistory
39.A$38.A$38.3A10$80.D$77.D$74.D$71.D$68.D$65.D$62.D$59.D$43.A2.A9.D$
47.A5.D$43.A3.A2.D$44.3AC$44.D$41.D$38.D$35.D$32.D$29.D16$20.A$19.A$
19.3A3$82.D$79.D$76.D$73.D$70.D$67.D$64.D$61.D$58.D$55.D$52.D$49.D$
46.D$43.D$40.D$37.D$34.D$31.D$28.D$25.D$22.D$19.D$16.D17$81.D$.A76.D$
A74.D$3A69.D$69.D$66.D$63.D!
That's not a huge portion of the plane. But if we take rephasings into account, we can actually move the track around a little bit. Allowing rephasings, the picture becomes a little better.
Code: Select all
x = 57, y = 71, rule = LifeHistory
20.A$6.D3.D3.D3.DA6.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.3A.D3.D3.D3.D3.
D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D2.AD.A.D3.D3.D3.D3.D3.D3.D$6.D3.
D3.D3.D3.D3.D.A.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.DA2.DA2.D3.D3.D3.D
3.D3.D3.D$4.D3.D3.D3.D3.D3.D3AC3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$.A4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$A6.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$3A.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D!
But it isn't enough. This has density 1/4 in the plane, and also it only allows the ship to have this shape. That means we are only able to make 1/16 of the possible LWSS. This 16 comes from the common factor of 64 and 208 above.
It would be impossible, for example, if the recipe required we place a ship here:
Code: Select all
x = 57, y = 71, rule = LifeHistory
20.A$6.D3.D3.D3.DA6.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.3A.D3.D3.D3.D3.
D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$
7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D2.AD.A.D3.D3.D3.D3.D3.D3.D$6.D3.
D3.D3.D3.D3.D.A.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.DA2.DA2.D3.D3.D3.D
3.D3.D3.D$4.D3.D3.D3.D3.D3.D3AC3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D.2ED3.D3.D3.D3.D3.D$7.D
3.D3.D3.D3.D3.D2.2E.2ED3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D.4E2.D3.D
3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D.2ED3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$.A4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$A6.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$3A.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$5.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$7.D3.D3.D3.D
3.D3.D3.D3.D3.D3.D3.D3.D3.D$4.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.
D$5.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D$6.D3.D3.D3.D3.D3.D3.D3.D3.D
3.D3.D3.D3.D$7.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D3.D!
We just need one more degree of freedom so that the tracks can build whatever we ask for. Frozen tracks have one extra built in degree of freedom - they can be stalled by any number of generations when they begin. This allows us to build any LWSS which differs from the ones on the red dots by some number of generations. That gives us all 4 shapes and gives us a half-density covering of the plane, leaving only a black vs white problem, and it is much easier to look for two recipes than 16.
This isn't LWSS specific, any recipe that has a moving output will be severely limited unless instigated by a frozen component. Look through the Waterbear for any places that a climber is climbing a beehive. I relied very heavily on those to get the timings right to built up the helix.
Hope this helps people understand the place for frozen tracks in the big picture.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So Hartmut, to respond directly to you,
HartmutHolzwart wrote:Coming from the caterpillar structure (which is the one engineered space ship I understand), what you have is a backbone with glider rakes that can send gliders with the correct timing on the lane you need them.
Not exactly, the available lanes are all the same color, so we have to work with monochromatic recipes like in the HBK. Also the timings are dreadfully constrained as mentioned above, so frozen tracks are needed to free that up.
You also have a x3 helix( or two) that work at the right slope and velocity. What we still need is a front end to first seed the Initial track and then build helper tracks. Correct?
I have codeholic's posted helix, but it doesn't have the properties I would like. I would much rather it liberate its glider to the northeast. A second helix which I have no idea how to design would then catch that glider, fan it out into support for the first set of climbers, and then they would take care of the rest of the ship. That front end is presently missing, correct.
Also finally we will need a clean up part at the en of the ship, but that's still in the distant future.
I'm relying on that being rather trivial. Gliders are pretty fragile and it is easy to find reactions that cleanly eliminate tracks, some which even eliminate the track which produced them.
Also, period multiplication to x3 needs to be solved.
Yep. I will eventually look into this.
We need an efficient way to multiply / redirect the helix glider.
See above, that's part of the front end that I don't know how to work out. I think the left helix will just produce this glider, and the right helix will do all the multiplication and redirection. The big issue is that we don't have recipes for all the helix in its present state. The waterbear used recipes that work for LWSS and MWSS on the right of the tracks (where the ship is travelling northeast). I was under the impression that it is easier to build ships on the left of the tracks, so the HWSS in the helix are made possible. However, for one of the HWSS, the recipe used in the caterpillar comes just short of the required clearance. (This is the one shown in yellow at the bottom of
this post). So we still need recipes for spaceships on the left, consisting of the ingredients listed in that post. If someone could find those it would be helpful, but I think it should probably wait until we have a helix which gives out a NE glider.
I'm not sure I really understood the reset thing, though. I understand this is an additional complexity coming from the obliques slope of the reaction.
It actually just comes from the fact that the track is made of gliders and so is in constant motion. We don't ever need to reset, but without resets the ship grows exponentially larger with every construction task, and I don't want to be responsible for a billion-cell claim to a spaceship that nobody could verify. It is much more straightforward to keep the constructor and its job close to one another so that the complications that I already ran into above a little don't get out of hand.
Physics: sophistication from simplicity.