Width-N Still-lifes Syntheses

[vilc]

This thread is dedicated to a new kind of synthesis project that I imagined back in early 2024. The goal is to provide proofs that still-lifes in infinite classes with a complex structure are glider-constructible. To keep things simple, I chose width-N still-lifes, for N as large as we can. I have already completed by myself the proofs for width 2 to 4 still-lifes, which are entirely computer-checked. Width 5 could be as difficult as one "X-bit still-lifes syntheses" project. The size of the proofs increases exponentially with width, and the difficulty of individual components could quickly reach the limits of current still-lifes syntheses method. Despite that, I still want to try, if only to see where we will hit a wall.

Status
Width 2 : Proof completed in early 2024
Width 3 : Proof completed in early 2024
Width 4 : Proof completed on July 10th, 2026
Width 5 : In progress, see below

Note : The number of missing transformations is only indicative and might sometimes increase with progress.

Organisation of the proofs
We consider all possible ends for width-N still-lifes in a tree where nodes at depth X have X rows in common. We find components that produce such ends from strictly shorter ones, and make sure that they work in all contexts. If we have one such component, we mark the corresponding node as solved. If all paths from the root of the tree must pass through a solved node, the proof is complete.

Indeed, to find a synthesis for a given width-N still-life from this set of components, one just has to find the solved node corresponding to its end in the tree, then to apply the component to produce this still-life from a shorter one, an repeat this process until the synthesis starts from vacuum. By induction and finiteness of the target still-life, this will always happen.
The resulting synthesis may look like this. Note that some extensions come in several steps.

Code: Select all

x = 3179, y = 65, rule = B3/S23
1158bo$1156bobo$1157b2o$1775bo$1202bo572bobo$1201bo573b2o$1201b3o3$
1152bo9bo$1150bobo7bobo8bo$1151b2o8b2o9bo93bo499bo$1170b3o91bobo500b2o
$706bo558b2o499b2o17bo$274bo429b2o1078bo151bo$275bo400bo28b2o1077b3o
150bo$273b3o398bobo8bo3bobo459bo116bo666b3o$675b2o9bo3b2o457bobo41bo
72bobo499bo1154bo$684b3o3bo15bo443b2o16bo22b2o74b2o500bo1151bobo$705bo
460bobo23b2o573b3o1152b2o$692bo12b3o459b2o510bo$692bobo983bo94bobo$
692b2o984b3o92b2o$1774bo860bo102bo189bo$490bobo1173bo870bo98b2o92bo8b
2o185bobo7bo$491b2o94bo884bo91bo102b2o193bo675b2o95b2o94b2o5b2o187b2o
6bo$491bo3bobo87bobo882bobo92bo100b2o192bobo674b2o191b2o203b3o$495b2o
89b2o197bo685b2o90b3o295b2o192bobo92bobo89bo11bo483bo191bobo94bobo$
489bo6bo289bo388bo105bo774b2o93b2o87bobo9b2o90bo96bo193b2o101b2o191b2o
95b2o101bo$392bobo92bobo294b3o389b2o101b2o87bo191bo490bo4bo94bo89b2o
10b2o90b2o95bo94b2o95bobo100bobo191bo96bo100b2o$2bo98b2o290b2o93b2o
685b2o103b2o87b2o97bo92bo104bo191bo193b2o290b2o94b3o93bobo97bo493b2o$
3bo96bo2bo289bo974b2o99bo89b3o102bobo91bo100bo191b2o94bo390bo485bo$b3o
96bo2bo103bo98bo98bo98bo91b2o5bo91b2o5bo84b2o3b2ob2o4bo89b2ob2o4bo89b
2ob2o4bo89b2ob2o4bo89b2ob2o4bo89b2ob2o4bo85b2o2b2ob2o4bo71b3o11b2o2b2o
b2o4bo82b2ob2o2b2ob2o4bo71b2o9b2ob2o2b2ob2o4bo63bobo12b2o2b2ob2o2b2ob
2o4bo65b3o11b2ob2ob2o2b2ob2o4bo76b2ob2ob2ob2o2b2ob2o4bo66bo9b2ob2ob2ob
2o2b2ob2o4bo59b2o10b2o3b2ob2ob2ob2o2b2ob2o4bo68b2ob2o3b2ob2ob2ob2o2b2o
b2o4bo64b2o2b2ob2o3b2ob2ob2ob2o2b2ob2o4bo64b2o2b2ob2o3b2ob2ob2ob2o2b2o
b2o4bo64b2o2b2ob2o3b2ob2ob2ob2o2b2ob2o4bo55bo8b2o2b2ob2o3b2ob2ob2ob2o
2b2ob2o4bo60b2o2b2o2b2ob2o3b2ob2ob2ob2o2b2ob2o4bo61bo2b2o2b2ob2o3b2ob
2ob2ob2o2b2ob2o4bo61bo2b2o2b2ob2o3b2ob2ob2ob2o2b2ob2o4bo45b2o10b2o2bo
2b2o2b2ob2o3b2ob2ob2ob2o2b2ob2o4bo54b2ob2o2bo2b2o2b2ob2o3b2ob2ob2ob2o
2b2ob2o4bo$101b2o103bobo96bobo96bobo91b2o3bobo91bo4bobo89bobo4bobo82bo
bo4bobo4bobo89bobo4bobo87bobobo4bobo87bobobo4bobo87bobobo4bobo87bobobo
4bobo84bo2bobobo4bobo84bo2bobobo4bobo82bobo2bobobo4bobo82bobo2bobobo4b
obo63b2o12bobo2bobo2bobobo4bobo78bo3bobo2bobobo4bobo76bobo3bobo2bobobo
4bobo66b2o8bobo3bobo2bobobo4bobo57b2o11bo5bobo3bobo2bobobo4bobo68bobo
5bobo3bobo2bobobo4bobo63b2o3bobo5bobo3bobo2bobobo4bobo62bobo3bobo5bobo
3bobo2bobobo4bobo55bo8bo3bobo5bobo3bobo2bobobo4bobo54b2o4b2o2bo3bobo5b
obo3bobo2bobobo4bobo59bobo2bo3bobo5bobo3bobo2bobobo4bobo59bobo2bo3bobo
5bobo3bobo2bobobo4bobo59bobo2bo3bobo5bobo3bobo2bobobo4bobo43b2o11bo2bo
bo2bo3bobo5bobo3bobo2bobobo4bobo54bobo2bobo2bo3bobo5bobo3bobo2bobobo4b
obo$207bo96bobo93b2obobo92bobobobo92bobobobo89bo2bobobobo85bo3bo2bobob
obo83bo4bobobobobobo88bobobobobobo88bobobobobobo74b3o11bobobobobobo88b
obobobobobo86bobobobobobobo86bobobobobobobo67b2o12bobo2bobobobobobobo
82bo3bobobobobobobo80bobo3bobobobobobobo80bobo3bobobobobobobo75bobo2bo
bo3bobobobobobobo66b2o4b2obobo2bobo3bobobobobobobo62b3o8bobobo2bobo3bo
bobobobobobo69bo3bobobo2bobo3bobobobobobobo53b2o14bo3bobobo2bobo3bobob
obobobobo54bo9bo4bo3bobobo2bobo3bobobobobobobo56b2o4b3o4bo3bobobo2bobo
3bobobobobobobo54bobo4bob2o4bo3bobobo2bobo3bobobobobobobo63b2o4bo3bobo
bo2bobo3bobobobobobobo60bo2b2o4bo3bobobo2bobo3bobobobobobobo60bo2b2o4b
o3bobobo2bobo3bobobobobobobo48b3o7bobo2b2o4bo3bobobo2bobo3bobobobobobo
bo39b2o14bo2bobo2b2o4bo3bobobo2bobo3bobobobobobobo$bo101bo200b2o94b2ob
2o94b2ob2o94b2ob2o90b2o2b2ob2o90b2o2b2ob2o82bobo4b2o3b2ob2o90bo3b2ob2o
90bo3b2ob2o77bo2b2o8bo3b2ob2o79b3o5b2obo3b2ob2o88bobo3b2ob2o75b2o9b2ob
2o3b2ob2o67bobo12b2o2b2ob2o3b2ob2o69b3o11b2ob2ob2o3b2ob2o80b2ob2ob2ob
2o3b2ob2o69b2o9b2ob2ob2ob2o3b2ob2o76b2o2b2ob2ob2ob2o3b2ob2o73b2ob2o2b
2ob2ob2ob2o3b2ob2o65bo7b2ob2o2b2ob2ob2ob2o3b2ob2o69b2o2b2ob2o2b2ob2ob
2ob2o3b2ob2o53bobo13b2o2b2ob2o2b2ob2ob2ob2o3b2ob2o56b2o11b2o2b2ob2o2b
2ob2ob2ob2o3b2ob2o56bobo4bo5b2o2b2ob2o2b2ob2ob2ob2o3b2ob2o69b2o2b2ob2o
2b2ob2ob2ob2o3b2ob2o69b2o2b2ob2o2b2ob2ob2ob2o3b2ob2o60b2o7b2o2b2ob2o2b
2ob2ob2ob2o3b2ob2o60b2o7b2o2b2ob2o2b2ob2ob2ob2o3b2ob2o51bo8b2o7b2o2b2o
b2o2b2ob2ob2ob2o3b2ob2o39bobo13b2o3b2o7b2o2b2ob2o2b2ob2ob2ob2o3b2ob2o$
b2o100b2o283b3o493b2o288bo4b2o4b3o90bo4bo2bo98bo83bobo91bo100bo89b3o
102bobo290bo188bo98b2o6bo580bo89bo$obo99bobo285bo787bo6bo84bo6bo5b2o
186bo191bo92bo104bo483bo101b2o284b2o$290b2o10b2o85bo197bo298b3o379bobo
484bo196b2o10b2o91b3o285b2o100bobo189b2o91bobo$198bo90bobo9b2o90b2o
192b2o299bo199b2ob3o175b2o680bobo9b2o94bo90bo193bobo194b2o95bobo93bo
292bo$199b2o90bo11bo88bobo191bobo298bo191bo8bo2bo181bo392b2o90b3o192bo
11bo92bo91b2o388bobo97bo86b2o114b2o85b2o95b2o$198b2o194bo196b3o485b2o
5bobo3bo180b2o196b2o192bobo92bo100b2o286bobo390bo183bobo114b2o84bobo
94bobo$211bo371b2o6bo486bobo5b2o77b2o105bobo97b2o12b3o83b2o193bo91bo
102b2o864bo202bo202b3o$197bo12b2o370bobo7bo398b2o171bobo3b3o200b2o11bo
84bo389bo883b3o386bo$196b2o12bobo371bo405b2o174bo5bo199bo9b2o3bo191bo
1165bo92b3o294bo$196bobo784b2o7bo178bo3b2o204bobo99b3o92b2o293b3o870bo
93bo$982bobo190bobo91b2o112bo99bo94bobo292bo856b3o106bo$984bo190bo94b
2o121bo90bo389bo857bo5b2o10bo$578b2o689bo122b2o178b3o1156bo7b2o8b2o$
577bobo812bobo179bo1163bo10bobo$579bo612bo380bo$1191b2o1031b3o$1175b2o
14bobo395b3o634bo$1176b2o411bo635bo$1175bo395b2o17bo$1201b2o369b2o$
1200b2o369bo$1188b2o12bo$1169b3o16bobo2b2o$1171bo16bo3b2o$1144bo25bo
23bo$1144b2o$1143bobo434b2o$1580bobo$1580bo!

Continuous synthesis to watch the still-life being extended progressively:

Code: Select all

x = 920, y = 917, rule = B3/S23
913bo$913bobo$913b2o18$31bo$32b2o$31b2o3$27bobo$28b2o11bo$28bo13bo$40b
3o4$46bo$47bo$45b3o831bo$879bobo$49bo829b2o$50b2o$49b2o6$66bo$58bo8b2o
$59b2o5b2o$58b2o10$75bo$76b2o$75b2o10$86bobo$87b2o$87bo8$95bo$96b2o$
95b2o4$96bo8bo$94bobo6bobo$95b2o7b2o23$126bo689bo$127b2o686bo$126b2o
687b3o22$160bo$158bobo$159b2o2$156bo11bo$157bo11bo$155b3o9b3o$164bo$
162bobo$163b2o$169bo$167bobo$168b2o9$176bo$174bobo$175b2o14$748bobo$
748b2o$749bo4$210bobo$211b2o$211bo20bo$230bobo$231b2o526bo$207bo549b2o
$208b2o548b2o$207b2o$232bo$233b2o$232b2o$747bo$746bo$746b3o3$747bo$
745b2o$746b2o2$236bo$234bobo$221bobo11b2o$222b2o$222bo2$233bobo$234b2o
$234bo9$247bo$248b2o$247b2o2$243bo$244b2o12bobo$243b2o14b2o$259bo3$
255bo$256b2o$255b2o5$263bo$264b2o$263b2o13$293bo$294bo$292b3o3$295bo$
296bo$294b3o11$680bobo$680b2o$681bo6$297bo$298bo$296b3o$324bo$325bo$
323b3o3$661bo$661bobo$661b2o2$318bo9bo$319bo9bo$317b3o7b3o8bo$336bobo$
337b2o3$317bo$318bo$316b3o15bo316bobo$335bo315b2o$333b3o316bo9$341bobo
$342b2o$342bo13$356bobo$357b2o$357bo$367bo$368bo$366b3o6$618bo$618bobo
$377bobo13bo224b2o$378b2o7bo6bo$378bo9b2o2b3o$387b2o231bo$618b2o$605bo
bo11b2o$605b2o$606bo2$386bobo$387b2o$387bo5$400bo$398bobo$399b2o198bo$
599bobo$396bo202b2o$397b2o$396b2o2$403bo$404b2o$403b2o10$409bo$410b2o$
409b2o32$453bo$454bo$452b3o$445bo$446b2o$445b2o100$452bo$452b2o$451bob
o3$450b2o$449bobo$451bo6$570bo$556bo12b2o$555b2o12bobo$555bobo5$426bo
147b2o$426b2o146bobo$425bobo146bo22$399b2o$398bobo$400bo2$403b3o$405bo
$404bo9$387b3o$389bo$388bo216b2o$384bo219b2o$384b2o220bo$383bobo4$379b
o$379b2o$378bobo3$369b2o$368bobo$370bo14$359b2o$360b2o$359bo2$638b2o$
340b2o295b2o6b2o$339bobo3bo12b2o279bo4b2o$341bo3b2o2b3o5bobo286bo$344b
obo4bo7bo$350bo5$331b3o3b2o$333bo2bobo$332bo5bo$634b3o$634bo$635bo3$
651b2o$342bo307b2o$342b2o308bo$341bobo$661bo$660b2o$660bobo$336b2o309b
3o3bo$335bobo309bo4b2o$337bo310bo3bobo$310b2o$311b2o$310bo12$304b2o$
303bobo$305bo4$300b2o$301b2o$300bo3$297bo$297b2o$296bobo28$267b2o452b
3o$258bo9b2o451bo$258b2o7bo9b2o443bo$257bobo16bobo$278bo$246bo481bo$
246b2o479b2o$245bobo11b2o466bobo$258bobo$260bo2$728b2o$727b2o$729bo3$
728b3o$728bo$729bo$256b2o$257b2o$256bo$231b2o$232b2o506b2o$231bo507b2o
$255b2o484bo$254bobo$235bo20bo$219b2o14b2o$220b2o12bobo$219bo2$223b2o$
224b2o505bo$223bo506b2o$730bobo8$210bo$210b2o$209bobo4$211b2o$210bobo$
212bo2$764b2o$763b2o$765bo2$767bo$191b3o572b2o$193bo572bobo$192bo26$
160bo8b2o$160b2o8b2o$159bobo7bo4$158b2o$157bobo$159bo33$110bo$110b2o$
109bobo8$100bo$100b2o$99bobo2$104b3o$106bo$105bo2$86b3o$88bo755b3o$87b
o756bo$845bo$90b2o$91b2o$90bo3$75b2o$74bobo13b3o$76bo15bo$91bo$79bo$
79b2o$78bobo4$79b2o$78bobo$66bo13bo$66b2o$65bobo8$61b2o$60bobo$62bo$
55b2o$54bobo$56bo$875b3o$875bo$876bo$58b3o$60bo5b2o812bo$59bo7b2o810b
2o$66bo812bobo3$48b3o$50bo$49bo$56b3o$58bo$57bo4$32b2o$31bobo$33bo4$
30b2o$31b2o$30bo14$bo$b2o$obo6$918b2o$917b2o$919bo!

Contributing
To contribute, select an unsolved transformation from the most recent list. Suppose that you picked this one :

Code: Select all

x = 7, y = 4, rule = LifeHistory
3B2CBC$2BDBCBC$2BDADBC$3BCA2B!

Your target is to make the part marked in red/white from a shorter still-life end. The ON cells are only a hint, you can modify them the way you want, as long as they are shorter than the marked cells, and that you keep at least two rows of unchanged cells in the right extremity of the transformation. If you have a component that seems to produce a needed transformation, post it here, preferably in the following format, with still-life elongation right to left :

Code: Select all

x = 14, y = 9, rule = LifeHistory
.A$2.A$3A3$3.2A3B2CBCE$2.A.A2BDBCBC$4.A2BDADBC.E$5.3BCA2B2E!

Components may have multiple stages. Be careful to verify which regions are modified during the application of the component. In the transformation, at least two stable rows must remain the same, to ensure that the component can be generalised. The rule is that for the last two such rows, a two cells margin on every side must remain off, and these rows are not allowed to change during the execution of the component.

Code: Select all

x = 14, y = 8, rule = LifeHistory
5.9F$5.9F$3B2CBC7F$2BDBCBC7F$2BDADBC7F$3BCA2B7F$5.9F$5.9F!

Here the region that cannot change corresponds to the semi-infinite rectangle that is partially marked in grey. These cells are not allowed to change. If your component affects this forbidden region, try to find a different one or to modify it. If this doesn't work try to add some marked rows of still-life, as this will move the forbidden region to the right. Note that it makes the component less general (more transformations might be required to cover the other completions).

Code: Select all

x = 16, y = 8, rule = LifeHistory
7.9F$7.9F$3B2CB2CB7F$2BDBCBC2B7F$2BDADBCBC7F$3BCA2B2C7F$7.9F$7.9F!

If you have doubts, especially in the beginning of this project, post your component anyway (but without LifeHistory marks), it could always be useful.

Verifying the proofs
One of the reasons why it took me so long before officially starting this project is that I wanted to write robust and scalable software before tackling large widths. The proofs are now entirely computer-verifiable. The software (available below) is written in C++ and relies on cpp_shinjuku and lifelib for the components, but there is also a standalone program with no dependency to verify that a transformation set covers all tree branches. There is also a practical verification : the program can use the proof to find a synthesis for any width-N still-life. Currently, I am not focusing on performance (which should suffice up to width at least 6 for the components and width 9 for the enumeration of transformations), but rather the readability, robustness and user-friendliness of the code. Please post any suggestion or bug in this thread.

If you have good programming skills, you are welcome to contribute an independant verification tool, even partial, or to look for bugs in my verification code.


History of the project
I began the project no later than February 2024, even before I joined the forums. The proof for width-2 still-lifes was found by hand entirely, and checked with help from JLS. For the proof of width-3 still-lifes, completed a few days later, I used a more systematic approach, still with JLS. The resulting proof was quite nice and optimised, but very hard to check (note that I modified the syntax of transformations since) :

Code: Select all

x = 408, y = 376, rule = LifeHistory
332.A$333.A$331.3A7$318.D$318.D$318.D$318.D$62.2D43.D210.D$61.D45.D
210.D$61.D13.D31.D210.D$61.D3.2CB8.D8.2CB7.2DB9.D240.2A2.2A.2DB$61.D
3.2C6.5D7.2CB7.2DB9.D239.A.A.2A2.2DB$61.D3.B10.D8.4B6.4B8.D241.A3.A.
4B$61.D13.D31.D$61.D$61.D$61.D$61.D$61.D$61.D$61.D$61.D$61.D$61.D$61.
D$61.D$61.D$61.D$61.D50.2D37.4D$61.D49.D13.D28.D$61.D49.D3.2CB8.D5.2C
2B5.DC2B9.D$61.D49.D3.CBC5.5D4.CBCB5.CBCB6.4D$61.D49.D3.BC.B7.D5.BC.B
5.BC.B6.D$61.D49.D13.D25.D163.4D$61.D49.D39.4D163.D14.D20.D16.A.A$61.
D49.D206.D13.D2.D4.D4.D.D.4D2.D16.2A$61.D49.D203.4D13.D2.D4.D3.D2.D4.
D2.D16.A$61.D20.2D27.D203.D16.D2.D4.D3.D2.D4.D2.D$42.2D17.D19.D29.D
203.D16.D2.D4.D3.D2.D.4D2.D14.2A$41.D19.D19.D13.D15.D203.4D13.D2.D4.D
2.D3.D.D5.D15.2A$41.D3.2CB12.D20.D3.2CB8.D8.2CB3.D220.D2.D4.D2.D3.D.D
5.D14.A4.DCB$41.D3.C15.D19.D3.CB6.5D7.CB3.D221.D2.D4.D.D4.D.4D2.D19.C
BC$41.D3.B15.D19.D3.BC9.D8.BC.B2.D221.D20.D20.BC$41.D19.D19.D13.D15.D
$41.D19.D19.D29.D$41.D19.D19.D29.D$41.D19.D19.D29.D$41.D19.D19.D29.D$
41.D19.D19.D29.D$41.D19.D19.D29.D13.D25.4D$41.D19.D19.D29.D3.2CB8.D5.
2C2B5.2D2B9.D$41.D19.D19.D29.D3.C2B5.5D4.C2BC5.DABC9.D$41.D19.D19.D
29.D3.BC.B7.D5.B2CB5.B2CB6.4D$41.D19.D19.D29.D13.D28.D$41.D19.D19.D
30.2D40.D$41.D19.D19.D69.4D194.A$41.D19.D19.D265.2A$41.D19.D19.D266.
2A$41.D19.D19.D$41.D19.D19.D258.A$41.D19.D19.D259.A$41.D19.D19.D257.
3A$41.D19.D19.D$41.D19.D19.D233.4D$41.D19.D19.D236.D$41.D19.D19.D236.
D15.A4.2A$41.D19.D19.D233.4D15.2A4.2A3.2D2B$41.D19.D19.D158.D2.D74.D
14.A.A3.A5.DABCA$41.D19.D19.D100.2D56.D2.D74.D26.B2CBA$41.D19.D19.D
99.D15.D42.D2.D71.4D$41.D19.D3.2CB12.D100.D3.2CB2C8.D6.2CB2CB14.2DB2C
B9.4D$41.D19.D3.CB14.D99.D3.CB2CB5.5D5.CB2CB15.DBDCB13.D$41.D19.D3.B
15.D99.D3.5B8.D6.5B15.5B13.D$41.D20.2D17.D99.D15.D45.D$41.D39.D99.D$
41.D39.D99.D152.3A$41.D39.D99.D154.A$41.D39.D99.D153.A$41.D39.D60.2D
37.D$41.D39.D59.D13.D25.D$41.D39.D59.D3.2CBC7.D8.2CBC12.D$41.D39.D59.
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38.D4.CB2CB11.D19.D3.CB2C2B7.D6.CB2C2B2CB6.DB2D2B2CB20.D$.D39.D3.C7.
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39.D3.B10.D8.3B13.D38.D4.4B12.D19.D3.4BC.B6.D6.4B2C2B7.4B2D2B18.4D$.D
39.D13.D25.D39.2D18.D19.D15.D$.D40.2D37.D59.D20.2D$.D79.D59.D$.D79.D
59.D$.D79.D59.D$.D79.D59.D47.4D$.D79.D59.D13.D33.D$.D79.D59.D3.CB2CB
6.D8.CB2CB5.DB2CB9.D$.D79.D59.D3.2CBCB3.5D7.2CBCB5.2DACB9.4D187.A$.D
79.D59.D3.5B6.D8.6B4.6B11.D145.D6.D33.A$.D79.D59.D13.D36.D122.4D18.D
2.4D2.D29.A2.3A$.D79.D60.2D45.4D125.D18.D2.D5.D27.A.A$.D79.D236.D18.D
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2A$44.D2.B2CB7.D8.B2C3B4.BDC2B21.D4.D275.A.A$44.D12.D45.D4.D$45.2D56.
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2.D$315.D2.D21.D2.D5.D$315.D2.D21.D2.D5.D$315.4D21.D2.4D2.D30.CB2C2B
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2.4D2.D$341.D6.D$384.2A$383.2A$380.2A3.A$381.2A$380.A2$385.2A$384.2A$
386.A8$345.A$345.A.A$345.2A$343.A$341.A.A$342.2A$315.D.4D$315.D.D2.D
23.A$315.D.D2.D23.2A$315.D.D2.D22.A.A$315.D.D2.D24.DBDC3B$315.D.D2.D
24.2DABCB$315.D.4D24.3B2CB23$357.A$315.D4.D30.A5.A.A$315.D4.D31.A4.2A
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349.A$350.A27.2A$315.D.4D27.3A4.BD3B17.A2.A$315.D4.D34.DBDB18.A2.A3.B
D3B$315.D4.D34.BD3B18.2A4.DBDB$315.D.4D27.A35.BD3B$315.D4.D27.2A30.A$
315.D4.D26.A.A30.2A$315.D.4D58.A.A!

I tried to apply the same reasonnings to width-4 still-lifes, but halfway in the construction of the tree I concluded that the manual method did not scale and was not easy to verify. I wrote software to check and enumerate transformations, and by July 2024 I had gathered or built most of the needed synthesis components. However, the process of organising and checking all those components was too cumbersome. After a year trying to organise the proof in a readable and checkable format, I decided that component verification should also be automated, and that is one of the reasons why I started developping cpp_shinjuku. I restarted the project in the end of June and wrote the rest of the verification software. This allowed me to find one unsolved transformation (a block on table construction), for which I made a component right away. The proof for width-4 still-lifes was completed in a computer-verifiable fashion on July 10th, 2026.
The width-5 still-lifes syntheses project was launched in the post below on July 14th, 2026.

[vilc]

This post will serve as a place to monitor the width-5 still-lifes syntheses project.

The latest set of needed transformations is here :

Code: Select all

x = 810, y = 680, rule = LifeHistory
2B2D4BC23.2B2D2A2B24.2B2DB2C2B23.2B2DB2D3B22.2B2DB2C2BC22.2B2DB2CB24.
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24.2B2DACB25.2B2DB2CB24.2B2DBDCB24.2B2DB2D2B23.2B2DB2D2B23.2B2DB2D2B
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25.2B2DBCB25.2BDCBCB25.2B2DB2CBC23.2B2DB2CB24.2B2DBDCB24.2B2DBDCB24.
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2B2DBDBC24.2B2DBDBC24.2B2DBDA2C$6BDCB23.6BDCB23.6B2C24.5B2CB24.6BC25.
7B25.3B2A2B25.9B23.8B24.8B24.8B24.5BACB24.6BDBC23.4BABCB24.5BACB24.5B
ACB24.6BDCB23.6B2D2B22.4BAB2C24.4BAB2C24.6BDCB23.4BAB2C24.4BAB2C24.6B
2C24.6B2C24.6BDBC21$2B2D4B24.2B2D4B24.2B2D4B24.2B2D4B24.2BDCA2B25.2B
2D2B2C24.2B2D2B26.2B2DB2CBC23.2B2DB2C2B23.2B2DB2D2B23.2B2DB2DBC23.2B
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2DBC2B24.2B2DB2CB24.2B2DB2CB$2BD2BDCB24.2BD2BDCB24.2BD2B2CB24.2BD2B2C
B24.2BDABCB25.2BD2BC2B24.2BD2BC26.3BDBC3B23.3BDBC2BC23.3BDBCABC23.3BD
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3BDBDCB24.3BDBC2B$3BDBCBC24.3BDBCBC24.3BDBC2B24.3BDBCBC24.3BDB2C25.3B
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2BA2B24.2BD3B2C$2B2DBCBC24.2B2DBC2B24.2B2DBDBC24.2B2DBDBC24.2B2DBCB
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2BDB2DBC24.2BDBDCBC24.2BDB2D2B$6BCB24.6B2C24.6B2C24.6B2C24.6BC25.6B2C
24.5BC26.9B23.8BC23.8BC23.8BC23.7BC24.7BCB23.7BDCB22.7B2CB22.7B2C23.
7BC24.6B26.3BD2B26.3BDBD3B23.3BDBCA2B23.3BDBCABC23.3BDACBC24.3BDBDBC
24.3BDACBC24.3BDBD2B21$2B2DB2D2B23.2B2DBDCB24.2B2DBDCB24.2B2DBCB25.2B
2DB2C25.2B2DBDBC24.2B2DBD2B24.2B2DB2CB24.2B2DB2D2B23.2B2DB2D2B23.2B2D
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B2CBC23.2B2DB2D2B23.2B2DBCDBC23.2B2DBCDBC23.2B2DBCBC24.2B2DBC2B24.2B
2DB2CB24.2B2DBDBC24.2B2DBD2B24.2B2DB2CB$3BDBD3B23.3BDBCBC24.3BDBCBC
24.3BDB2C25.3BDB2C25.3BDBDCB24.3BDBD2C24.3BDBDCB24.3BDBD2BC23.3BDBD3B
23.3BDBD3B23.3BDBCBC24.3BDBCBC24.3BDBC3B23.3BDBC2BC23.3BDBCBC24.3BDBC
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3BDBDCB24.3BDBD2C24.3BDBDCB$2BD3BD2B23.2BD2BA2B24.2BD2BA2B24.2BD4B25.
2BD4B25.2BD2BA2B24.2BD2BA2B24.2BD2BA2B24.2BD2BD3B23.2BD2BD3B23.2BD2BD
3B23.2BD2BD2B24.2BD2BD2B24.2BD3BA2C23.2BD3BA2C23.2BD2BABC24.2BD6B23.
2BD2BA2BC23.2BD6B23.2BD6B23.2BD5B24.2BD5B24.2BDBA3B24.2BD2BA2B24.2BD
2BA2B24.2BD2BA2B$2BDB2DBCB23.2BDB2D2C24.2BDB2DCB24.2BDBD2C25.2BDBD2C
25.2BDBDCBC24.2BDBDCBC24.2BDBDCBC24.2BDBDB3C23.2BDBDB2CB23.2BDBDB2CB
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2BDBDCBC24.2BDBDCBC24.2BDBDCBC$3BDBDB2C23.3BDBD2B24.3BDBDBC24.3BDBCB
25.3BDBCB25.3BDBDCB24.3BDBDCB24.3BDBDCB24.3B2DBC2B23.3B2DBCBC23.3B2DB
CBC23.3B2DBCB24.3BCDB2C24.3B2D4B23.3B2D3BC23.3B2D3B24.3B2DBACB23.3B2D
BACB23.3B2D2BCB23.3B2D2B2C23.3BDCABC24.3BDCABC24.3B2D2BC24.3B2DB2C24.
3B2DB2C24.3B2DB2C21$2BDB2D2BC23.2BDB2D3B23.2BDB2D2BC23.2BDB2DBC24.2BD
BDC2B24.2BDACD2B24.2BDBDCA2B23.2BDB2D3B23.2BDBDCABC23.2BDB2DBC24.2BDB
2CBC24.2BDBDCB25.2BDB2DBC24.2BDB2D2B24.2BD2B2CB24.2BD2B2CB24.2BD2BD2B
C23.2BD2BD3B23.2BD2BD2BC23.2BD2BDBC24.2BD2BC2B24.2BD2AD2B24.2BD2BDCB
24.2BD2BDCB24.2BD2B2C25.2BDB2D2B$2B2DBD3C23.2B2DB2DCB23.2B2DBD3C23.2B
2DBDCB24.2B2DB3C24.2BDCBC2B24.2B2DBC2BC23.2B2DBCABC23.2B2DBDABC23.2B
2DBDBC24.2B2DBCBC24.2B2DB2C25.2B2DBDCB24.2B2DBD2C24.2B2DCDBC24.2B2DCD
BC24.2B4D3C23.2B5DCB23.2B4D3C23.2B4DCB24.2B3D3C24.2BDCDC2B24.2B3DCBC
24.2B3DCBC24.2B3DCB25.2BDCBACB$5BA3B23.6BABC23.5BA3B23.5BA2B24.8B24.
5BA2C24.6BABC23.5BA3B23.5BA3B23.8B24.5BA2B24.7B25.5BA2B24.5BA2B24.3BA
BA2B24.4B2ABC24.5BA3B23.6BABC23.5BA3B23.5BA2B24.8B24.5BA2C24.5BA2B24.
5BA2B24.7B25.3B2ADCB$2B3DCABC23.2B3DC2BC23.2B4DABC23.2B3DCBC24.2B4DBC
24.2B2DCD2B24.2B5DCB23.2B4D3C23.2B4D3C23.2B3D3C24.2B4DCB24.2B3D2C25.
2B3DCBC24.2B3DCBC24.2BDCDCBC24.2B4DBC24.2B3DCABC23.2B3DC2BC23.2B4DABC
23.2B3DCBC24.2B4DBC24.2B2DCD2B24.2B4D2C24.2B4DCB24.2B3DCB25.2B2DBD2B$
2BD2BD3B23.2BD2BCA2B23.2BD2BCABC23.2BDBACBC24.2BD2BDBC24.2BDBAC2B24.
2BD2BD3B23.2BD2BD2BC23.2BD2BD2BC23.2BD2BC2B24.2BD2BDBC24.2BD2BCB25.2B
D2BDCB24.2BD2BDCB24.2BDBACBC24.2BD2BDBC24.2BD2BD3B23.2BD2BCA2B23.2BD
2BCABC23.2BDBACBC24.2BD2BDBC24.2BDBAC2B24.2BD2BD2B24.2BD2BDBC24.2BD2B
2C25.2BDBD2BC21$2BDB2CB25.2BDBDCB25.2BDB2D2B24.2BDB2CBC24.2BDB2DBC24.
2BDB2CBC24.2B2DBC26.2BDCA2BC24.2BDCABC25.2B2D3B25.2B2D2BC25.2B2DBD2BC
23.2B2DBD3B23.2B2DBD2BC23.2B2DBDBC24.2B2DBC2B24.2B2DB2CB24.2B2DB2CB
24.2B2DB2D2B23.2B2DBDCB24.2B2DBDCB24.2B2DBCB25.2B2DB2C25.2B2DBDBC24.
2B2DBD2B24.2B2DB2CB$2B2DACB25.2B2DB2C25.2B2DBD2B24.2B2DBCBC24.2B2DBDB
C24.2B2DACBC24.2B2DBC26.2BDC2BCB24.2B2DABC25.2B2D3B25.2B2D3B25.2B2DBD
3C23.2B2DB2DCB23.2B2DBD3C23.2B2DBDCB24.2B2DB3C24.2B2DBDCB24.2B2DBC2B
24.2B2DBD3B23.2B2DBCBC24.2B2DBCBC24.2B2DB2C25.2B2DB2C25.2B2DBDCB24.2B
2DBD2C24.2B2DBDCB$7B25.7B25.5BDBC24.4BADBC24.5BD2B24.5BDBC24.3BABC26.
5BACB24.3BA3B25.7B25.7B25.5BA3B23.6BABC23.5BA3B23.5BA2B24.8B24.5BA2B
24.6B2C24.6BD2B23.5BA2B24.5BA2B24.7B25.7B25.5BA2B24.5BA2B24.5BA2B$2B
2DACB25.2B2DB2C25.2B2DBD2B24.2B2DAC2B24.2B2DBDBC24.2B2DACBC24.2BD2CB
26.2B4DBC24.2BDCD2C25.2B3DCB25.2B3DCB25.2B3DCABC23.2B3DC2BC23.2B4DABC
23.2B3DCBC24.2B4DBC24.2B3DCBC24.2B4D2B24.2B4DBCB23.2B4D2C24.2B4DCB24.
2B3D2C25.2B3D2C25.2B3DCBC24.2B3DCBC24.2B3DCBC$2BDB2CB25.2BDBDCB25.2BD
B2D2B24.2BDB2D2B24.2BDB2DBC24.2BDB2CBC24.2BD3B26.2BD2BDBC24.2BDBACB
25.2BD2B2C25.2BD2B2C25.2BD2BD3B23.2BD2BCA2B23.2BD2BCABC23.2BDBACBC24.
2BD2BDBC24.2BDBACBC24.2BD2BD2B24.2BD2BDB2C23.2BD2BD2B24.2BD2BDBC24.2B
D2BCB25.2BD2BCB25.2BD2BDCB24.2BD2BDCB24.2BD2BDCB21$2B2DB2CB24.2B2DB2C
2B23.2B2DB2D2B23.2B2DB2D3B22.2B2DB2C2BC22.2B2DB2CB24.2B2DB2DBC23.2B2D
B2CBC23.2B2DB2C2B23.2B2DBDCB24.2B2DB2CB24.2B2DB2CB24.2B2DB2C25.2B2DB
2CB24.2B2DBDCB24.2B2DB2D2B23.2B2DB2D2B23.2B2DB2DBC23.2B2DB2D2B23.2B2D
B2D2B23.2B2DB2D2B23.2B2DB2CB24.2B2DB2CB24.2B2DAB2C24.2B2D2B2C24.2B2D
2B2CB$2B2DBCBC24.2B2DBC2BC23.2B2DBD3B23.2B2DBDBACB22.2B2DBC2BCB22.2B
2DBCBC24.2B2DBDA2C23.2B2DBC3B23.2B2DBC2BC23.2B2DBCBC24.2B2DADBC24.2B
2DADBC24.2B2DB2C25.2B2DBC2B24.2B2DBCBC24.2B2DBD3B23.2B2DBD3B23.2B2DBD
3B23.2B2DBD2BC23.2B2DBD3B23.2B2DBD3B23.2B2DADBC24.2B2DADBC24.2BDBCABC
24.2BDBD2BC24.2BDBDAB2C$5BD2B24.5BDB2C23.5BDBCB23.5BDBDCB22.5BDADCB
22.5BDBC24.5BC3B23.5BDA2C23.5BDA2C23.5BCBC24.3BABA2B24.4B2ABC24.7B25.
5BDBC24.4BADBC24.5BD3B23.5BD3B23.5BD3B23.5BD3B23.5BD2BC23.5BD3B23.3BA
BC2B24.4BACBC24.4B2DBC24.4B2DBC24.4BDC3B$2B2DBD2B24.2B2DBCBCB23.2B2DB
DB2C23.2B2DBDBC2B22.2B2DBDBC2B22.2B2DBDBC24.2B2DBACBC23.2B2D2BDBC23.
2B2D2BD2B23.2B2D2BCB24.2BDCBCBC24.2B2DBDBC24.2B2DB2C25.2B2DBD2B24.2B
2DAC2B24.2B2DBDB2C23.2B2DBDBCB23.2B2DBDBCB23.2B2DBDBCB23.2B2DBDBCB23.
2B2DBDB2C23.2BDCBCBC24.2B2DBDBC24.2BD2BDBC24.2BD2BD2B24.2BD2BDA2C$2BD
BD3B24.2BDBD2A2B23.2BDBD4B23.2BDBD3B2C22.2BDBD3B2C22.2BDBD3B24.2BDB2D
3B23.2BDB2D3B23.2BDB2D2BC23.2BDB2D2B24.2BDB2CBC24.2BDB2DBC24.2BDBDCB
25.2BDB2D2B24.2BDB2D2B24.2BDB2DBCB23.2BDB2DB2C23.2BDB2DB2C23.2BDB2DB
2C23.2BDB2DB2C23.2BDB2DB2C23.2BDB2CBC24.2BDB2DBC24.2B2D4B24.2B2D3BC
24.2B2D2BDBC21$2B2D2B2C24.2B2DAB2C24.2B2DAB2C24.2B2DAB2C24.2B2DACB25.
2B2DB2CB24.2B2DB2CB24.2B2DBD2BC23.2B2DBD3B23.2B2DBD2BC23.2B2DBDBC24.
2B2DBC2B24.2BDCAD2B24.2B2DBDCB24.2B2DBDCB24.2B2DB2C25.2BDCA2B25.2B2DA
B2C24.2B2DB2CBC23.2B2DB2D2B23.2B2DB2CBC23.2B2DB2CBC23.2B2DBDCA2B22.2B
2DB2D2BC22.2B2DB2C2BC22.2B2DB2CB$2BDBD2BC24.2BDBCABC24.2BDBCABC24.2BD
BCABC24.2BDB2CB25.2BDBCDBC24.2BDBCDBC24.2BDB2D3C23.2BDB3DCB23.2BDB2D
3C23.2BDB2DCB24.2BDBD3C24.2BDADC2B24.2BDBDCBC24.2BDBDCBC24.2BDBDCB25.
2BDADBC25.2BDBCABC24.2B2DBCB2C23.2B2DBDACB23.2B2DBCB2C23.2B2DBC3B23.
2B2DBDABCB22.2B2DBD2BCB22.2B2DBC2BCB22.2B2DBCBC$4B2DBC24.4B2DBC24.4B
2D2B24.4B2DBC24.7B25.3BABA2B24.4B2ABC24.5BA3B23.6BABC23.5BA3B23.5BA2B
24.8B24.5BA2C24.5BA2B24.5BA2B24.7B25.4BCBC25.4B2DBC24.5BD3B23.5BDABC
23.5BD3B23.5BDA2C23.5BDBDCB22.5BDBDCB22.5BDADCB22.5BDBC$2BD2BCBC24.2B
DBAC2B24.2BDBACBC24.2BD2BDBC24.2BDB2CB25.2BDADCBC24.2BDB2DBC24.2BDBDC
ABC23.2BDBDC2BC23.2BDB2DABC23.2BDBDCBC24.2BDB2DBC24.2BDBCD2B24.2BDB2D
2C24.2BDB2DCB24.2BDBDCB25.2BDACBC25.2BDBD2BC24.2B2DBD3B23.2B2DBD3B23.
2B2DBD3B23.2B2DBD2BC23.2B2DBDBACB22.2B2DBDBACB22.2B2DBCABCB22.2B2DBC
2B$2B2DBACB24.2B2DAB2C24.2B2DAB2C24.2B2D2B2C24.2B2DACB25.2B2DACBC24.
2B2DBDBC24.2B2DBD3B23.2B2DBCA2B23.2B2DBCABC23.2B2DACBC24.2B2DBDBC24.
2B2DAC2B24.2B2DBD2B24.2B2DBDBC24.2B2DB2C25.2B2D3B25.2B2D2B2C24.2B2DB
2D2B23.2B2DB2D2B23.2B2DB2DBC23.2B2DB2D2B23.2B2DB2D3B22.2B2DB2D3B22.2B
2DB2D2BC22.2B2DB2CB21$2B2DB2CB$2B2DBCBC$5BD2B$2B2DBCBC$2B2DB2CB!

There are still many easy conversions. When you solve an easy conversion, please :
- use the component with the best clearance that is available, cost is a very secondary metric in this project, generality matters most
- format the components as explained in the first post, or (even better) use the program to convert them to the standardised RLE+comments format (use commands "input" or "parse", see readme.txt for details)

Do not hesitate to modify the transformation (as long as the initial still-life is shorter than the target). The hint is quite useless sometimes.

Progress:
13/07/2026 : 0 known components, 999 transformations needed
14/07/2026 : 441 known components, 814 transformations needed
15/07/2026 : 712 known components, 722 transformations needed
16/07/2026 : 733 known components, 703 transformations needed
17/07/2026 : 814 known components, 666 transformations needed

[Goldtiger997]

Interesting project! The software you've written looks very nice. It breaks down the process of writing a complex proof into a bunch of little puzzles. To try the software out, I've done a few easy conversions:

Code: Select all

#C 9:26 -7///11 0 16 6
x = 7, y = 5, rule = LifeHistory
BBBCCBB$
BBDBCBB$
BBBCBBB$
BBBBCCC$
BBBBBBC!

#C 9:15 -1/11 -2 21 0//
x = 6, y = 5, rule = LifeHistory
BBDACB$
BBDCBC$
BBBBBC$
BBBBBC$
BBBBCC!

#C 34:20 -2///2 2 30 0
x = 7, y = 5, rule = LifeHistory
BBBDBBB$
BBDACBB$
BBBCBCB$
BBBBBCB$
BBBBBCC!

#C 64:6 4 32 9 63 -12 66 -2/30 1//-1 4 32 0 72 -6
x = 9, y = 5, rule = LifeHistory
BBBDBBBBB$
BBDBDBBBB$
BBBDDBBBB$
BBBBBCCBC$
BBBBBCBCC!

#C 40:28 2 48 3///7 2 26 0
x = 11, y = 5, rule = LifeHistory
BBDDACBCCBB$
BBDBCCBCBBC$
BBBBBBBCBCC$
BBBBBBBCBBB$
BBBBBBCCBBB!

#C 40:13 -2 24 0///38 -2 62 -3
x = 11, y = 5, rule = LifeHistory
BBDBCCBCCBB$
BBDDACBCBBC$
BBBBBBBCBCC$
BBBBBBBCBBB$
BBBBBBCCBBB!

#C 40:13 -2 24 0///38 -2 62 -3
x = 7, y = 5, rule = LifeHistory
BBDBCCB$
BBDDACB$
BBBBBBB$
BBBBBBB$
BBBBBBB!

#C 26:4 -6//2 9/36 -4
x = 7, y = 5, rule = LifeHistory
BBDDBBB$
BBDACBB$
BBBBCBB$
BBBBCBC$
BBBBBCC!

#C 18:15 0///14 5 27 -3
x = 10, y = 5, rule = LifeHistory
BBBCCBCCBB$
BBDACBCBBC$
BBBDBBCBCC$
BBBBBBCBBB$
BBBBBCCBBB!

#C 64:6 4 32 9 63 -12 66 -2/30 1//-1 4 32 0 72 -6
#C 21:11 5///3 4
x = 9, y = 5, rule = LifeHistory
BBDDBBBBB$
BBDBDBBBB$
BBBDDBBBB$
BBBBBCCBC$
BBBBBCBCC!

[vilc]

Interesting project! The software you've written looks very nice. It breaks down the process of writing a complex proof into a bunch of little puzzles. To try the software out, I've done a few easy conversions:

Thank you! Nice to see that the program is usable by someone else than me. I have included your components, along with similar ones that I gathered, in an update of the components database. I also included a new variant of my table stacking component which has better clearance :

Code: Select all

x = 78, y = 70, rule = LifeHistory
.A$2.A$3A24.A$28.A$26.3A4$67.A.A$67.2A$68.A7.A$24.A50.A$22.A.A3.A46.
3A$23.2A4.2A$28.2A5$38.A22.A$39.A20.A$37.3A20.3A4$22.A$20.A.A$21.2A$
35.A$33.A.A$34.2A3$22.A.A9.A.A$23.2A10.2A$23.A11.A2$38.12BCE.2E$38.2B
2DB2DB2CBCBE.E.E$38.2B2DBD3BCBCBE.E.E$38.5BD3BC2BC3.E$38.5B2DB2C3B5$
21.A$21.2A13.2A$20.A.A8.2A2.A.A$32.2A3.A$31.A12$60.A$59.2A$59.A.A2$
27.A$27.2A35.3A$26.A.A35.A$65.A!

I have also fixed some harmless bugs in the software : sometimes the program would output too many missing transformations needed to solve a branch, plus the weird formatting of syntheses should not happen anymore.

[Chris857]

should solve (at least) 13? of them - pretty sure one of the block-on-table can applied in more than just the super blank situation

Code: Select all

x = 775, y = 1429, rule = LifeHistory
96$549.A.A97.A.A$550.2A98.2A$550.A99.A4$598.A99.A$596.2A98.2A$597.2A
98.2A$428.A$429.2A132.A99.A$428.2A134.2A98.2A$563.2A98.2A$559.A99.A$
557.A.A97.A.A$558.2A98.2A3$460.A$459.A$459.3A2$447.A$448.2A$447.2A4$
447.A$445.A.A$446.2A3.2B2D2BCE122.2B2DBCE93.2B2DBC$451.2BDBD2BE122.2B
2DBCE93.2B2DBC2E$451.4BDBC123.6B94.6B2.E$443.3A5.2BDBDBCE122.2B2DBCE
93.2B2DBC2E$445.A5.2B2D3B123.2B2DBCE93.2B2DBC$444.A3$447.2A$446.A.A$
448.A10$423.2A$424.2A$423.A131.2A6.2A90.2A6.2A$554.A.A5.A.A89.A.A5.A.
A$427.2A127.A7.A91.A7.A$428.2A$427.A169.2A98.2A$597.A.A97.A.A$597.A
99.A4$550.A99.A$550.2A98.2A$549.A.A97.A.A44$460.A$459.A$459.3A2$447.A
$448.2A$447.2A4$447.A$445.A.A$446.2A3.2B2D2BCE$451.2BDBD2BE$451.4BDBC
$443.3A5.3B2DBCE$445.A5.7B$444.A3$447.2A$446.A.A$448.A59$438.A35.A$
436.A.A34.A$437.2A3.A.A23.A4.3A$443.2A23.A.A$443.A24.2A2$440.A$441.A$
439.3A13$451.2BD2BCB$451.2B3D2CE$451.7B.E$451.2B3D2CE$451.2BD2BCB13$
439.3A$441.A$440.A2$443.A24.2A$443.2A23.A.A$437.2A3.A.A23.A$436.A.A$
438.A44$419.A.A$420.2A$420.A9$432.A$433.A$431.3A2$426.A.A$427.2A$427.
A14$451.2B2D2B$451.3BD2B$451.2BD3B$451.2BDACB$451.3B2CB18$431.2A$430.
A.A$432.A2$415.2A5.A$414.A.A5.2A$416.A4.A.A47$408.A.A$409.2A$409.A12$
419.A$417.A.A$418.2A4$425.A.A$426.2A$426.A5$436.A.A$437.2A$437.A3$
588.A.A$589.2A$589.A11.A$599.2A$600.2A$583.A.A$584.2A$584.A6$451.10B
130.3BD2B$451.2B2DB2D3B130.2BDBCB$451.2B2DBD4B130.2BDABC$451.5BD4B
120.2A8.3BCBC$451.5B2D3B121.2A7.4BCB$581.A5$584.A$584.2A2.3A$583.A.A
2.A$589.A2$591.2A$591.A.A$591.A5$434.A$434.2A$433.A.A$423.A$423.2A$
422.A.A$418.2A$419.2A$418.A5$406.A$406.2A$405.A.A11$399.2A$398.A.A$
400.A55$430.A$428.A.A$429.2A11$460.A$459.A$459.3A2$447.A$448.2A$447.
2A4$447.A$445.A.A$446.2A3.3BD3B$451.2BDBDBCE$451.2BDBDBC$443.3A5.3B2D
2BE$445.A5.6BCE$444.A3$447.2A$446.A.A$448.A10$426.3A$428.A$427.A73$
191.A.A197.A.A$192.2A198.2A$192.A199.A12$199.A199.A$200.2A198.2A$199.
2A198.2A6$208.A.A197.A.A$209.2A198.2A$209.A199.A3$203.A.A197.A.A$204.
2A198.2A$204.A199.A$630.A.A$630.2A$631.A$572.A$570.A.A$571.2A12$237.A
199.A138.A.A$238.A199.A138.2A$236.3A197.3A138.A16$251.2B2D4B192.2B2D
3BC142.4BACB$251.3BD2BCB2E190.3BD2BCBE141.3BD2CB$251.2BD3B2C.E190.2BD
3B2C142.2BD4B$251.3B3D2B192.3B3D2B142.3BD2CB$251.5BD2B192.5BD2B142.4B
ACB2$237.A199.A$237.2A198.2A$236.A.A197.A.A2$225.A199.A$225.2A198.2A$
224.A.A6.3A188.A.A6.3A$235.A199.A137.A$234.A199.A138.2A$572.A.A3$579.
A$579.2A$578.A.A3$274.A199.A$273.2A198.2A$273.A.A197.A.A$232.2A198.2A
$233.2A198.2A$232.A199.A6$571.2A$570.A.A$572.A$631.A$561.2A67.2A$562.
2A66.A.A$561.A4$562.2A$561.A.A$563.A78.2A$208.A199.A233.A.A$208.2A
198.2A232.A$207.A.A197.A.A2$199.2A198.2A$200.2A198.2A$199.A199.A3$
191.2A198.2A$192.2A198.2A$191.A199.A2$189.A199.A$189.2A198.2A$188.A.A
197.A.A73$505.A$505.A.A$505.2A$395.A.A$396.2A$396.A$503.A$391.A.A108.
A$392.2A108.3A$392.A12$402.A.A$403.2A$403.A2$621.A$404.A217.2A$405.2A
214.2A$404.2A$619.A$620.A11.A.A$618.3A12.2A$633.A2$425.A55.A$423.A.A
54.A214.A$424.2A3.A.A43.A4.3A210.2A$430.2A43.A.A216.2A$430.A44.2A2$
427.A$428.A216.A.A$426.3A217.2A33.A.A$646.A4.A29.2A$652.A29.A$650.3A
9$448.A15.A$446.A.A14.A$447.2A3.A.A3.A4.3A$453.2A3.A.A$453.A4.2A2$
450.A$451.A$449.3A3$451.5BCB.E201.2BDBACB$451.3B2D2C2E201.2B2D2CB$
451.2BD4B203.7B$451.3B2D2C2E201.4B2CB$451.5BCB.E201.4B2CB3$449.3A$
451.A$450.A2$453.A4.2A$453.2A3.A.A$447.2A3.A.A3.A$446.A.A$448.A10$
631.2A$632.2A$426.3A202.A$428.A$427.A2$430.A44.2A$430.2A43.A.A$424.2A
3.A.A43.A$423.A.A$425.A8$619.2A$620.2A$619.A$402.2A$401.A.A$403.A12$
392.A$392.2A108.3A$391.A.A108.A$503.A$396.A$396.2A$395.A.A$505.2A$
505.A.A$505.A74$397.A$398.A$396.3A3$400.A.A$401.2A$401.A20$421.2B2DAC
B$421.2BDB2CB$421.7B$421.7B$421.7B10$404.3A$406.A$405.A2$402.A$402.2A
$401.A.A!

edit:
should be better clearance for one of them

Code: Select all

x = 105, y = 146, rule = LifeHistory
3.A$4.2A$3.2A2$.A$2.A11.A.A$3A12.2A$15.A28$32.A69.A.A$33.A68.2A$31.3A
69.A$44.A$42.A.A$43.2A12$48.A.A$49.2A$49.A16$73.2BDBACB$73.2B2D2CB$73.
7B$73.4B2CB$73.4B2CB9$45.A$45.2A$44.A.A3$51.A$51.2A$50.A.A14$43.2A$42.
A.A$44.A$103.A$102.2A$102.A.A6$35.A$35.2A$34.A.A8$13.2A$14.2A$13.A16$
.2A$2.2A$.A!

some more

Code: Select all

x = 361, y = 619, rule = LifeHistory
70.A$71.2A$70.2A3$73.A$71.A.A$72.2A2$85.2B2DB2C.E$85.3BDBCB2E$85.3BD3B
$85.4BD2B$85.3B2D2B2$81.A$81.2A$80.A.A7$98.A$97.2A$97.A.A69$105.A$105.
A.A$105.2A$65.A$63.A.A$64.2A19$85.2BDCA2B$85.2BCBC2B$85.3BC3B$85.4B3C
$85.6BC14$65.3A$67.A$66.A41$256.A$255.A$255.3A2$176.A$177.A$175.3A77.
A$254.A$254.3A12$184.A.A$185.2A$185.A2$72.A38.A$70.A.A38.A.A$71.2A38.
2A2$66.A.A$67.2A36.A.A88.A$67.A37.2A90.A$106.A88.3A2$190.A.A$191.2A$191.
A14$85.2B2D2B124.2B2D2B2E$85.2BD3B124.2BD3B2E$85.3BD2B124.3BD2B$85.3B
ACB124.3BACB$85.3B2CB124.3B2CB14$62.2A$63.2A$62.A2$195.2A$194.A.A$196.
A8$182.2A$183.2A$182.A9$174.2A$173.A.A$175.A49$99.A.A$99.2A$96.A3.A$70.
A.A21.2A$71.2A22.2A$71.A11$85.2BDACB2.2E$85.2BDCBC.E.E$85.5BC.E$85.2B
DCBC.E.E$85.2BDACB2.2E11$71.A$71.2A22.2A$70.A.A21.2A$96.A3.A$99.2A$99.
A.A87$A$.2A$2A16$145.A$14.A129.A$15.2A127.3A$14.2A2$23.A$21.A.A$22.2A
256.A.A$281.2A$281.A2$358.A$358.A.A$358.2A3$40.A$41.2A$40.2A24$298.A$
299.2A$298.2A3$47.A$45.A.A$46.2A6$62.A252.2BD4B$60.A.A252.2B3D2B$61.2A
252.5BCB$315.4BCBC$315.4BDCB6$85.6B2C$85.2B2DBDBC$85.3BDBDBC.E$85.3BD
BD2B2E$85.4B2D2B9$56.3A$58.A$57.A3$56.2A239.2A$55.A.A238.A.A$57.A217.
A22.A$275.2A$274.A.A12$44.2A$43.A.A$45.A$37.2A$38.2A$37.A224.2A$263.2A
$262.A27$146.2A$145.2A$147.A9$160.2A$160.A.A$160.A$154.3A$2.A151.A$2.
2A151.A$.A.A2$165.3A$165.A$166.A!

Code: Select all

x = 89, y = 158, rule = LifeHistory
10.A$11.A$9.3A16$11.A.A$12.2A$12.A27$31.A$32.2A$31.2A$39.A$37.A.A$38.
2A14$51.A$49.A.A$50.2A3$51.A$52.A$50.3A9$79.2B2D4B$79.2BD5B2E$79.3B3D
BC.E$79.5BDBC$79.6B2C8$55.2A$54.A.A$56.A6$40.2A$39.A.A$41.A29$34.2A$35.
2A$34.A6$9.3A$11.A$10.A2$6.2A$7.2A$6.A8$3A$2.A$.A!

Code: Select all

x = 355, y = 364, rule = LifeHistory
53$241.A.A$241.2A$242.A3$37.A$35.A.A$36.2A195.A$233.A.A$233.2A$35.A$
33.A.A$34.2A6$43.A$41.A.A$42.2A16$78.A$76.A.A$77.2A2$202.A$201.A$201.
3A3$72.A9.A$70.A.A7.A.A8.A$71.2A8.2A9.A$90.3A4$71.A$69.A.A121.A$70.2A
16.A102.2A$86.A.A103.2A$87.2A8$95.A$96.2A$95.2A24$119.A$117.A.A$118.
2A16$131.A10.2B2D2B2C$132.A9.2BD2BCBC2.E$130.3A9.3BDBCBC.E.E$142.4BDB
CB.E.E$142.5BD2B.2E15$159.A$158.2A$158.A.A3$136.3A$138.A$137.A16$93.
3A$95.A2.2A$94.A4.2A$98.A5$85.2A$84.A.A3.3A$86.A5.A$91.A83.2A$175.A.A
$175.A3$192.A$191.2A$95.2A94.A.A$96.2A$95.A$201.2A$200.2A$188.2A12.A$
89.3A96.A.A2.2A$91.A96.A3.2A$64.A25.A103.A$64.2A$63.A.A9$48.A$48.2A$
47.A.A16$41.2A$40.A.A$36.2A4.A$35.A.A$37.A5$32.3A$34.A$33.A3$243.A$
242.2A$242.A.A3$247.2A$246.2A$248.A!

Code: Select all

x = 418, y = 226, rule = LifeHistory
5.A159.A189.A$6.2A158.2A188.2A$5.2A158.2A188.2A$2.A159.A189.A$A.A157.
A.A187.A.A$.2A158.2A188.2A17$29.A159.A189.A$30.A159.A189.A$28.3A157.3A
187.3A16$43.2B2D4B152.2B2D4B2E180.2B2D3BC$43.2B2D2BCB152.2B2D2BCB.E180.
2B2D2BCBE$43.6B2CE151.6B2C182.6B2C$43.2B4D2B.E150.2B4D2B182.2B4D2B$43.
2BD2BD2B2E150.2BD2BD2B182.2BD2BD2B2$29.A159.A189.A$29.2A158.2A188.2A$
28.A.A157.A.A187.A.A2$17.A159.A189.A$17.2A158.2A188.2A$16.A.A6.3A148.
A.A6.3A178.A.A6.3A$27.A159.A189.A$26.A159.A189.A9$66.A159.A189.A$65.2A
158.2A188.2A$65.A.A157.A.A187.A.A$24.2A158.2A188.2A$25.2A158.2A188.2A
$24.A159.A189.A15$4.2A158.2A188.2A$3.A.A157.A.A187.A.A$5.A159.A189.A55$
5.A159.A$6.2A158.2A$5.2A158.2A$2.A159.A$A.A157.A.A$.2A158.2A18$25.A159.
A$23.A.A157.A.A$24.2A158.2A15$43.2B2D3B153.2B2D2BCE.2E$43.2B2D3B153.2B
2D3BE.2E$43.7B153.7BE$43.2B2D2CB153.2B2D2CBE$43.2BDBACB153.2BDBACB2E17$
20.A159.A$20.2A158.2A$19.A.A157.A.A2$24.3A157.3A$26.A159.A$25.A159.A16$
4.2A158.2A$3.A.A157.A.A$5.A159.A!

Code: Select all

x = 142, y = 60, rule = LifeHistory
4.A.A97.A.A$5.2A98.2A$5.A99.A5$4.A99.A$2.A.A97.A.A$3.2A98.2A3$4.A.A97.
A.A$5.2A98.2A$5.A99.A2$18.A$19.2A$18.2A3$21.A$19.A.A$20.2A2$33.2B2DB2C
.E91.2B2CB2C.E$33.BDBDBCB2E91.BDBCBCB2E$33.BDBD3B93.BDBC3B$33.2BDBD2B
93.2BDBC2B$33.3B2D2B93.3B2C2B2$29.A$29.2A$28.A.A7$46.A$45.2A$45.A.A15$
.2A98.2A$A.A97.A.A$2.A99.A!

Code: Select all

x = 198, y = 163, rule = LifeHistory
37$138.A$138.A.A$58.A79.2A$59.A$57.3A$49.A.A$50.2A86.A$50.A86.A$137.
3A5$48.A$46.A.A$47.2A2$61.A$59.A.A$60.2A12$71.A$72.2A$71.2A17$92.3B2D
2B2.E$92.2BD2BCB.E.E$92.2BDBCBC2.E$92.3BDBCB$92.4BD2B18$74.A$74.2A$
73.A.A4$63.2A$62.A.A$64.A13$51.2A$44.3A3.A.A$46.A5.A$45.A!

[vilc]

A very nice set of components. Most of them are perfectly valid, but I have a few remarks, which should make some rules clearer for all future contributors:
- watch the forbidden region ! For example, here, the grey and salmon cells should not change throughout the entire component.

Code: Select all

x = 52, y = 46, rule = LifeSuper
10.A38.A$8.A.A38.A.A$9.2A38.2A2$4.A.A$5.2A36.A.A$5.A37.2A$44.A16$27.
6T$27.6T$23.2B2D6T$23.2BDB6T$23.3BD6T$23.3BAO5T$23.3BCO5T$27.6T$27.6T
12$2A$.2A$A!

Perhaps you noticed it in this case since you provide another solution with perfect clearance, but all your intermediate boat-ties are also slightly incorrect (by one cell). These components should work instead :

Code: Select all

x = 152, y = 66, rule = B3/S23
116bo$117bo$115b3o3$136bobo$136b2o$137bo9$107bo$105bobo$106b2o4$111b3o
$113bo$11bo100bo$12b2o$11b2o2$9bo$10bo$8b3o$23bo$12b3o8b3o$14bo11bo$
13bo11b2o2$131bo$130bobo$130b2o3$3o9b2o$2bo10b2o$bo10bo15$102b2o$103b
2o$102bo4b2o$106bobo$108bo$149b3o$149bo$150bo!

- you solve the two following transformations, but these are the same since the (non-yellow) marked regions coincide. A solution for a transformation that respects all the constraints explained in the first post will automatically be valid for all possible continuations. If your component works in all real cases but crosses the forbidden region at this length, you can indeed provide all cases up to a longer length, but the relevant rows should also be marked.

Code: Select all

x = 33, y = 26, rule = LifeHistory
2B2D4B15.2B2D4B2E$2B2D2BCB15.2B2D2BCB.E$6B2CE14.6B2C$2B4D2B.E13.2B4D
2B$2BD2BD2B2E13.2BD2BD2B6$16.D$16.D$16.D$14.D.D.D$15.3D$16.D6$2B2D5B
14.2B2D4BCE$2B2D2BC2B14.2B2D2BC2BE$6B3C14.6B2CB$2B4D3BE13.2B4D3B$2BD
2BD2BCE13.2BD2BD3B!

- This is more customary, but in the following component the first step is not really useful since it does not prepare the still-life for the next step. Only the second step participates in the elongation. This is one of the cases where you want to slightly modify the suggested transformation.

Code: Select all

x = 99, y = 100, rule = LifeHistory
18.A.A$19.2A$19.A2$96.A$96.A.A$96.2A29$36.A$37.2A$36.2A11$53.2BD4B$
53.2B3D2B$53.5BCB$53.4BCBC$53.4BDCB24$35.2A$34.A.A$13.A22.A$13.2A$12.
A.A17$2A$.2A$A!

- This transformation is invalid since it does not elongate the still-life. If it was suggested in a previous transformations set, I apologise : this would indicate a bug.

Code: Select all

x = 45, y = 45, rule = LifeHistory
42.A$42.A.A$42.2A$2.A$A.A$.2A19$22.2BDCA2B$22.2BCBC2B$22.3BC3B$22.4B
3C$22.6BC14$2.3A$4.A$3.A!

I have corrected the various problems myself and your components will be in the next update.

[ElijahKen]

Here are a few. Please correct me if I made any mistakes.
Four unrelated ones:

Code: Select all

x = 731, y = 231, rule = LifeHistory
78$253.2B2D2B$253.2BDACB$253.3BCBC$253.5BC$253.5BC21$481.A$479.A.A$480.
2A3$584.A.A$585.2A$287.A297.A$245.A39.A.A$246.A39.2A293.A$244.3A235.A
99.2A5.2B2D2B2.A$483.2A96.2A6.3BD2B3A$65.A416.2A101.3A.3BDBC$63.A.A521.
A.2B2D2BA$64.2A520.A2.5BCA$494.5B2C.2A$254.2B2D2B30.2BDC2B198.2B2D2BC
.A$254.2BDACB24.3A3.2BCBCB198.2B2DBCB.A81.A$75.4B2CB172.3BCBC26.A3.3B
CBC198.5BCBA82.2A$75.3BC2BC172.5BC25.A4.5BC198.5BDC82.A.A$75.2BDACBC165.
3A4.5BCA29.5BCA$75.3BD2BC.2A164.A$75.6BCA.A163.A2$71.A173.2A$65.2A2.A
.A172.A.A$64.A.A3.2A174.A$66.A415.3A$484.A$72.2A396.3A10.A$73.2A397.A
$72.A398.A2$508.2A$483.2A22.2A$484.2A23.A$483.A19.3A$503.A$504.A!

And a pretty edgy block-on-table adder that I found in old forum posts. This one solves a lot of the block-on-table additions.

Code: Select all

x = 598, y = 70, rule = LifeHistory
4.9BC24.10B24.9BC24.10B24.9BC24.10BC23.10BC23.10B24.9BC24.10B24.9BC24.
10B24.9BC28.8BC25.9BC24.10BC23.10BC24.10BC$4.2B2DB2D3B24.2B2DB2D2BC24.
2B2DB2D2BC24.2B2DB2D3B24.2B2DB2D3B24.2B2DB2D2BCB23.2B2DB2D2BCB23.2B2D
B2D3B24.2B2DB2D3B24.2B2DB2D2BC24.2B2DB2D2BC24.2B2DB2D3B24.2B2DB2D3B28.
2B2DB2D2B25.2B2DB2DBCB24.2B2DB2D2BCB23.2B2DB2D2BCB24.2B2DB2D2BCB$4.2B
2DBD4B24.2B2DBD4B24.2B2DBD4B24.2B2DBD3BC24.2B2DBD3BC24.2B2DBD3B2C23.2B
2DBD3BCB23.2B2DBD4B24.2B2DBD4B24.2B2DBD4B24.2B2DBD4B24.2B2DBD3BC24.2B
2DBD3BC28.2B2DBD3B25.2B2DBD3BC24.2B2DBD2BCBC23.2B2DBD2BC2B24.2B2DBD2B
CBC$4.5BD4B24.5BD4B24.5BD4B24.5BD4B24.5BD4B24.5BD5B23.5BD4BC23.5BD3BC
24.5BD3BC24.5BD3BC24.5BD3BC24.5BD3BC24.5BD3BC28.5BD3B25.5BD4B24.5BD3B
CB23.5BD3B2C24.5BD3BCB$4.5B2D3B24.5B2D3B24.5B2D3B24.5B2D3B24.5B2D3B24.
5B2D4B23.5B2D4B23.5B2D3B24.5B2D3B24.5B2D3B24.5B2D3B24.5B2D3B24.5B2D3B
28.5B2D2B25.5B2D3B24.5B2D4B23.5B2D4B24.5B2D3BC37$A$.2A$2A5$6.A$4.2A$5.
2A2$110.A$3.2A98.A4.A.A$2.2A100.A4.2A$4.A10BCA36.10BCA37.3A6.10BCA41.
10BCA$5.2B2DB2D2BCB.A35.2B2DB2C2BCB.A45.2B2DB2C2BCB.A40.2B2CB2C2BCB.A
$5.2B2DBD2BCBCA.A29.A4.2B2DBC2BCBCA.A44.2B2DBC2BCBCA.A39.2BDCBC2BCBCA
.A$5.5BD3BCB.A31.A3.3BABC3BCB.A45.3BABC3BCB.A40.3BABC3BCB.A$5.5B2D3BC
A30.3A3.3B2A2D3BCA41.A4.2BABA2D3BCA41.4BA2D3BCA$106.2A6.A$51.A53.A.A$
51.2A$.2A47.A.A$A.A105.2A51.A6.A$2.A53.3A50.2A50.2A5.2A8.A$56.A51.A51.
A.A4.A.A7.2A$57.A114.2A3.A.A$171.A.A$173.A!

By moving the block to the other side afterward, a few more can be solved.

Code: Select all

x = 231, y = 66, rule = LifeHistory
4.10B58.10B58.10B52.9B$4.2B2DB2D3B58.2B2DB2D3B58.2B2DB2D3B52.2B2DB2D2B
$4.2B2DBD4B58.2B2DBD3BC58.2B2DBD4B52.2B2DBD3B$4.5BD4B58.5BD4B58.5BD3B
C52.5BD2BC$4.5B2D2BC58.5B2D2BC58.5B2D2BC52.5B2D2B33$173.A$171.A.A$57.
A114.2A3.A.A27.A4.A$56.A51.A51.A.A4.A.A7.2A29.A4.2A$2.A53.3A50.2A50.2A
5.2A8.A27.3A3.2A$A.A105.2A51.A6.A$.2A47.A.A$51.2A160.2A$51.A53.A.A106.
2A$106.2A6.A98.A3.2B2DB2C3BCA$5.2B2DB2D3BCA30.3A3.2BDCA2D3BCA41.A4.2B
CDA2D3BCA41.2B2DA2D3BCA41.2B2DBC3BCB.A$5.2B2DBD3BCB.A31.A3.2BDCBC3BCB
.A45.2BDCBC3BCB.A40.2BDCBC3BCB.A40.2B2ABC2BCBCA.A$5.5BD2BCBCA.A29.A4.
5BC2BCBCA.A44.5BC2BCBCA.A39.3BABC2BCBCA.A39.2B2AB2C2BCB.A$5.5B2D2BCB.
A35.5B2C2BCB.A45.5B2C2BCB.A40.2B2AB2C2BCB.A40.10BCA$4.A10BCA36.10BCA37.
3A6.10BCA41.10BCA36.3A$2.2A100.A4.2A103.A$3.2A98.A4.A.A102.A$110.A2$5.
2A$4.2A$6.A5$2A$.2A$A!

Converting the block to a table solves a few more.

Code: Select all

x = 286, y = 57, rule = LifeHistory
46.2B2DB2DB2C2B33.2B2DB2D2B25.2B2DB2D2B25.2B2DB2D3B$6.2B2DB2D2B31.3BD
BD3BC2B33.3BDBD2BC25.3BDBD3B25.3BDBD4B$6.3BDBD3B31.3BDBD3BCBC33.3BDBD
3B25.3BDBD2BC25.3BDBD3BC$6.3BDBD3B31.2B2DB2D3B2C33.2B2DB2D2B25.2B2DB2D
2B25.2B2DB2DBCB$6.2B2DB2D2B31.12B33.9B25.9B25.9BC$6.9B23$A$.2A$2A5$6.
A$4.2A$5.2A2$110.A$3.2A98.A4.A.A100.A$2.2A100.A4.2A101.2A10BCA46.10BC
A$4.A10BCA36.10BCA37.3A6.10BCA41.10BCA31.2A2.2A.2B2CB2C2BCB.A45.2B2CB
2C2BCB.A$5.2B2DB2D2BCB.A35.2B2DB2C2BCB.A45.2B2DB2C2BCB.A40.2B2CB2C2BC
B.A29.A.A5.2BACBC2BCBCA.A44.BABCBC2BCBCA.A$5.3BDBD2BCBCA.A29.A4.3BDBC
2BCBCA.A44.3BDBC2BCBCA.A39.3BCBC2BCBCA.A30.A5.3BDBC3BCB.A45.2BADBC3BC
B.A$5.3BDBD3BCB.A31.A3.3BCBC3BCB.A45.3BCBC3BCB.A40.3BCBC3BCB.A35.A.2B
2DB2C3BCA46.2B2DB2C3BCA$5.2B2DB2D3BCA30.3A3.2BDCA2D3BCA41.A4.2BCDA2D3B
CA41.2B2DA2D3BCA36.2A$106.2A6.A96.A.A59.2A$51.A53.A.A161.A3.A.A$51.2A
214.A.A3.A$.2A47.A.A215.2A$A.A105.2A51.A6.A$2.A53.3A50.2A50.2A5.2A8.A
$56.A51.A51.A.A4.A.A7.2A$57.A114.2A3.A.A$171.A.A$173.A!

And adding a small transformation before solves these two too:

Code: Select all

x = 336, y = 96, rule = LifeHistory
48.A$49.2A$48.2A4$6.A$7.A46.A$5.3A44.2A$53.2A2$158.A$51.2A98.A4.A.A$50.
2A100.A4.2A$5.10BCA35.A10BCA36.10BCA37.3A6.10BCA41.10BCA$5.2B2DB2D2BC
B.A35.2B2DB2D2BCB.A35.2B2DB2C2BCB.A45.2B2DB2C2BCB.A40.2B2CB2C2BCB.A$5.
2B2DBD2BDBC.A35.2B2DBD2BCBC.A30.A4.2B2DBC2BCBC.A45.2B2DBC2BCBC.A40.2B
DCBC2BCBC.A$5.5BD3B2C.2A34.5BD3B2C.2A30.A3.3BABC3B2C.2A44.3BABC3B2C.2A
39.3BABC3B2C.2A$5.5B2D4B37.5B2D4B31.3A3.3B2A2D4B42.A4.2BABA2D4B42.4BA
2D4B$4.A149.2A6.A$4.2A93.A53.A.A$3.A.A93.2A$49.2A47.A.A$48.A.A105.2A51.
A6.A$50.A53.3A50.2A50.2A5.2A8.A$104.A51.A51.A.A4.A.A7.2A$105.A114.2A3.
A.A$219.A.A$221.A36$.A49.A$2.A49.2A$3A48.2A5$57.A$55.2A$2.A53.2A$3.A$
.3A157.A$54.2A98.A4.A.A100.A$53.2A100.A4.2A101.2A$55.A97.3A102.2A2.2A
.2B2CB2CB2C2B46.2B2CB2CB2C2B$56.2B2DB2DB2C2B36.2B2DB2CB2C2B46.2B2DB2C
2B2C2B40.2B2CB2CB2C2B30.A.A5.2BACBC3BC2B46.BABCBC3BC2B$5.2B2DB2DB2D2B
39.3BDBD3BC2B31.A4.3BDBC3BC2B46.3BDBC4BC2B40.3BCBC3BC2B32.A5.3BDBC3BC
BC46.2BADBC3BCBC$5.3BDBD3BD2B39.3BDBD3BCBC32.A3.3BCBC3BCBC46.3BCBC4BC
BC40.3BCBC3BCBC36.A.2B2DB2C3BCBA45.2B2DB2C3BCBA$5.3BDBD3BDBC39.2B2DB2D
3BCBA29.3A3.2BDCA2D3BCBA40.A4.2BCDA2D4BCBA39.2B2DA2D3BCBA35.2A11BC46.
11BC$5.2B2DB2D3BCBA38.11BC36.11BC41.2A3.3BA8BC40.11BC35.A.A59.2A$5.11B
C85.A53.A.A161.A3.A.A$4.A97.2A214.A.A3.A$4.2A46.2A47.A.A215.2A$3.A.A45.
A.A105.2A51.A6.A$53.A53.3A50.2A50.2A5.2A8.A$107.A51.A51.A.A4.A.A7.2A$
108.A114.2A3.A.A$222.A.A$224.A$2.2A$3.2A$2.A!

These were all pulled directly from the list you posted in the first post. Again, please do let me know if I made a mistake!

[Chris857]

A very nice set of components. Most of them are perfectly valid, but I have a few remarks, which should make some rules clearer for all future contributors:
- watch the forbidden region ! For example, here, the grey and salmon cells should not change throughout the entire component.

Perhaps you noticed it in this case since you provide another solution with perfect clearance, but all your intermediate boat-ties are also slightly incorrect (by one cell). These components should work instead :

Yeah, I think I really only noticed the grey-cell clearance requirement part way in and missed it for a couple, but I figured posting something was better than nothing.

Another one for adding a hook w/ tail (row 13, col 4). Not sure if the eater head version is on the board, but included it anyway.

Code: Select all

x = 246, y = 119, rule = LifeHistory
110.A$110.A.A$6.A103.2A$7.A$5.3A25$203.A$201.A.A$26.A175.2A$24.A.A$25.
2A12$224.A$225.2A$47.A176.2A$48.2A$47.2A8$237.7B$237.2B2D3B$60.2B2D3B
170.2BD4B$60.3BD3B170.3B2DCB2E$60.2BD4B170.5B2C.E$60.3B2DCB2E$60.5B2C
.E7$224.2A$225.2A$47.2A169.2A4.A$48.2A167.A.A$41.2A4.A171.A$40.A.A$42.
A4$217.2A$218.2A$40.2A175.A$41.2A$40.A32$.2A$A.A$2.A!

2026-07-16:
another 5

Code: Select all

x = 158, y = 165, rule = LifeHistory
.A$2.A$3A13$20.A$21.2A$20.2A2$18.A$19.A$17.3A11$37.A3.A$38.A3.2A$36.3A
2.2A16$99.A.A$99.2A$100.A$61.A$59.A.A$60.2A17$69.A.A$70.2A$70.A$80.2B
DBACB$80.2B2D2CB$80.7B$80.2B2D2CB$80.2BDBACB6$68.A$68.2A$67.A.A2$64.2A
$65.2A$64.A8$60.2A$59.A.A$61.A$100.A$99.2A$99.A.A$32.2A$33.2A$32.A31$
18.2A$19.2A$18.A22$155.3A$155.A$156.A!

Code: Select all

x = 52, y = 59, rule = LifeHistory
A.A$.2A$.A11$16.A$17.A$15.3A11$25.2B2DBCB.E$25.2B2DB2C2E$25.7B$25.2B2D
B2C2E$25.2BDBDCB.E11$15.3A$17.A$16.A2$38.3A$38.A$39.A9$4.3A43.A$6.A42.
2A$5.A43.A.A!

Code: Select all

x = 72, y = 85, rule = LifeHistory
14$13.A$14.A$12.3A$58.A$56.2A$57.2A6$49.A$48.A$48.3A2$26.A$27.A$25.3A
11$35.2B2DBCB.E$35.2BDBD2C2E$35.7B$35.2BDBD2C2E$35.2B2DBCB.E11$25.3A$
27.A$26.A2$48.3A$48.A$49.A6$57.2A$56.2A$58.A$12.3A$14.A$13.A!

Code: Select all

x = 38, y = 41, rule = LifeHistory
.A$2.A$3A10$16.3B2DB2C3.2E$16.2BDBDBCBE.E.E$16.2BD2BD2BE.E$16.3B2D3BE
.E$16.7BCE.2E7$8.A$8.2A$7.A.A11$3.2A$4.2A$3.A31.2A$35.A.A$35.A!

Code: Select all

x = 598, y = 228, rule = LifeHistory
47.A339.A$48.2A338.2A$47.2A338.2A4$47.A339.A$45.A.A337.A.A$46.2A338.2A
12$215.A.A337.A.A$215.2A338.2A$216.A339.A12$A.A337.A.A$.2A338.2A$.A339.
A11$67.A.A337.A.A$68.2A338.2A$68.A339.A4$69.A339.A$67.A.A337.A.A$68.2A
338.2A12$92.A339.A$93.2A11.A326.2A11.A$92.2A10.A.A325.2A10.A.A$105.2A
338.2A4$124.A339.A$122.A.A337.A.A$123.2A338.2A34$152.2BD4BCE331.2BD5B
$152.2B3D3BE331.2B3D2BCE$152.5BD2BE.E329.5BD2BE$152.4BD3B.2E329.4BD3B
E.E$152.4B2D2B332.4B2D2B.2E21$126.2A338.2A$125.A.A337.A.A$127.A339.A19$
101.A339.A$101.2A338.2A$100.A.A337.A.A5$99.2A338.2A$100.2A338.2A$99.A
339.A6$4.A339.A$4.2A137.3A198.2A137.3A$3.A.A137.A199.A.A137.A$144.A339.
A6$71.3A337.3A$73.A339.A$72.A339.A8$64.A339.A$64.2A338.2A$63.A.A337.A
.A12$37.2A338.2A$38.2A338.2A$37.A339.A7$42.A339.A$42.2A338.2A$41.A.A337.
A.A$46.3A337.3A$48.A339.A$47.A4.2A333.A4.2A$51.A.A337.A.A$53.A339.A$45.
3A207.3A127.3A207.3A$47.A207.A131.A207.A$46.A209.A129.A209.A2$13.3A337.
3A$15.A339.A$14.A339.A!

not sure if this is one is explicitly on the board, but ones with further block-on-table stacking are, so hopefully this can just be combined with them.

Code: Select all

x = 33, y = 45, rule = LifeHistory
2.A.A$3.2A$3.A3$5.A$6.A$4.3A14$23.2B2D2B$23.3BD2B2E$23.3BDBC2.E$23.2B
2D2BE.E$23.5BCE.2E13$2A$.2A$A2$4.A$4.2A$3.A.A!

another

Code: Select all

x = 111, y = 123, rule = LifeHistory
9.A$7.A.A$8.2A$2.A$3.2A$2.2A4$109.A$108.A$108.3A$27.A$25.A.A$21.A4.2A
$22.2A$21.2A34$31.A$32.A$30.3A2$63.2B2DBD2B$63.2BDB2D2B$63.6B2C$63.6B
CBE$63.7BCE38$25.2A$24.A.A$26.A7$7.2A$8.2A$7.A88.A$95.2A$95.A.A3$34.3A
$7.3A26.A$9.A25.A$8.A5$2A$.2A$A!

more clearance if that becomes necessary

Code: Select all

x = 218, y = 274, rule = LifeHistory
68.A$66.A.A$67.2A2$186.A$184.2A$185.2A25$9.A$7.A.A$8.2A$2.A16.A$3.2A15.
2A$2.2A15.2A4$24.A$22.A.A$23.2A3$21.A$22.2A$21.2A34$31.A$32.A$30.3A35$
63.2A$62.A.A$64.A25$123.2B2DBD2B$123.2BDB2D2B$123.6B2C$123.6BCBE$123.
7BCE98$25.2A$24.A.A$26.A7$7.2A$8.2A$7.A208.A$215.2A$215.A.A3$34.3A$7.
3A26.A$9.A25.A$8.A5$2A$.2A$A!

[vilc]

A few recipes gathered over the past two days. The red cross indicates a component that fails in half of cases.

Code: Select all

x = 451, y = 1828, rule = LifeHistory
76.A.A$77.2A$77.A4$80.A$72.A8.A$73.2A4.3A.6BCE$72.2A9.5BCBE$83.3B2DCB
$83.2BD3BC$83.2B2DB2C3$79.2A$78.A.A$80.A7.3A$88.A$84.2A3.A$83.A.A$85.
A10$104.A$74.A.A28.2A$75.2A27.2A$75.A36.A4.A$110.2A3.2A$111.2A3.2A2$
78.A$70.A8.A27.A$71.2A4.3A.2B2D2BCE16.A.A3.2B2D2BCE$70.2A9.2BD2BCBE
17.2A3.2BD2BCBE$81.3B2DCB23.3B3CB$81.6BC23.2BA3BC$81.5B2C17.A5.2B2AB
2C$106.A$104.3A$77.2A$76.A.A29.2A$78.A7.3A18.A.A$86.A22.A$82.2A3.A$
81.A.A$83.A9$82.A$81.A$81.3A2$79.A$80.A$78.3A.2B2D2B$82.2BDACB2E$82.
4BCBE$82.3BC2BE$82.4B2C$76.2A$75.A.A$77.A9$76.A$77.2A$76.2A$81.3B2CB
2A$81.4BCB2A$78.2A.4BCB$72.3A4.2A2BDACB$74.A3.A2.2B2D2B$73.A5$101.A
199.A$100.A199.A$100.3A197.3A15$85.A199.A$83.A.A154.D42.A.A$84.2A153.
D44.2A$238.D$237.2D$84.2A124.D26.D46.2A$85.2A124.2D22.2D48.2A$84.A
128.D20.D49.A$80.A.3B2D4B123.3D16.D46.A.3B2D2BCE.2E$81.A3B2D4B126.D
14.D48.A3B2D3BE.2E$79.3A9B127.3D10.D47.3A8BE$82.2BDBD2CBC129.D10.D50.
2BDBD2CBE$82.2B2DBCB2C130.D8.D51.2B2DBCBC$82.3A137.D6.D52.3A$84.A137.
2D4.D55.A$83.A140.D2.D55.A$224.D.2D$224.D.D$225.2D$224.D2.D$224.D2.D$
222.2D4.D$222.D6.2D$221.D9.2D$221.D11.2D$220.D13.2D$219.D15.2D$219.D
17.D$218.D19.2D$217.D21.D$216.D22.D$215.D$214.D$213.D$212.D2$105.2A
198.2A$105.A.A197.A.A$105.A199.A$58.2A198.2A$59.2A198.2A$58.A199.A37$
87.A4.A$85.A.A2.A.A$86.2A3.2A$92.3BD2B$92.2BDACB$86.2A4.2BDCBC$87.2A
3.5BC$86.A5.5BCE28$81.A$82.A3.A$80.3A4.2A$86.2A2$89.6BD2B.E$89.5BDACB
E.E$89.5BCBCBE.E$89.2B2DBCBCBE.E.2E$89.2B2DBDC2B.2E.2E3$82.2A$83.2A$
82.A9$125.A4.A$81.A44.A4.2A$82.A3.A37.3A3.2A$80.3A4.2A$86.2A$131.2A$
89.6BD2B.E32.2A.6BC2B.E$89.2B2DBDACBE.E30.A3.2B2DBCBCBE.E$89.2B2DBCBC
BE.E34.2B2DBCBCBE.E$89.5BCBCBE.E.2E31.2B2ABCBCBE.E.2E$89.5BDC2B.2E.2E
31.2B2AB2C2B.2E.2E2$130.3A$82.2A48.A$83.2A46.A$82.A23$86.A$87.A3.A$
85.3A4.2A$91.2A2$94.6BD2B.E$94.2B2DBDACBE.E$94.3BDBCBCBE.E$94.3BDBCBC
BE.E.2E82.2A$94.2B2DBDC2B.2E.2E81.A.A3.A$192.A3.A.A$134.A.A59.2A$87.
2A46.2A6BC2B.E47.6BC2B.E$88.2A45.A.2B2DBCBCBE.E46.2B2DBCBCBE.E$87.A
43.A5.3BDBCBCBE.E46.2BADBCBCBE.E$129.A.A5.2BACBCBCBE.E.2E43.BABCBCBCB
E.E.2E$130.2A2.2A.2B2CB2C2B.2E.2E43.2B2CB2C2B.2E.2E$135.2A$134.A100$
204.A$205.2A$204.2A3$249.A$249.A.A$200.A.A46.2A$201.2A$201.A4.A.A$
207.2A$207.A2$205.A$206.A$204.3A$40.A$41.A$39.3A145.A$188.A$186.3A5$
41.A$39.A.A81.A$40.2A82.A$45.7B2C.2E65.3A$45.2BDB2D2BC.E69.7B2C.2E$
45.2B2DBDBCB.E69.2BDB2C2BC.E$45.7BCBE70.2B2DBCBCB.E$42.2A.6B2CB2E66.
2A.5BABCBE$43.2A78.2A6B2CB2E$42.A79.A103.3B2A2B2C.2E$226.2BDADC2BC.E$
226.2B2DBCBCB.E198.A$122.A103.5BABCBE200.2A$110.2A10.2A102.6B2CB2E
198.2A$41.2A68.2A8.A.A$42.2A66.A328.7B2C.2E$41.A397.2BDB2C2BC.E$434.A
4.BADCBCBCB.E$189.3A24.2A217.2A2.B2A4BCBE$191.A23.2A217.2A3.6B2CB2E$
190.A26.A2$436.2A$435.A.A$437.A8$201.2A$196.A5.2A7.A.A$196.2A3.A4.3A
3.2A$195.A.A10.A3.A$207.A$250.2A$250.A.A$250.A4$257.2A$257.A.A$257.A
2$234.2A$234.A.A$234.A2$216.A$216.2A$215.A.A21$201.A$202.2A$201.2A3$
246.A$246.A.A$197.A.A46.2A$198.2A$198.A4.A.A$204.2A$204.A2$202.A$203.
A$201.3A3$184.A$185.A$183.3A2$40.A$41.A$39.3A7$41.A$39.A.A81.A$40.2A
82.A$45.7B2C.2E65.3A98.3B2A2B2C.2E$45.4B2D2BC.E69.7B2C.2E86.3BADC2BC.
E$45.3BDBDBCB.E69.4B2C2BC.E87.3BDBCBCB.E$45.3BD3BCBE70.3BDBCBCB.E87.
3BDBABCBE$42.2A.2B2D2B2CB2E66.2A.3BDBABCBE88.2B2D2B2CB2E$43.2A78.2A2B
2D2B2CB2E$42.A79.A$433.A$434.A$122.A63.3A24.2A217.3A$110.2A10.2A64.A
23.2A$41.2A68.2A8.A.A63.A26.A222.7B2C.2E$42.2A66.A326.4B2C2BC.E$41.A
395.BABCBCBCB.E$431.A5.B2AD3BCBE$432.2A3.2B2D2B2CB2E$431.2A2$439.A$
438.2A$438.A.A$433.3A$435.A$198.2A234.A$193.A5.2A7.A.A$193.2A3.A4.3A
3.2A$192.A.A10.A3.A$204.A$247.2A$247.A.A$247.A4$254.2A$254.A.A$254.A
2$231.2A$231.A.A$231.A2$213.A$213.2A$212.A.A19$203.A$204.2A$203.2A3$
248.A$248.A.A$199.A.A46.2A$200.2A$200.A4.A.A$206.2A$206.A$41.A$42.A
161.A$40.3A162.A$203.3A3$186.A$187.A$185.3A$42.A$40.A.A81.A$41.2A82.A
$46.7B2C.2E65.3A$46.4B2D2BC.E69.7B2C.2E$46.2BD2BDBCB.E69.4B2C2BC.E$
46.2B2D3BCBE70.2BD2BCBCB.E$43.2A.6B2CB2E66.2A.2B2DBABCBE$44.2A78.2A6B
2CB2E$43.A79.A$422.A$422.A.A3.A$123.A298.2A4.A.A$111.2A10.2A100.3B2A
2B2C.2E191.2A$42.2A68.2A8.A.A100.3BADC2BC.E$43.2A66.A113.3BDBCBCB.E$
42.A182.3BDBABCBE$225.2B2D2B2CB2E188.7B2C.2E$424.4B2C2BC.E$424.BADABC
BCB.E$418.2A4.BACD3BCBE$419.2A3.6B2CB2E$188.3A24.2A201.A$190.A23.2A$
189.A26.A12$200.2A$195.A5.2A7.A.A$195.2A3.A4.3A3.2A$194.A.A10.A3.A$
206.A$249.2A$249.A.A$249.A4$256.2A$256.A.A$256.A2$233.2A$233.A.A$233.
A2$215.A$215.2A$214.A.A213$245.A57.A$246.2A55.A.A$245.2A6.A49.2A$254.
A$252.3A16$266.A.A$267.2A$267.A5$28.A$26.A.A230.A$27.2A231.A$258.3A$
23.3A137.9B2E$25.A.9B2E125.2BDB2D2BC2.E$24.A2.2BDBDCABC2.E50.9B2E63.
2B2DBD3B2E104.9B2E$27.2B2DBC3B2E51.2BDB2D2BC2.E62.6B3C106.2BDB2D2BC2.
E$27.6B3C53.2B2DBD3B2E63.5BA2BC106.2B2DBD3B2E$25.2A8BC53.6B3C69.A.A
108.6B3C$24.A.A62.5BA2BC70.A109.5BA2BC$26.A67.2A186.A.A$161.3A117.A.A
$163.A118.A$30.2A3.2A125.A$29.2A3.2A129.2A$31.A4.A53.A74.A.A96.2A7.A$
23.2A65.2A73.A99.2A7.2A$24.2A63.A.A172.A8.2A$23.A70.2A$94.A.A$94.A
180.2A$103.2A169.A.A$89.2A12.A.A170.A$88.A.A12.A165.2A$90.A179.2A$
269.A$262.2A$261.A.A$263.A2$290.3A$290.A$291.A2$242.A$242.2A$241.A.A$
246.A$246.2A$245.A.A4$256.2A$244.2A9.A.A$239.2A4.2A10.A58.2A$240.2A2.
A71.A.A$239.A76.A2$254.3A$256.A62.2A$255.A63.A.A$319.A53$243.A57.A$
244.2A55.A.A$243.2A6.A49.2A$252.A$250.3A16$264.A.A$265.2A$265.A5$26.A
$24.A.A230.A$25.2A231.A$256.3A$21.3A137.9B2E215.A.A$23.A.9B2E125.4B2D
2BC2.E215.2A$22.A2.4BDCABC2.E50.9B2E63.2BD2BD3B2E104.9B2E101.A$25.2BD
2BC3B2E51.4B2D2BC2.E62.2B2D2B3C106.4B2D2BC2.E$25.2B2D2B3C53.2BD2BD3B
2E63.5BA2BC106.2BD2BD3B2E$23.2A8BC53.2B2D2B3C69.A.A108.2B2D2B3C110.9B
2E$22.A.A62.5BA2BC70.A109.5BA2BC110.2BAB2C2BC2.E$24.A67.2A186.A.A112.
2BCABC3B2E$159.3A117.A.A113.2B2D2B3C$161.A118.A109.A4.8BC$28.2A3.2A
125.A230.2A$27.2A3.2A129.2A225.2A$29.A4.A53.A74.A.A96.2A7.A$21.2A65.
2A73.A99.2A7.2A$22.2A63.A.A172.A8.2A119.A$21.A70.2A292.3A3.2A$92.A.A
293.A2.A.A$92.A180.2A112.A$101.2A169.A.A$87.2A12.A.A170.A$86.A.A12.A
165.2A$88.A179.2A$267.A$260.2A$259.A.A$261.A2$288.3A$288.A$289.A2$
240.A$240.2A$239.A.A$244.A$244.2A$243.A.A4$254.2A$242.2A9.A.A$237.2A
4.2A10.A58.2A$238.2A2.A71.A.A$237.A76.A2$252.3A$254.A62.2A$253.A63.A.
A$317.A45$245.A57.A$246.2A55.A.A$245.2A6.A49.2A$254.A$252.3A16$266.A.
A$267.2A$267.A5$28.A361.A$26.A.A230.A129.A$27.2A231.A128.3A$258.3A$
23.3A137.9B2E211.A$25.A.9B2E125.4B2D2BC2.E211.A$24.A2.4BDCABC2.E50.9B
2E63.3BDBD3B2E104.9B2E95.3A3.9B2E$27.3BDBC3B2E51.4B2D2BC2.E62.3BD2B3C
106.4B2D2BC2.E100.2BAB2C2BC2.E$27.3BD2B3C53.3BDBD3B2E63.2B2DBA2BC106.
3BDBD3B2E101.2BACBC3B2E$25.2A2B2D4BC53.3BD2B3C69.A.A108.3BD2B3C103.3B
D2B3C$24.A.A62.2B2DBA2BC70.A109.2B2DBA2BC103.2B2D4BC$26.A67.2A186.A.A
$161.3A117.A.A$163.A118.A102.A5.A$30.2A3.2A125.A222.2A4.2A$29.2A3.2A
129.2A217.A.A3.A.A$31.A4.A53.A74.A.A96.2A7.A121.2A$23.2A65.2A73.A99.
2A7.2A119.A.A$24.2A63.A.A172.A8.2A120.A$23.A70.2A$94.A.A$94.A180.2A$
103.2A169.A.A$89.2A12.A.A170.A$88.A.A12.A165.2A$90.A179.2A$269.A$262.
2A$261.A.A$263.A2$290.3A$290.A$291.A2$242.A$242.2A$241.A.A$246.A$246.
2A$245.A.A4$256.2A$244.2A9.A.A$239.2A4.2A10.A58.2A$240.2A2.A71.A.A$
239.A76.A2$254.3A$256.A62.2A$255.A63.A.A$319.A91$22.A$20.A.A$21.2A4$
41.A$41.A.A57.A$41.2A58.A.A$97.A3.2A$98.A$96.3A2$31.A$32.2A$31.2A4.2B
2D6B52.2B2D6B$37.3BD2B2D2B52.3BD2B2C2B$37.3BDBCBACB.2E.E47.2BACBC2BCB
.2E.E$30.2A5.4BDCABCB.E.2E47.2BAB2C2BCB.E.2E$31.2A4.9BCE51.9BCE$30.A
2$91.3A$34.3A56.A$36.A55.A$35.A10.2A55.2A$46.A.A53.2A$46.A57.A76$19.A
48.A$17.A.A46.A.A$18.2A47.2A$71.2B2DB2CB2.2A.2A$71.2BDCACBC.A.A.2A$
25.2B2DB2CB2.2A.2A31.2BA2BDBC.A.A$25.2B2DBCBC.A.A.2A28.2A.BA2DACBC.A.
A.2A$21.2A2.5BDBC.A.A30.A.A.2B2CB2CB2.2A.2A$20.A.A2.2B2DBCBC.A.A.2A
29.A$22.A2.2B2DB2CB2.2A.2A14$28.A$29.2A$28.2A4$28.3A$30.A$29.A4$32.3A
$32.A$33.A64$7.A$5.A.A$6.2A5.A$11.A.A$12.2A3.2BDBACB2A$17.2B2D2CBA.A$
17.7BA.A$12.2A3.4B2CBA.2A$13.2A2.4BCBC$12.A2$6.3A$8.A$7.A8$.2A$A.A$2.
A25$15.A10.A$16.A10.2A$14.3A9.2A$65.A$66.2A$65.2A3$32.3B2D3B25.3BCD3B
$27.A4.2BD2BDBCA22.2A2BCBADBCA$28.A3.3B2D3BA21.A.A3B2C3BA$26.3A3.5B3C
24.A5B3C$32.5BC2B25.5BC2B$22.3A$24.A$23.A2$25.2A$26.2A$25.A22$7.A.A$
8.2A$8.A54.A$62.A$62.3A$59.A$57.A.A$58.2A$58.6B2C.2E$8.2A3.6B2C.2E34.
2B2DBDBC.2E$7.A.A3.2B2DBDBC.2E34.3BCADBC$9.A3.3BDBDBC37.2BADBCBC$13.
3BDACBC37.3BADCBCE$11.A.4B2CBCE40.A$10.2A44.2A$10.A.A44.2A$56.A23$13.
A$14.A13.A.A$12.3A13.2A$29.A5$7.A$8.2A$7.2A3$16.3B2D3B$16.2BDBD3B$16.
2BD5B$13.2A.3B2D2CBA$14.2A5BCBCA$13.A3$8.2A$9.2A$8.A3$2.A$2.2A$.A.A
19.2A$22.2A$24.A16$13.A$14.A13.A.A$12.3A13.2A$29.A5$7.A$8.2A$7.2A3$
16.3B2D3BE$16.2BDBD2BC.E$16.2BD5BE$13.2A.3B2D3C$14.2A5BC2B$13.A3$8.2A
$9.2A$8.A3$2.A$2.2A$.A.A19.2A$22.2A$24.A25$88.A.A$89.2A$89.A2$10.A$
11.2A$10.2A2$90.A$88.A.A$27.3B2CB2C54.2A$27.2BDBCBCBA57.3A$21.A5.2BDB
C3BA59.A2.3B2CB2C$19.2A6.3BCAD2BA.2A55.A3.2BDBCBCBA$20.2A5.4BD2BCA.2A
59.2BDBC3BA$98.2BACBC2BA.2A$98.BA2BC2BCA.2A$22.2A75.2A$21.2A$23.A3$
21.2A$21.A.A14.2A$21.A15.2A$39.A2$25.2A$24.A.A$26.A5$17.2A$16.A.A$18.
A2$71.2A$70.A.A$72.A25$20.A$21.A$19.3A$20.3BD2B$20.2BDACB2E$17.2A.2BD
BCBE$16.A.A.3BC2BE$18.A.4B2C!

I have also experimented transfer.cpp, but it turned out my approach was too naive. Filtering interesting components is harder than I thought.

[Chris857]

not sure if already covered, but this synthesis of xs24_rahr0rhar may have useful things (edit, fixed link)

Code: Select all

#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH xs24_rahr0rhar costs 64 gliders (pseudo).
#CLL state-numbering golly
x = 704, y = 162, rule = B3/S23
639bo$637bobo$638b2o3$655bo$656bo$654b3o$645bo$646bo$644b3o$314bo$
315bo$313b3o3$305bo$306b2o334bo$305b2o336b2o$642b2o4$300bo$301b2o$
300b2o18$550bobo$166bo383b2o$164b2o385bo$165b2o$456bo92bo51bo$158b
o296bo91bobo42b2o7bobo86b2o6bo$159b2o294b3o90b2o42b2o7b2o87b2o5bob
o$70bo87b2o5bo96bo434bobo$19bobo47bo93b2o98b2o339b2o92bo$19b2o48b
3o92b2o96b2o185bo154bobo$20bo92bo336b2o152bo$67bo43b2o336b2o3bobo$
68bo43b2o340b2o$obo13bo49b3o143b2o48b2o191bo$b2o12bo45bo48bo52bo
48bo49bo187bo$bo13b3o44b2o44bobo4bo46bobo48bo49bo184bobo55b2o43b2o
42b2o96b2o$61b2o11b2obo31b2o3bobob2obo32bo8bobob2obo43bob2obo32bo
11bob2obo92b2o3b2ob2obo75b2o6b2ob2obo42bo3b2ob2obo34bo3b2ob2obo33b
o3b2ob2obo87bo3b2ob2obo$74bob2o37b2obob2o30bobo9b2obob2o31bobo8b2o
bob2o30bobo10b2obob2o92bobobobobob2o82bobobob2o40bobo2bobobob2o31b
2obo2bobobob2o30b2obo2bobobob2o84b2obo2bobobob2o$14bo138b2o48b2o
46b2o9bo101bobo89bo38bo8b2o3bo38bobo3bo37bobo3bo91bobo3bo$13b2o59b
ob2o37b2obob2o35b2o5b2obob2o32bo3b2o4b2obob2o35b2o6b2obob2o93b2obo
bobob2o81b2obobob2o32bo11b2obobob2o36b2obobob2o35b2obobob2o89b2obo
bob2o$13bobo58b2obo31b2o3bobob2obo34bobo4bobob2obo35bobo5bob2obo
34bobo7bob2obo97b2ob2obo80bo2b2ob2obo30b3o10bo2b2ob2obo35bo2b2ob2o
bo34bo2b2ob2obo88bo2b2ob2obo$108bobo4bo42bo3bobo43bo4bo42bo6bo190b
2o51b2o43b2o42b2o96b2o$25b2o83bo52bo37b2o9bo49bo$25bobo30b2o6b2o
134b2o8b2o48b2o233b2o$25bo33b2o6b2o43b2o87bo50b2o242bobo$58bo7bo
44b2o138bobo244bo$113bo139bo$70b2o92b2o96b2o245bo$69b2o92b2o98b2o
243b2o$71bo86b2o5bo96bo245bobo$159b2o$158bo2$165b2o$164b2o$166bo
24$310bo$310b2o$309bobo2$307bo$307b2o5b2o$306bobo4bobo$315bo$408b
2o$408bobo$316bo91bo$316b2o$315bobo$410b2o$410bobo$410bo4b2o$415bo
bo$415bo$309b2o96b2o$310b2o94b2o$309bo98bo28$687bobo$688b2o$688bo$
361bo$359b2o$355bo4b2o$353bobo332b2o$354b2o331bobo$360b2o327bo$
360bobo329b2o$360bo331bobo$692bo!

[WhiteHawk]

not sure if already covered, but this synthesis of xs24_rahr0rhar may have useful things

I think you mean xs24_rahr0rhar (an extra space links to the wrong pattern)

[Chris857]

Thanks.

Another - block to hook w/ tail

Code: Select all

x = 380, y = 199, rule = LifeHistory
70$172.A159.A$171.A159.A$171.3A157.3A$88.A.A157.A.A$89.2A158.2A$89.A
159.A11$103.A159.A$101.A.A157.A.A$102.2A158.2A3$98.A159.A$96.A.A157.A
.A$97.2A158.2A5$112.A159.A$110.A.A157.A.A$111.2A158.2A15$130.2B2D3B
153.2B2D2BCE.2E$130.3BD3B153.3BD3BE.2E$130.2BD4B153.2BD4BE$130.3BD2CB
153.3BD2CBE$130.4BACB153.4BACB2E17$107.A159.A$107.2A158.2A$106.A.A
157.A.A2$111.3A157.3A$113.A159.A$112.A159.A6$101.2A158.2A$100.A.A157.
A.A$102.A159.A4$89.2A158.2A$88.A.A157.A.A$90.A159.A!

another

Code: Select all

x = 92, y = 89, rule = LifeHistory
77.A$76.A$76.3A15$11.A43.A.A$9.A.A43.2A$10.2A44.A18$44.2B2D2B2C$44.2B
D2BDBC$44.3BDBDBC.E$44.4BD3B2E$44.8B24$52.2A$51.2A$53.A15$84.2A$84.A.
A$84.A$90.2A$.2A86.2A$A.A88.A$2.A!

snake to canoe (is this okay? it affects one cell in the rightmost two columns in the snake->carrier step)

Code: Select all

x = 98, y = 107, rule = LifeHistory
15$27.A$25.A.A$26.2A20$82.A$43.A38.A.A$44.A37.2A$42.3A5$44.A$45.A$43.
3A4$42.A.A$43.2A$43.A5$63.2B2D2B$63.2BD3B$63.3BD2B$63.3BACBE$63.3BABC
E23$44.2A$43.A.A$45.A8$24.3A$26.A$25.A!

another

Code: Select all

x = 68, y = 77, rule = LifeHistory
52.A$52.A.A$52.2A3$13.A.A$14.2A$14.A14$31.3B2D4B.2E$31.2BD2BDB2C2.E$31.
2B2DBDBCB2E$31.5BD3B$31.5B2D2B18$49.A$48.2A$48.A.A15$3A$2.A$.A2$66.2A
$61.2A2.2A$60.2A5.A$62.A7$66.2A$65.2A$67.A!

[vilc]

snake to canoe (is this okay? it affects one cell in the rightmost two columns in the snake->carrier step)

Code: Select all

x = 98, y = 107, rule = LifeHistory
15$27.A$25.A.A$26.2A20$82.A$43.A38.A.A$44.A37.2A$42.3A5$44.A$45.A$43.
3A4$42.A.A$43.2A$43.A5$63.2B2D2B$63.2BD3B$63.3BD2B$63.3BACBE$63.3BABC
E23$44.2A$43.A.A$45.A8$24.3A$26.A$25.A!

No, it is not okay as presented. A component should always work independantly of the yellow cells, which is not the case here :

Code: Select all

x = 168, y = 84, rule = LifeHistory
110.A$3.A104.A.A$.A.A105.2A$2.2A19$165.A$58.A67.A38.A.A$19.A38.A.A66.
A37.2A$20.A37.2A65.3A$18.3A4$127.A$20.A107.A$21.A104.3A$19.3A3$125.A.
A$18.A.A105.2A$19.2A105.A$19.A4$146.2B2D2B$39.2B2D2B101.2BD3B2E$39.2B
D3B101.3BD2BE$39.3BD2B101.3BACBE$39.3BACBE100.3BABC$39.3BABCE22$127.
2A$20.2A104.A.A$19.A.A106.A$21.A7$107.3A$3A106.A$2.A105.A$.A!

The requirement that no cell can be modified in a two-cell-thick margin around the yellow cells region is actually meant to be a sufficient condition for this. It is a bit rigid and might change in the future, but it makes checks easier.

Pragmatically, if the component does not work in all cases, extend the white/blue region. You can then use JLS to enumerate all possible continuations (I find the fact that direct implications of choices are displayed very useful). Here, your component works in three cases out of four.

Code: Select all

x = 286, y = 112, rule = LifeHistory
6$28.A$26.A.A$27.2A20$83.A$44.A38.A.A$45.A37.2A$43.3A5$45.A$46.A$44.
3A4$43.A.A$44.2A$44.A5$64.2B2D3B105.2B2D3B20.2B2D3B12.2B2D3B2E$64.2BD
4B105.2BD4B20.2BD3BCE11.2BD3BC2.E$64.3BD3B105.3BD2BCE19.3BD2BC12.3BD
2BC.2E$64.3BACBC105.3BAC2BE19.3BACBC12.3BACBC$64.3BAB2C105.3BAB2C20.
3BABCB12.3BAB2C23$45.2A$44.A.A$46.A8$25.3A$27.A$26.A!

By the way, if we added this component to the database, it would increase the number of needed transformations by two instead of decreasing it (which is fine since the new transformations are more specific). However, transfer.cpp found a component which works in all cases (note that the extension of the marked region is technically still required) :

Code: Select all

x = 322, y = 28, rule = LifeHistory
7.A125.A89.A$5.A.A123.A.A87.A.A$6.2A124.2A88.2A$10.A125.A89.A$10.A.A
123.A.A87.A.A$10.2A124.2A88.2A$6.A125.A89.A$4.A.A123.A.A87.A.A$5.2A
124.2A88.2A91.A$5.2B2D3B119.2B2D3B83.2B2D3B84.A.A$5.2BD4B119.2BD4B83.
2BD3BCE84.2A$4.A3BD3B118.A3BD2BCE81.A3BD2BC89.A$2.A.A3BACBC116.A.A3BA
C2BE79.A.A3BACBC89.A.A$3.2A3BAB2C117.2A3BAB2C81.2A3BABCB89.2A$313.A$
311.A.A$312.2A$2A124.2A88.2A94.2B2D3B2E$.2A124.2A88.2A93.2BD3BC2.E$A
125.A89.A94.A3BD2BC.2E$309.A.A3BACBC$310.2A3BAB2C4$307.2A$308.2A$307.
A!

[Goldtiger997]

Attach sidewalk:

Code: Select all

#C 139:15 1 38 -3 66 4 112 -5/67 1 103 -7/59 3 119 10/50 4 65 -9 124 8 147 -6
x = 9, y = 5, rule = LifeHistory
BBDDBDDBB$
BBBDBDBBC$
BBBDBBDBC$
BBBBDBCBC$
BBBDDBCCB!

As a synthesis:

Code: Select all

x = 72, y = 68, rule = LifeHistory
59.A$57.2A$58.2A$12.A$13.A$11.3A$24.A$22.A.A$23.2A$58.A$56.2A$57.2A9$
31.A$29.A.A$30.2A3.A.A$36.2A$36.A3$40.9B$40.8BCE$40.8BC$40.6BCBC$40.
6B2CB8$23.3A$25.A$24.A$33.A$33.2A20.A$32.A.A19.2A$54.A.A12$.2A$A.A$2.
A4$9.2A$10.2A$9.A60.A$69.2A$69.A.A!

[vilc]

I added this useful (known) recipe for skewed snake stacks :

Code: Select all

x = 453, y = 29, rule = LifeHistory
296.A$294.A.A$295.2A3$303.A112.A$5.A298.A110.A$3.A.A296.3A103.A6.3A$
4.2A292.2A109.2A$299.2A107.2A$115.A109.A72.A$.A111.A.A56.A53.2A127.2A
55.2A$2.A6.2B2D2B44.2B2D2B49.2A2.2B2D2B49.A3.A3.2B2D2B38.2A127.A2.A
54.A.A$3A6.2BD2BCA43.2BCABCA52.2BCABCA46.3A4.2A.2BCABCA43.A8.BACD2B
61.BACD2B41.2ADC2B48.2A.2BDC2B$9.3BDBC39.A4.3BCBC53.BABCBC53.2A2.3BCB
C45.2A6.BADABCA60.BADABCA36.2A2.2BDABCA46.A.A.2BCABCA$9.2B2D2BA39.A3.
BADC2BA52.BADC2BA56.2BDC2BA43.2A7.3BCBC61.3BCBC36.A.A2.3BCBC49.A.3BDB
C29.2B2C2B$3.2A4.5BCA37.3A3.B2A2BCA52.2BA2BCA56.2B2ABCA52.2BDC2BA60.
2B2C2BA37.A2.2B2C2BA50.2B2C2BA28.2BC2BCA$2.A.A170.2A7.A55.2B2ABCA60.
3BABCA40.3BABCA50.3BABCA28.3BCBC$4.A171.2A4.A.A58.A66.A46.A56.A31.2B
2C2BA$56.2A60.2A55.A6.2A47.A9.A.A64.A.A44.A.A54.A.A28.A2.3BABCA$55.A.
A59.A.A109.A.A9.2A64.A.A44.A.A54.A.A27.A.A5.A$57.A61.A110.2A75.2A45.
2A55.2A29.2A3.A.A$4.2A116.3A321.A.A$5.2A115.A323.2A$4.A118.A108.2A$
233.2A$16.3A213.A$16.A$17.A!

I also improved the clearance of one of my block-on-table inserting components.

Code: Select all

x = 63, y = 73, rule = B3/S23
13bo$14bo4bo$12b3o2bobo$18b2o37bo$57bobo$57b2o3$17bo$18bo33bo$16b3o32b
o8bobo$51b3o6b2o$61bo5$bo$2bo$3o5bo$6bobo$7b2o5$19bo$20b2o$19b2o3$21bo
$19bobo$20b2o9$24b3o$26bo$25bo2$21bo$21b2o$20bobo7$2b3o$4bo$3bo3$18b2o
$17bobo$19bo$50b2o$49b2o$51bo2$8b2o6b3o$9b2o7bo$8bo8bo$58bo$57b2o$57bo
bo!

Now only four types of X-on-table insertions remain :

Code: Select all

x = 99, y = 5, rule = LifeHistory
2B2DB2D2BC20.2B2DB2D3B20.2B2DB2D2BC20.2B2DB2D2B$2B2DBD3BC20.2B2DBD2B
2C20.2B2DBD4B20.2B2DBD2BC$5BD4B20.5BD3BC20.5BD3BC20.5BD3B$5B2D2BC20.
5B2D2BC20.5B2D2BC20.5B2D2B$9BC20.10B20.8B2C20.8BC!

Edit:
Two known recipes.

Code: Select all

x = 217, y = 245, rule = LifeHistory
116.A$117.A$115.3A8$65.A$63.A.A$64.2A79.A$77.A66.A$77.A.A64.3A$68.A.A
6.2A41.A.A$68.2A51.2A$69.A47.A3.A$78.A36.A.A$67.A9.A38.2A$13.A51.A.A
9.3A33.A91.A$14.A51.2A43.A.A91.A.A$12.3A97.2A87.A3.2A$21.A.A178.A$21.
2A177.3A$22.A2$138.A$58.2A76.3A64.2B2D6B$59.2A5.2A67.A67.3BD2BC3B$14.
2B2D6B34.A2.2B2DBA4B60.2B2DBA4B62.2BACBCBC2B$14.3BD2BCA2B37.3BD2BC3B
56.A3.3BD2BC3B62.2BAB2C2BCB$11.A2.3BDBDAD2B37.3BDBDBC2B57.A2.3BDBDBC
2B62.7B2CB$11.2A.4B2D2BCB37.4B2D2BCB55.3A2.4B2D2BCB$10.A.A.7B2CB37.7B
2CB60.7B2CB$195.3A$129.2A66.A$128.A.A65.A$130.A76.2A$206.2A$117.A90.A
$117.2A$116.A.A3$123.A$123.2A$111.A10.A.A$111.2A2.3A21.2A$110.A.A4.A
20.2A$116.A23.A39$116.A$117.A$115.3A8$65.A$63.A.A$64.2A79.A$77.A66.A$
77.A.A64.3A$68.A.A6.2A41.A.A$68.2A51.2A$69.A47.A3.A$78.A36.A.A$67.A9.
A38.2A$65.A.A9.3A33.A91.A$8.A57.2A43.A.A91.A.A$9.A102.2A87.A3.2A$7.3A
192.A$16.A.A181.3A$16.2A$17.A$138.A$58.2A76.3A64.2B2D5BCE.2E$59.2A5.
2A67.A67.3BD2BC3BE.2E$58.A2.2B2DBA3BCE.2E56.2B2DBA3BCE.2E58.2BACBCBC
2BE$9.2B2D5BCE.2E38.3BD2BC3BE.2E52.A3.3BD2BC3BE.2E58.2BAB2C2BCBE$9.3B
D2BCA2BE.2E38.3BDBDBC2BE56.A2.3BDBDBC2BE61.7B2CB2E$6.A2.3BDBDAD2BE41.
4B2D2BCBE54.3A2.4B2D2BCBE$6.2A.4B2D2BCBE41.7B2CB2E58.7B2CB2E$5.A.A.7B
2CB2E174.3A$129.2A66.A$128.A.A65.A$130.A76.2A$206.2A$117.A90.A$117.2A
$116.A.A3$123.A$123.2A$111.A10.A.A$111.2A2.3A21.2A$110.A.A4.A20.2A$
116.A23.A90$8.A$9.2A$8.2A53.A$2.A58.A.A$A.A59.2A$.2A65.7B$13.7B48.2B
2D3B$4.2A7.2B2D3B48.2BCAB2C.A$5.2A6.2BD2B2C.A36.A9.2BADACB2A$4.A8.3BD
BCB2A36.2A8.4BD2B$13.4BD2B37.A.A2$8.2A$7.A.A51.3A$9.A53.A$62.A!

Edit 2:
Snakes on length-3 surface :

Code: Select all

x = 318, y = 480, rule = LifeHistory
123.A$121.A.A$122.2A2$167.A$166.A$166.3A3$117.A9.A$115.A.A7.A.A8.A$
116.2A8.2A9.A$135.3A4$116.A102.A$114.A.A41.A58.A.A$115.2A16.A22.2A60.
2A$131.A.A23.2A$132.2A$221.A$219.A.A$18.A201.2A$16.A.A$17.2A3$140.A$
141.2A$140.2A$31.2B2D2B2C.2E$31.2BD2BCBC.E106.2B2D2B2C.2E$31.3BDBCBC.
E.E104.2BD2BCBC.E77.A$31.2B2DBDCB2.2E95.3A6.3BDBCBC.E.E73.2A$31.8B
101.A2.2A2.2B2DBDCB2.2E74.2A$139.A4.2A.3B3A2B$143.A6.A83.2B2D2B2C.2E
46.A$234.2BD2BCBC.E48.2A$234.3BDBCBC.E.E45.2A$38.A190.3A2.2BDCADCB2.
2E57.2B2C2B2C.2E$30.A6.2A192.A2.2BA2BA2B61.2BC2BCBC.E$31.A5.A.A90.2A
91.A6.A5.2A65.3BCBCBC.E.E$29.3A97.A.A3.3A83.A.A79.2B2DADCB2.2E$131.A
5.A84.2A79.5BA2B$35.3A98.A3.2A84.A$37.A102.A.A83.2A$36.A103.A84.A.A3$
157.A137.2A12.3A$156.2A64.2A72.2A11.A$140.2A14.A.A64.2A70.A9.2A3.A$
141.2A79.A81.A.A$140.A165.A$166.2A148.A$165.2A148.2A$153.2A12.A147.A.
A$134.3A16.A.A2.2A$136.A16.A3.2A$109.A25.A23.A$109.2A$108.A.A61$85.A$
83.A.A$84.2A44.A$128.A.A$129.2A$87.A$88.A$86.3A43.A$130.A.A$131.2A2$
85.2A$86.2A9.A$85.A9.2A$90.A5.2A$90.A.A$90.2A3$145.A$143.2A30.A$144.
2A30.2A$175.2A$29.2B2D2BDC2B47.2B2D2BDC2B49.2B2D2B2C2B32.2B2C2B2C2B$
29.2BD2BDABCB47.2BD2BDABCB49.2BD2BC2BCB32.2BC2BC2BCB$29.3BDBDBCBC47.
3BDBCBCBC49.3BDBCBCBC32.3BCBCBCBC$29.2B2DB2D2BC47.2B2DADC2BC44.3A2.2B
DCADC2BC32.2B2DADC2BC$29.9BCA46.5BA3BCA45.A2.2BA2BA3BCA31.5BA3BCA$27.
A106.A6.A5.2A$28.2A50.2A50.A.A$27.2A50.A.A51.2A$81.A55.A$137.2A$29.2A
105.A.A40.2A12.3A$28.A.A149.2A11.A$30.A48.2A98.A9.2A3.A$23.2A55.2A
106.A.A$24.2A53.A53.2A55.A$23.A110.2A64.A$72.3A58.A65.2A$74.A124.A.A$
73.A33$81.A$79.A.A$80.2A44.A$124.A.A$125.2A$83.A$84.A$82.3A43.A$126.A
.A$127.2A2$81.2A$82.2A9.A$81.A9.2A$86.A5.2A$86.A.A$86.2A3$141.A$139.
2A$140.2A2$25.2B2D2BDC2B47.2B2D2BDC2B49.2B2D2B2C2B47.A$25.2BD2BDABCB
47.2BD2BDABCB49.2BD2BC2BCB48.2A$25.3BDBDBC2B47.3BDBCBC2B49.3BDBCBC2B
47.2A$25.2B2DB2D3B47.2B2DADC3B44.3A2.2BDCADC3B59.2B2C2B2C2B$25.10B47.
5BA4B46.A2.2BA2BA4B59.2BC2BC2BCB$23.A106.A6.A5.2A65.3BCBCBC2B$24.2A
50.2A50.A.A79.2B2DADC3B$23.2A50.A.A51.2A79.5BA4B$77.A55.A$133.2A$25.
2A105.A.A$24.A.A$26.A48.2A$19.2A55.2A124.2A12.3A$20.2A53.A53.2A72.2A
11.A$19.A110.2A70.A9.2A3.A$68.3A58.A81.A.A$70.A142.A$69.A153.A$222.2A
$222.A.A119$74.A$72.A.A$73.2A3$76.A$74.A.A$75.2A8$A$.2A$2A87.A$87.2A
65.A$88.2A65.2A$154.2A$16.2B2D2B2CB2A62.2B2D2B2CB2A66.2B2C2B2CB2A$16.
2BD2BCBCBA63.2BD2BCBCBA67.2BC2BCBCBA$11.A4.3BDBC3BA63.3BDBC3BA67.3BCB
C3BA$9.2A5.2B2DACD2BA.2A55.3A2.2BDCADC2BA.2A64.2B2DADC2BA.2A$10.2A4.
8BCA.2A57.A2.2BA2BA2BCA.2A64.5BA2BCA.2A$78.A6.A5.2A$76.A.A$12.2A63.2A
$11.2A68.A$13.A67.2A$80.A.A75.2A12.3A$159.2A11.A$11.2A145.A9.2A3.A$
11.A.A14.2A137.A.A$11.A15.2A48.2A90.A$29.A48.2A99.A$77.A100.2A$15.2A
161.A.A$14.A.A$16.A5$7.2A$6.A.A$8.A26$74.A$72.A.A$73.2A3$76.A$74.A.A$
75.2A8$A$.2A$2A87.A$87.2A65.A$88.2A65.2A$154.2A$16.2B2D2B2CB64.2B2D2B
2CB68.2B2C2B2CB$16.2BD2BCBCB64.2BD2BCBCB68.2BC2BCBCB$11.A4.3BDBC3B64.
3BDBC3B68.3BCBC3B$9.2A5.2B2DACD2B59.3A2.2BDCADC2B68.2B2DADC2B$10.2A4.
9B61.A2.2BA2BA3B68.5BA3B$78.A6.A5.2A$76.A.A$12.2A63.2A$11.2A68.A$13.A
67.2A$80.A.A75.2A12.3A$159.2A11.A$11.2A145.A9.2A3.A$11.A.A14.2A137.A.
A$11.A15.2A48.2A90.A$29.A48.2A99.A$77.A100.2A$15.2A161.A.A$14.A.A$16.
A5$7.2A$6.A.A$8.A!

Edit 3:

not sure if already covered, but this synthesis of xs24_rahr0rhar may have useful things (edit, fixed link)

With some modifications this solves one hard case :

Code: Select all

x = 659, y = 165, rule = LifeHistory
594.A$592.A.A$593.2A3$610.A$611.A$609.3A$600.A$601.A$599.3A$269.A$
270.A$268.3A3$260.A$261.2A334.A$260.2A336.2A$597.2A4$255.A$256.2A$
255.2A12$514.A.A$491.A.A5.A14.2A$40.A.A449.2A3.A.A15.A$40.2A450.A5.2A
$41.A464.A$2.A501.2A$A.A502.2A$.2A118.A$119.2A$120.2A$411.A$113.A296.
A234.2A6.A$114.2A294.3A232.2A5.A.A$113.2A5.A96.A434.A.A$118.2A98.2A
433.A$119.2A96.2A185.A$68.A336.2A$66.2A336.2A3.A.A$67.2A340.2A$167.2A
48.2A191.A$65.A52.A48.A49.A187.A$63.A.A4.A46.A.A48.A49.A184.A.A55.2A
38.2A145.2A$64.2A2BDADCB2A.A32.A5.2BDADCB2A.A38.2BDBDCB2A.A32.A6.2BDB
DCB2A.A92.2ABDB2CB2A.A75.2A2.2BDB2CB2A.A42.ABDB2CB2A.A29.ABDB2CB2A.A
136.ABDB2CB2A.A$66.2B2DACBA.2A30.A.A5.2B2DACBA.2A31.A.A4.2B2DACBA.2A
30.A.A6.2B2DACBA.2A92.ABADCBCBA.2A79.2BDCBCBA.2A40.A.ABDCBCBA.2A26.2A
.ABDCBCBA.2A133.2A.ABDCBCBA.2A$10.A.A53.7B35.2A5.7B36.2A4.7B35.2A6.3B
A3B97.BABA3B83.3BA3B35.A8.2A3BA3B30.A.A3BA3B137.A.A3BA3B$11.2A53.2B2D
ACBA.2A35.2A.2B2DACBA.2A32.A3.2A2B2DACBA.2A35.2A2.2B2DACBA.2A93.2ADCB
CBA.2A79.2B2CBCBA.2A32.A9.2B2CBCBA.2A29.2B2CBCBA.2A136.2B2CBCBA.2A$
11.A52.2A2BDADCB2A.A34.A.A.2BDADCB2A.A35.A.A2BDBDCB2A.A34.A.A2.2BDBDC
B2A.A93.2BDB2CB2A.A79.BADB2CB2A.A30.3A9.BADB2CB2A.A29.BADB2CB2A.A136.
BADB2CB2A.A$21.2BDB2CB2A.A31.A.A4.A42.A3.A.A43.A4.A42.A6.A190.2A51.2A
38.2A145.2A$21.2B2DACBA.2A33.A52.A37.2A9.A49.A$21.7B129.2A8.2A48.2A
233.2A$21.2B2DACBA.2A35.2A87.A50.2A242.A.A$21.2BDB2CB2A.A34.2A138.A.A
244.A$68.A139.A$119.2A96.2A245.A$118.2A98.2A243.2A$113.2A5.A96.A245.A
.A$114.2A$9.A103.A$9.2A$8.A.A109.2A$119.2A$5.2A114.A$6.2A$5.A8$.2A$A.
A$2.A$41.A$40.2A$40.A.A9$265.A$265.2A$264.A.A2$262.A$262.2A5.2A$261.A
.A4.A.A$270.A$363.2A$363.A.A$271.A91.A$271.2A$270.A.A$365.2A$365.A.A$
365.A4.2A$370.A.A$370.A$264.2A96.2A$265.2A94.2A$264.A98.A28$642.A.A$
643.2A$643.A4$643.2A$642.A.A$307.A6.3A327.A$308.2A4.A332.2A$307.2A6.A
331.A.A$647.A$311.2A$312.2A$311.A!

Edit 4:
Another recipe for mirrored snakes, from the other side.

Code: Select all

x = 362, y = 55, rule = LifeHistory
40.A.A$40.2A$41.A$2.A$A.A$.2A$163.A$163.A.A$163.2A4$255.A$5.A250.2A
93.A$6.2A247.2A95.A$5.2A343.3A$83.A174.A86.A.A$8.A.A70.A.A9.A70.A93.A
.A85.2A$9.2A71.2A5.2BDCBCB64.2BDCBCB91.2A86.A$9.A79.2BDB2CB64.2BDB2CB
86.A$89.7B64.7B84.A.A96.A6.2A$89.2BDB2CB64.2BCA2CB85.2A2.2BCDBCB88.A
3.2BCDBCB$89.2BDCBCB57.2A5.2BCDBCB89.2BCA2CB86.3A3.2BDA2CB$93.A58.A.A
101.7B82.2A8.7B$154.A101.2BCA2CB83.2A7.2BDA2CB$21.2B2DACB224.2A2.2BCD
BCB82.A9.2BCDBCB$21.2BDB2CB223.A.A103.2A$21.7B225.A$21.2BDB2CB230.2A$
21.2B2DACB230.A.A$11.A246.A$11.2A337.3A$10.A.A79.2A161.2A95.A$92.A.A
161.2A93.A$92.A162.A15$.2A$A.A$2.A$41.A$40.2A$40.A.A!

[Chris857]

The catalyst can be constructed in three stages, like this:

Code: Select all

x = 202, y = 43, rule = B3/S23
10bo$9bobo$10b2o$5bo10b3o$4bobo$4bobo$5bo5b2o$11bobo69b2ob2o75b2ob2o$
12bo68bo2bob2o73bo2bob2o$bo79b2obo76b2obo$obo81bo79bo13b3o4b2o$obo81b
2o78b2o18bo2bo$bo160b2o20bo2bo$161bobo21b2o$81b2o2b2o2b3o70bo$24b3o53b
obo2bobo88b3o$24bo50b3o3bo4bo$25bo66b2o68b2o20b2o$92b2o68b2o19bo2bo$
73b2o108bobo$73b2o7bo101bo$82bo$82bo83b2o$95b2o68bo2bo$95b2o68bo2bo$
166b2o2$81b2o11b2o$81bobo9bobo74b2o$82bobo9bo75bobo$83bo87bo$199b3o$
199bo$200bo7$99b2o$99bobo$99bo!

Does that mid step of attaching a boat help any situations that don't already work?