Which life-like rules contain still lifes?

[amling]

Starting with...

This is the complete list of the 295 OT rules without still lifes and where they are not proven impossible, as found in Eppstein (2009):

Code: Select all

B25/S157
B258/S157
B246/S257
B246/S24
B246/S248
B246/S247
B246/S2478
B2468/S257
B2468/S24
B2468/S248
B2468/S247
B2468/S2478
B2467/S256
B2467/S2568
B2467/S24
B2467/S248
B2467/S247
B2467/S2478
B2467/S246
B2467/S2468
B2467/S2467
B2467/S24678
B24678/S2568
B24678/S24
B24678/S248
B24678/S247
B24678/S2478
B24678/S246
B24678/S2468
B24678/S2467
B24678/S24678
B245/S25
B245/S258
B245/S257
B245/S2578
B245/S256
B245/S2568
B245/S2567
B245/S25678
B245/S246
B245/S2468
B245/S2467
B245/S24678
B245/S245
B245/S2458
B245/S2457
B245/S24578
B245/S2456
B245/S24568
B245/S24567
B245/S245678
B245/S23
B245/S238
B245/S237
B245/S2378
B245/S236
B245/S2368
B245/S2367
B245/S23678
B245/S12
B245/S128
B245/S127
B245/S1278
B245/S126
B245/S1268
B245/S1267
B245/S12678
B245/S125
B245/S1258
B245/S1257
B245/S12578
B245/S1256
B245/S12568
B245/S12567
B245/S125678
B2458/S25
B2458/S258
B2458/S257
B2458/S2578
B2458/S256
B2458/S2568
B2458/S2567
B2458/S25678
B2458/S246
B2458/S2468
B2458/S2467
B2458/S24678
B2458/S245
B2458/S2458
B2458/S2457
B2458/S24578
B2458/S2456
B2458/S24568
B2458/S24567
B2458/S245678
B2458/S23
B2458/S238
B2458/S237
B2458/S2378
B2458/S236
B2458/S2368
B2458/S2367
B2458/S23678
B2458/S12
B2458/S128
B2458/S127
B2458/S1278
B2458/S126
B2458/S1268
B2458/S1267
B2458/S12678
B2458/S125
B2458/S1258
B2458/S1257
B2458/S12578
B2458/S1256
B2458/S12568
B2458/S12567
B2458/S125678
B2457/S25
B2457/S258
B2457/S257
B2457/S2578
B2457/S256
B2457/S2568
B2457/S2567
B2457/S25678
B2457/S245
B2457/S2458
B2457/S2457
B2457/S24578
B2457/S2456
B2457/S24568
B2457/S24567
B2457/S245678
B2457/S23
B2457/S238
B2457/S237
B2457/S2378
B2457/S236
B2457/S2368
B2457/S2367
B2457/S23678
B2457/S12
B2457/S128
B2457/S127
B2457/S1278
B2457/S126
B2457/S1268
B2457/S1267
B2457/S12678
B2457/S125
B2457/S1258
B2457/S1257
B2457/S12578
B2457/S1256
B2457/S12568
B2457/S12567
B2457/S125678
B24578/S25
B24578/S258
B24578/S257
B24578/S2578
B24578/S256
B24578/S2568
B24578/S2567
B24578/S25678
B24578/S245
B24578/S2458
B24578/S2457
B24578/S24578
B24578/S2456
B24578/S24568
B24578/S24567
B24578/S245678
B24578/S23
B24578/S238
B24578/S237
B24578/S2378
B24578/S236
B24578/S2368
B24578/S2367
B24578/S23678
B24578/S12
B24578/S128
B24578/S127
B24578/S1278
B24578/S126
B24578/S1268
B24578/S1267
B24578/S12678
B24578/S125
B24578/S1258
B24578/S1257
B24578/S12578
B24578/S1256
B24578/S12568
B24578/S12567
B24578/S125678
B2456/S23
B2456/S238
B2456/S237
B2456/S2378
B2456/S236
B2456/S2368
B2456/S2367
B2456/S23678
B2456/S12
B2456/S128
B2456/S127
B2456/S1278
B2456/S126
B2456/S1268
B2456/S1267
B2456/S12678
B2456/S125
B2456/S1258
B2456/S1257
B2456/S12578
B2456/S1256
B2456/S12568
B2456/S12567
B2456/S125678
B24568/S23
B24568/S238
B24568/S237
B24568/S2378
B24568/S236
B24568/S2368
B24568/S2367
B24568/S23678
B24568/S12
B24568/S128
B24568/S127
B24568/S1278
B24568/S126
B24568/S1268
B24568/S1267
B24568/S12678
B24568/S125
B24568/S1258
B24568/S1257
B24568/S12578
B24568/S1256
B24568/S12568
B24568/S12567
B24568/S125678
B24567/S23
B24567/S238
B24567/S237
B24567/S2378
B24567/S236
B24567/S2368
B24567/S2367
B24567/S23678
B24567/S12
B24567/S128
B24567/S127
B24567/S1278
B24567/S126
B24567/S1268
B24567/S1267
B24567/S12678
B24567/S125
B24567/S1258
B24567/S1257
B24567/S12578
B24567/S1256
B24567/S12568
B24567/S12567
B24567/S125678
B245678/S23
B245678/S238
B245678/S237
B245678/S2378
B245678/S236
B245678/S2368
B245678/S2367
B245678/S23678
B245678/S12
B245678/S128
B245678/S127
B245678/S1278
B245678/S126
B245678/S1268
B245678/S1267
B245678/S12678
B245678/S125
B245678/S1258
B245678/S1257
B245678/S12578
B245678/S1256
B245678/S12568
B245678/S12567
B245678/S125678

In particular, all of the unknown cases are B2 rules. Based on the kind of proofs given in this source, it is likely that any proofs of nonexistence in this ruleset requires a demonstration that an infinite repeating component is forced, like in the p1 ship project.

I'm compiling a comprehensive list of rules with small (width and height ≤10, likely lower for large periods), low-period oscillators using a Python LLS wrapper. The cases evaluated, at time of writing, include all still lifes with bounding box area ≤64.

EDIT: B2467/S24678 solved:

Code: Select all

x = 72, y = 72, rule = B2467/S24678
15bo$13bob2o$12b2ob2obo$10bob2o2bob2o$9b2obo5b2obo$7bob2o8bob2o$6b2obo
7b2obob2o$5b2obob2o6b2obo$7bob2o4bob4ob3o$4b3ob4obob3ob3ob3o$3b3ob3ob
3ob5obo$7bob5o2b3o5b3o$2b3o5b2obob5o5b3o$b3o5b5ob3ob2o$15bo4b2o2b3o$3o
5b3ob3obo2b3ob3o$b3o5b5ob3ob2o$6bob6o2bob4o2b3o$2b3ob3ob3o4bo7b3o$3b3o
b4ob2ob3ob2o$6bob2o3b5obo6b3o$4b2obob2o3b2obo9b3o$5b2obo$6bob2o5bo12b
3o$8b2obo2b2obo11b3o$9bob2ob2ob2o$11b2obo2b2obo9b3o$12bo5bob2o9b3o$20b
2obo$21bob2o7b3o$23b2obo6b3o$24bob2o$26b2obo4b3o$27bob2o4b3o$29b2obob
2ob2o$30bob3o3b2o$32b2o3b3obo$33b2ob2obob2o$34b3o4b2obo$35b3o4bob2o$
44b2obo$36b3o6bob2o$37b3o7b2obo$48bob2o$38b3o9b2obo5bo$39b3o9bob2o2bob
2o$53b2ob2ob2obo$40b3o11bob2o2bob2o$41b3o12bo5b2obo$63bob2o$42b3o9bob
2o3b2obob2o$43b3o6bob5o3b2obo$51b2ob3ob2ob4ob3o$44b3o7bo4b3ob3ob3o$45b
3o2b4obo2b6obo$51b2ob3ob5o5b3o$46b3ob3o2bob3ob3o5b3o$45b3o2b2o4bo$51b
2ob3ob5o5b3o$44b3o5b5obob2o5b3o$45b3o5b3o2b5obo$50bob5ob3ob3ob3o$46b3o
b3ob3obob4ob3o$47b3ob4obo4b2obo$50bob2o6b2obob2o$48b2obob2o7bob2o$49b
2obo8b2obo$50bob2o5bob2o$52b2obo2b2obo$53bob2ob2o$55b2obo$56bo!

EDIT2: Much smaller, and solves all rules with at least S246 and at most B24678.

Code: Select all

x = 49, y = 49, rule = B24678/S24678
16bo$15b2obo$13bob2ob2o$8bo3b2obo2b2obo$7b2obob2o5bob2o$6b2ob2obo8b2ob
o$5b2o2bobob2o7bob2o$4b2o5b2obobo7b2obo$3b2o8bob2obo6bob2o$5b2o3b3ob3o
b2o7b2obo$4b2o3b3ob3o2b2obo6bob2o$6b2ob2obo6bob2o3b2obob2o$3b3obobobob
2o6b2obobob2o2b2o$2b3obobobob2o8bob2obo5b2o$6b2ob2obo7b2obobob2o5b2o$b
3o4b3o10b2obobob2o5b2o$3o4b3o12bob2obo8b2o$24b3ob3o6b2o$b3o4b3o14b3ob
3o6b2o$2b3o4b3o16bob2obo2b2o$14bo11b2obobob2obob3o$3b3o4b3ob2o11b2obob
ob2obob3o$4b3o4b3ob2o11bob2obo2b2o$14bo15b3ob2o4b3o$5b3o4b2ob3o13b3ob
2o4b3o$6b3o4b2ob3o15bo$11b2o2bob2obo11b2ob3o4b3o$7b3obob2obobob2o11b2o
b3o4b3o$8b3obob2obobob2o11bo$11b2o2bob2obo16b3o4b3o$9b2o6b3ob3o14b3o4b
3o$10b2o6b3ob3o$11b2o8bob2obo12b3o4b3o$12b2o5b2obobob2o10b3o4b3o$13b2o
5b2obobob2o7bob2ob2o$14b2o5bob2obo8b2obobobob3o$15b2o2b2obobob2o6b2obo
bobob3o$16b2obob2o3b2obo6bob2ob2o$17b2obo6bob2o2b3ob3o3b2o$18bob2o7b2o
b3ob3o3b2o$20b2obo6bob2obo8b2o$21bob2o7bobob2o5b2o$23b2obo7b2obobo2b2o
$24bob2o8bob2ob2o$26b2obo5b2obob2o$27bob2o2bob2o3bo$29b2ob2obo$30bob2o
$32bo!

Let's collect results for this here and try to burn down that list! For starters...

The following 13 rules are handled (shown to contain no finite still lifes) by arbitrary width level searches in LLSSS (geom "p1"):

Code: Select all

B245/S25
B245/S258
B2457/S25
B2457/S258
B24578/S25
B24578/S258
B2458/S25
B2458/S258
B246/S257
B2467/S256
B2467/S2568
B24678/S2568
B2468/S257

Similar with geometry raw:1:1:0:0:0:1:0:1:0 ("p1" with U=X+Y) rules out:

Code: Select all

B258/S157

All remaining rules lasted at least ~10s in both searches (on my very weak and highly overloaded laptop) so it's possible more could be ruled out this way with more concerted effort. LaundryPizza03, how do you want to split this up? Left to my own devices I will probably turn my attention to using the various tools from the "Life-like p1 photon project" thread to try to eliminate rules or perhaps try to figure out a way to run some small searches hoping to get lucky with positive results.

Subtracting the known results (positive and negative) leaves me with the following 273 rules:

Code: Select all

B25/S157
B246/S24
B246/S248
B246/S247
B246/S2478
B2468/S24
B2468/S248
B2468/S247
B2468/S2478
B2467/S24
B2467/S248
B2467/S247
B2467/S2478
B24678/S24
B24678/S248
B24678/S247
B24678/S2478
B245/S257
B245/S2578
B245/S256
B245/S2568
B245/S2567
B245/S25678
B245/S246
B245/S2468
B245/S2467
B245/S24678
B245/S245
B245/S2458
B245/S2457
B245/S24578
B245/S2456
B245/S24568
B245/S24567
B245/S245678
B245/S23
B245/S238
B245/S237
B245/S2378
B245/S236
B245/S2368
B245/S2367
B245/S23678
B245/S12
B245/S128
B245/S127
B245/S1278
B245/S126
B245/S1268
B245/S1267
B245/S12678
B245/S125
B245/S1258
B245/S1257
B245/S12578
B245/S1256
B245/S12568
B245/S12567
B245/S125678
B2458/S257
B2458/S2578
B2458/S256
B2458/S2568
B2458/S2567
B2458/S25678
B2458/S246
B2458/S2468
B2458/S2467
B2458/S24678
B2458/S245
B2458/S2458
B2458/S2457
B2458/S24578
B2458/S2456
B2458/S24568
B2458/S24567
B2458/S245678
B2458/S23
B2458/S238
B2458/S237
B2458/S2378
B2458/S236
B2458/S2368
B2458/S2367
B2458/S23678
B2458/S12
B2458/S128
B2458/S127
B2458/S1278
B2458/S126
B2458/S1268
B2458/S1267
B2458/S12678
B2458/S125
B2458/S1258
B2458/S1257
B2458/S12578
B2458/S1256
B2458/S12568
B2458/S12567
B2458/S125678
B2457/S257
B2457/S2578
B2457/S256
B2457/S2568
B2457/S2567
B2457/S25678
B2457/S245
B2457/S2458
B2457/S2457
B2457/S24578
B2457/S2456
B2457/S24568
B2457/S24567
B2457/S245678
B2457/S23
B2457/S238
B2457/S237
B2457/S2378
B2457/S236
B2457/S2368
B2457/S2367
B2457/S23678
B2457/S12
B2457/S128
B2457/S127
B2457/S1278
B2457/S126
B2457/S1268
B2457/S1267
B2457/S12678
B2457/S125
B2457/S1258
B2457/S1257
B2457/S12578
B2457/S1256
B2457/S12568
B2457/S12567
B2457/S125678
B24578/S257
B24578/S2578
B24578/S256
B24578/S2568
B24578/S2567
B24578/S25678
B24578/S245
B24578/S2458
B24578/S2457
B24578/S24578
B24578/S2456
B24578/S24568
B24578/S24567
B24578/S245678
B24578/S23
B24578/S238
B24578/S237
B24578/S2378
B24578/S236
B24578/S2368
B24578/S2367
B24578/S23678
B24578/S12
B24578/S128
B24578/S127
B24578/S1278
B24578/S126
B24578/S1268
B24578/S1267
B24578/S12678
B24578/S125
B24578/S1258
B24578/S1257
B24578/S12578
B24578/S1256
B24578/S12568
B24578/S12567
B24578/S125678
B2456/S23
B2456/S238
B2456/S237
B2456/S2378
B2456/S236
B2456/S2368
B2456/S2367
B2456/S23678
B2456/S12
B2456/S128
B2456/S127
B2456/S1278
B2456/S126
B2456/S1268
B2456/S1267
B2456/S12678
B2456/S125
B2456/S1258
B2456/S1257
B2456/S12578
B2456/S1256
B2456/S12568
B2456/S12567
B2456/S125678
B24568/S23
B24568/S238
B24568/S237
B24568/S2378
B24568/S236
B24568/S2368
B24568/S2367
B24568/S23678
B24568/S12
B24568/S128
B24568/S127
B24568/S1278
B24568/S126
B24568/S1268
B24568/S1267
B24568/S12678
B24568/S125
B24568/S1258
B24568/S1257
B24568/S12578
B24568/S1256
B24568/S12568
B24568/S12567
B24568/S125678
B24567/S23
B24567/S238
B24567/S237
B24567/S2378
B24567/S236
B24567/S2368
B24567/S2367
B24567/S23678
B24567/S12
B24567/S128
B24567/S127
B24567/S1278
B24567/S126
B24567/S1268
B24567/S1267
B24567/S12678
B24567/S125
B24567/S1258
B24567/S1257
B24567/S12578
B24567/S1256
B24567/S12568
B24567/S12567
B24567/S125678
B245678/S23
B245678/S238
B245678/S237
B245678/S2378
B245678/S236
B245678/S2368
B245678/S2367
B245678/S23678
B245678/S12
B245678/S128
B245678/S127
B245678/S1278
B245678/S126
B245678/S1268
B245678/S1267
B245678/S12678
B245678/S125
B245678/S1258
B245678/S1257
B245678/S12578
B245678/S1256
B245678/S12568
B245678/S12567
B245678/S125678

[amling]

Moderate attempts mainly with proj002 have failed to get anywhere on B25/S157 or B24678/S24 (the most restrictive of that cluster).

Proj002 for B245/245678 (the most permissive of this cluster, I think) with 3x4 blocks stabilizes after 9 steps with these 53 blocks:

Code: Select all

[1,0,0,0]
[1,0,0,1]
[1,0,0,2]
[1,0,0,4]
[1,0,3,1]
[1,0,3,7]
[1,3,0,1]
[1,3,0,2]
[1,3,0,4]
[1,3,6,1]
[1,3,6,2]
[1,3,6,3]
[1,3,6,4]
[1,3,6,5]
[1,3,6,6]
[1,3,6,7]
[1,3,7,0]
[1,3,7,1]
[1,3,7,2]
[1,3,7,3]
[1,3,7,4]
[1,3,7,5]
[1,3,7,6]
[1,3,7,7]
[2,6,0,1]
[2,6,0,2]
[2,6,0,4]
[2,6,3,1]
[2,6,3,2]
[2,6,3,3]
[2,6,3,4]
[2,6,3,5]
[2,6,3,6]
[2,6,3,7]
[2,6,7,0]
[2,6,7,1]
[2,6,7,2]
[2,6,7,3]
[2,6,7,4]
[2,6,7,5]
[2,6,7,6]
[2,6,7,7]
[4,5,0,1]
[4,5,0,2]
[4,5,0,4]
[4,5,7,0]
[4,5,7,1]
[4,5,7,2]
[4,5,7,3]
[4,5,7,4]
[4,5,7,5]
[4,5,7,6]
[4,5,7,7]

I believe this covers these 64 rules from what I had left of the list:

Code: Select all

B245/S257
B245/S2578
B245/S256
B245/S2568
B245/S2567
B245/S25678
B245/S246
B245/S2468
B245/S2467
B245/S24678
B245/S245
B245/S2458
B245/S2457
B245/S24578
B245/S2456
B245/S24568
B245/S24567
B245/S245678
B2458/S257
B2458/S2578
B2458/S256
B2458/S2568
B2458/S2567
B2458/S25678
B2458/S246
B2458/S2468
B2458/S2467
B2458/S24678
B2458/S245
B2458/S2458
B2458/S2457
B2458/S24578
B2458/S2456
B2458/S24568
B2458/S24567
B2458/S245678
B2457/S257
B2457/S2578
B2457/S256
B2457/S2568
B2457/S2567
B2457/S25678
B2457/S245
B2457/S2458
B2457/S2457
B2457/S24578
B2457/S2456
B2457/S24568
B2457/S24567
B2457/S245678
B24578/S257
B24578/S2578
B24578/S256
B24578/S2568
B24578/S2567
B24578/S25678
B24578/S245
B24578/S2458
B24578/S2457
B24578/S24578
B24578/S2456
B24578/S24568
B24578/S24567
B24578/S245678

[amling]

Proj002 for B245/S23678 with 3x4 blocks stabilizes after just a few steps with these 6 blocks:

Code: Select all

[1,0,0,0]
[1,0,0,1]
[1,0,0,2]
[1,3,0,1]
[2,6,0,2]
[4,5,0,4]

This covers these 64 rules:

Code: Select all

B245/S23
B245/S238
B245/S237
B245/S2378
B245/S236
B245/S2368
B245/S2367
B245/S23678
B2458/S23
B2458/S238
B2458/S237
B2458/S2378
B2458/S236
B2458/S2368
B2458/S2367
B2458/S23678
B2457/S23
B2457/S238
B2457/S237
B2457/S2378
B2457/S236
B2457/S2368
B2457/S2367
B2457/S23678
B24578/S23
B24578/S238
B24578/S237
B24578/S2378
B24578/S236
B24578/S2368
B24578/S2367
B24578/S23678
B2456/S23
B2456/S238
B2456/S237
B2456/S2378
B2456/S236
B2456/S2368
B2456/S2367
B2456/S23678
B24568/S23
B24568/S238
B24568/S237
B24568/S2378
B24568/S236
B24568/S2368
B24568/S2367
B24568/S23678
B24567/S23
B24567/S238
B24567/S237
B24567/S2378
B24567/S236
B24567/S2368
B24567/S2367
B24567/S23678
B245678/S23
B245678/S238
B245678/S237
B245678/S2378
B245678/S236
B245678/S2368
B245678/S2367
B245678/S23678

Proj002 for B245/S125678 with 3x4 blocks stabilizes after just a few steps with these 33 blocks:

Code: Select all

[1,0,0,0]
[1,0,0,1]
[1,0,0,2]
[1,0,0,4]
[1,0,3,1]
[1,0,5,4]
[1,3,0,1]
[1,3,0,2]
[1,3,7,1]
[1,3,7,2]
[1,3,7,3]
[1,3,7,4]
[1,3,7,5]
[1,3,7,6]
[1,3,7,7]
[2,6,0,2]
[2,6,0,4]
[2,6,7,1]
[2,6,7,2]
[2,6,7,3]
[2,6,7,4]
[2,6,7,5]
[2,6,7,6]
[2,6,7,7]
[4,5,0,1]
[4,5,0,4]
[4,5,7,1]
[4,5,7,2]
[4,5,7,3]
[4,5,7,4]
[4,5,7,5]
[4,5,7,6]
[4,5,7,7]

This covers these 128 rules:

Code: Select all

B245/S12
B245/S128
B245/S127
B245/S1278
B245/S126
B245/S1268
B245/S1267
B245/S12678
B245/S125
B245/S1258
B245/S1257
B245/S12578
B245/S1256
B245/S12568
B245/S12567
B245/S125678
B2458/S12
B2458/S128
B2458/S127
B2458/S1278
B2458/S126
B2458/S1268
B2458/S1267
B2458/S12678
B2458/S125
B2458/S1258
B2458/S1257
B2458/S12578
B2458/S1256
B2458/S12568
B2458/S12567
B2458/S125678
B2457/S12
B2457/S128
B2457/S127
B2457/S1278
B2457/S126
B2457/S1268
B2457/S1267
B2457/S12678
B2457/S125
B2457/S1258
B2457/S1257
B2457/S12578
B2457/S1256
B2457/S12568
B2457/S12567
B2457/S125678
B24578/S12
B24578/S128
B24578/S127
B24578/S1278
B24578/S126
B24578/S1268
B24578/S1267
B24578/S12678
B24578/S125
B24578/S1258
B24578/S1257
B24578/S12578
B24578/S1256
B24578/S12568
B24578/S12567
B24578/S125678
B2456/S12
B2456/S128
B2456/S127
B2456/S1278
B2456/S126
B2456/S1268
B2456/S1267
B2456/S12678
B2456/S125
B2456/S1258
B2456/S1257
B2456/S12578
B2456/S1256
B2456/S12568
B2456/S12567
B2456/S125678
B24568/S12
B24568/S128
B24568/S127
B24568/S1278
B24568/S126
B24568/S1268
B24568/S1267
B24568/S12678
B24568/S125
B24568/S1258
B24568/S1257
B24568/S12578
B24568/S1256
B24568/S12568
B24568/S12567
B24568/S125678
B24567/S12
B24567/S128
B24567/S127
B24567/S1278
B24567/S126
B24567/S1268
B24567/S1267
B24567/S12678
B24567/S125
B24567/S1258
B24567/S1257
B24567/S12578
B24567/S1256
B24567/S12568
B24567/S12567
B24567/S125678
B245678/S12
B245678/S128
B245678/S127
B245678/S1278
B245678/S126
B245678/S1268
B245678/S1267
B245678/S12678
B245678/S125
B245678/S1258
B245678/S1257
B245678/S12578
B245678/S1256
B245678/S12568
B245678/S12567
B245678/S125678

I believe of the original list this leaves just B25/S157 and that B246(78)/S24(78) cluster.

[LaundryPizza03]

I don't think I can rule out B246/S2478 using proj002 with 3x3 blocks. I found at least 50 blocks in the last run before it reached zero.

Code: Select all

./rlife llsss-recentering-wao p1 --rule 'B246/S2478' '@zero' --wao-left-pad 00 --wao-right-pad 00 --wao-idx ALL --ends proj002:01:03:03:A01.blocks XX

...
20250418 13:58:35 [INFO] Proj002Step depth 1 updating to 3 blocks...
...

[1,0,0]
[1,0,3]
[1,3,0]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A01.blocks' --ends proj002:01:03:03:A02.blocks XX

...
20250418 14:31:31 [INFO] Proj002Step depth 1 updating to 5 blocks...
20250418 14:31:31 [DEBUG] Completed w_pos 3: 7.51 KB, 488.186041ms
...

[1,0,0]
[1,0,3]
[1,3,0]
[1,3,6]
[2,6,0]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A02.blocks' --ends proj002:01:03:03:A03.blocks XX

...
20250418 14:36:50 [INFO] Proj002Step depth 1 updating to 9 blocks...
20250418 14:36:50 [DEBUG] Completed w_pos 3: 8.73 KB, 716.918169ms
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,3,0]
[1,3,6]
[1,5,5]
[2,6,0]
[2,6,5]
[4,5,0]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A03.blocks' --ends proj002:01:03:03:A04.blocks XX

...
20250418 14:36:50 [INFO] Proj002Step depth 1 updating to 9 blocks...
20250418 14:36:50 [DEBUG] Completed w_pos 3: 8.73 KB, 716.918169ms
...
20250418 14:51:55 [INFO] Proj002Step depth 1 updating to 12 blocks...
20250418 14:51:55 [DEBUG] Completed w_pos 3: 11.12 KB, 370.628112ms
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,3,0]
[1,3,3]
[1,3,6]
[1,5,5]
[2,3,3]
[2,6,0]
[2,6,5]
[4,5,0]
[4,5,3]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A04.blocks' --ends proj002:01:03:03:A05.blocks XX

...
20250418 15:00:09 [INFO] Proj002Step depth 1 updating to 15 blocks...
20250418 15:00:09 [DEBUG] Completed w_pos 3: 12.51 KB, 231.352214ms
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,3,0]
[1,3,3]
[1,3,6]
[1,5,5]
[2,3,3]
[2,6,0]
[2,6,3]
[2,6,5]
[2,6,6]
[4,5,0]
[4,5,3]
[4,6,6]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A05.blocks' --ends proj002:01:03:03:A06.blocks XX

...
20250418 15:05:33 [INFO] Proj002Step depth 1 updating to 17 blocks...
20250418 15:05:33 [DEBUG] Completed w_pos 3: 14.37 KB, 213.481341ms
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,3,0]
[1,3,3]
[1,3,6]
[1,5,5]
[2,3,3]
[2,6,0]
[2,6,3]
[2,6,5]
[2,6,6]
[4,5,0]
[4,5,3]
[4,5,5]
[4,5,6]
[4,6,6]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A06.blocks' --ends proj002:01:03:03:A07.blocks XX

...
20250418 15:13:26 [INFO] Proj002Step depth 1 updating to 24 blocks...
20250418 15:13:26 [DEBUG] Completed w_pos 3: 15.73 KB, 257.497577ms
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,3,0]
[1,3,3]
[1,3,5]
[1,3,6]
[1,5,5]
[2,3,0]
[2,3,3]
[2,3,5]
[2,3,6]
[2,5,0]
[2,5,3]
[2,5,5]
[2,6,0]
[2,6,3]
[2,6,5]
[2,6,6]
[4,5,0]
[4,5,3]
[4,5,5]
[4,5,6]
[4,6,6]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A07.blocks' --ends proj002:01:03:03:A08.blocks XX

...
20250418 15:20:08 [INFO] Proj002Step depth 1 updating to 32 blocks...
20250418 15:20:08 [DEBUG] Completed w_pos 3: 19.85 KB, 263.932704ms
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,3,0]
[1,3,3]
[1,3,5]
[1,3,6]
[1,5,3]
[1,5,5]
[1,5,6]
[2,3,0]
[2,3,3]
[2,3,5]
[2,3,6]
[2,5,0]
[2,5,3]
[2,5,5]
[2,6,0]
[2,6,3]
[2,6,5]
[2,6,6]
[4,3,0]
[4,3,3]
[4,3,6]
[4,5,0]
[4,5,3]
[4,5,5]
[4,5,6]
[4,6,0]
[4,6,3]
[4,6,5]
[4,6,6]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A08.blocks' --ends proj002:01:03:03:A09.blocks XX

...
20250418 15:27:01 [INFO] Proj002Step depth 1 updating to 50 blocks...
20250418 15:27:01 [DEBUG] Completed w_pos 3: 24.91 KB, 324.165124ms
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,0,6]
[1,3,0]
[1,3,3]
[1,3,5]
[1,3,6]
[1,5,0]
[1,5,3]
[1,5,5]
[1,5,6]
[1,6,0]
[1,6,5]
[1,6,6]
[2,3,0]
[2,3,3]
[2,3,5]
[2,3,6]
[2,5,0]
[2,5,3]
[2,5,5]
[2,6,0]
[2,6,3]
[2,6,5]
[2,6,6]
[4,0,0]
[4,0,3]
[4,0,5]
[4,0,6]
[4,3,0]
[4,3,3]
[4,3,5]
[4,3,6]
[4,5,0]
[4,5,3]
[4,5,5]
[4,5,6]
[4,6,0]
[4,6,3]
[4,6,5]
[4,6,6]
[7,0,0]
[7,0,3]
[7,0,5]
[7,0,6]
[7,5,0]
[7,5,3]
[7,5,5]
[7,6,0]

./rlife llsss-recentering p1 --rule 'B246/S2478' '@proj002:03:A09.blocks' --ends proj002:01:03:03:A10.blocks XX

...
20250418 15:34:27 [INFO] Proj002Step depth 1 found zero bottom!
thread 'main' panicked at src/llsss/proj/proj002.rs:123:29:
explicit panic
note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace

EDIT: This also happened B25/S157 with 4x3 blocks; maybe 3x4 blocks will work, though.

Code: Select all

./rlife llsss-recentering-wao p1 --rule 'B25/S157' '@zero' --wao-left-pad 00 --wao-right-pad 00 --wao-idx ALL --ends proj002:01:04:03:A01.blocks XX

...
20250418 15:38:25 [INFO] Proj002Step depth 1 updating to 4 blocks...
20250418 15:38:25 [DEBUG] Completed w_pos 4: 840 B [+56.10%], 340.041758ms [+130.95%]
...

[1,0,0]
[1,0,3]
[1,0,5]
[2,1,1]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A01.blocks' --ends proj002:01:04:03:A02.blocks XX

...
20250418 15:44:19 [INFO] Proj002Step depth 1 updating to 6 blocks...
20250418 15:44:19 [DEBUG] Completed w_pos 4: 28.72 KB, 312.576388ms
...
20250418 15:44:21 [INFO] Proj002Step depth 1 updating to 5 blocks...
20250418 15:44:21 [DEBUG] Completed w_pos 6: 235.53 KB [+96.42%], 806.866073ms [+6.97%]
...

[1,0,0]
[1,0,3]
[1,0,5]
[2,1,1]
[2,1,11]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A02.blocks' --ends proj002:01:04:03:A03.blocks XX

...
20250418 15:49:00 [INFO] Proj002Step depth 1 updating to 8 blocks...
20250418 15:49:00 [DEBUG] Completed w_pos 4: 29.07 KB, 318.080773ms
...
20250418 15:49:01 [INFO] Proj002Step depth 1 updating to 7 blocks...
20250418 15:49:01 [DEBUG] Completed w_pos 5: 82.80 KB [+96.06%], 893.699733ms [+95.00%]
...
20250418 15:49:02 [INFO] Proj002Step depth 1 updating to 6 blocks...
20250418 15:49:02 [DEBUG] Completed w_pos 6: 236.59 KB [+96.30%], 815.356098ms [-9.17%]
...

[1,0,0]
[1,0,3]
[1,0,5]
[2,1,1]
[2,1,11]
[4,3,7]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A03.blocks' --ends proj002:01:04:03:A04.blocks XX

...
20250418 15:53:56 [INFO] Proj002Step depth 1 updating to 13 blocks...
20250418 15:53:56 [DEBUG] Completed w_pos 4: 29.46 KB, 315.231355ms
...
20250418 15:53:57 [INFO] Proj002Step depth 1 updating to 12 blocks...
20250418 15:53:57 [DEBUG] Completed w_pos 5: 83.60 KB [+95.77%], 853.853865ms [+92.14%]
...
20250418 15:53:58 [INFO] Proj002Step depth 1 updating to 11 blocks...
20250418 15:53:58 [DEBUG] Completed w_pos 6: 238.02 KB [+96.03%], 849.986359ms [-0.45%]
...
20250418 15:53:59 [INFO] Proj002Step depth 1 updating to 10 blocks...
20250418 15:53:59 [DEBUG] Completed w_pos 7: 674.36 KB [+95.65%], 1.650491171s [+64.03%]

[1,0,0]
[1,0,3]
[1,0,5]
[1,0,8]
[2,1,1]
[2,1,11]
[4,3,7]
[8,7,15]
[9,6,15]
[9,7,14]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A04.blocks' --ends proj002:01:04:03:A05.blocks XX

...
20250418 15:58:01 [INFO] Proj002Step depth 1 updating to 22 blocks...
20250418 15:58:01 [DEBUG] Completed w_pos 4: 31.50 KB, 504.333584ms
...
20250418 15:58:02 [INFO] Proj002Step depth 1 updating to 21 blocks...
20250418 15:58:02 [DEBUG] Completed w_pos 5: 86.62 KB [+93.33%], 705.482175ms [+33.25%]
...
20250418 15:58:02 [INFO] Proj002Step depth 1 updating to 20 blocks...
20250418 15:58:02 [DEBUG] Completed w_pos 6: 242.89 KB [+94.85%], 825.945977ms [+15.73%]
...
20250418 15:58:03 [INFO] Proj002Step depth 1 updating to 19 blocks...
20250418 15:58:03 [DEBUG] Completed w_pos 7: 683.49 KB [+95.12%], 749.662466ms [-9.68%]

[1,0,0]
[1,0,3]
[1,0,5]
[1,0,8]
[1,0,15]
[1,3,15]
[1,14,15]
[1,15,14]
[2,1,1]
[2,1,11]
[2,12,14]
[4,3,7]
[8,7,15]
[9,6,15]
[9,7,14]
[15,15,0]
[15,15,6]
[15,15,11]
[15,15,13]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A05.blocks' --ends proj002:01:04:03:A06.blocks XX

...
20250418 16:06:38 [INFO] Proj002Step depth 1 updating to 27 blocks...
20250418 16:06:38 [DEBUG] Completed w_pos 4: 36.66 KB, 594.065226ms
...
20250418 16:06:39 [INFO] Proj002Step depth 1 updating to 25 blocks...
20250418 16:06:39 [DEBUG] Completed w_pos 5: 94.26 KB [+87.98%], 523.78185ms [-12.57%]
...
20250418 16:06:39 [INFO] Proj002Step depth 1 updating to 24 blocks...
20250418 16:06:39 [DEBUG] Completed w_pos 6: 256.45 KB [+92.50%], 861.106313ms [+48.72%]
...
20250418 16:06:40 [INFO] Proj002Step depth 1 updating to 23 blocks...
20250418 16:06:40 [DEBUG] Completed w_pos 7: 707.97 KB [+93.63%], 962.110661ms [+11.08%]
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,0,8]
[1,0,15]
[1,3,7]
[1,3,15]
[1,5,8]
[1,14,15]
[1,15,14]
[2,1,1]
[2,1,11]
[2,1,14]
[2,12,14]
[4,3,7]
[4,8,13]
[8,7,15]
[9,6,15]
[9,7,14]
[15,15,0]
[15,15,6]
[15,15,11]
[15,15,13]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A06.blocks' --ends proj002:01:04:03:A07.blocks XX

...
20250418 16:11:35 [INFO] Proj002Step depth 1 updating to 30 blocks...
20250418 16:11:35 [DEBUG] Completed w_pos 4: 37.54 KB, 326.808454ms
...
20250418 16:11:36 [INFO] Proj002Step depth 1 updating to 28 blocks...
20250418 16:11:36 [DEBUG] Completed w_pos 5: 96.40 KB [+87.89%], 822.823876ms [+86.29%]
...
20250418 16:11:36 [INFO] Proj002Step depth 1 updating to 27 blocks...
20250418 16:11:36 [DEBUG] Completed w_pos 6: 260.67 KB [+92.01%], 842.395094ms [+2.35%]
...
20250418 16:11:38 [INFO] Proj002Step depth 1 updating to 26 blocks...
20250418 16:11:38 [DEBUG] Completed w_pos 7: 717.84 KB [+93.44%], 1.03186348s [+20.22%]
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,0,8]
[1,0,15]
[1,3,7]
[1,3,15]
[1,5,8]
[1,8,0]
[1,14,15]
[1,15,14]
[2,1,1]
[2,1,11]
[2,1,14]
[2,10,0]
[2,12,14]
[4,3,7]
[4,8,13]
[8,0,10]
[8,7,15]
[9,6,15]
[9,7,14]
[15,15,0]
[15,15,6]
[15,15,11]
[15,15,13]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A07.blocks' --ends proj002:01:04:03:A08.blocks XX

...
20250418 16:21:05 [INFO] Proj002Step depth 1 updating to 37 blocks...
20250418 16:21:05 [DEBUG] Completed w_pos 4: 39.98 KB, 247.537135ms
...
20250418 16:21:06 [INFO] Proj002Step depth 1 updating to 35 blocks...
20250418 16:21:06 [DEBUG] Completed w_pos 5: 100.88 KB [+86.47%], 639.727325ms [+88.40%]
...
20250418 16:21:06 [INFO] Proj002Step depth 1 updating to 34 blocks...
20250418 16:21:06 [DEBUG] Completed w_pos 6: 270.81 KB [+91.44%], 804.339793ms [+22.80%]
...
20250418 16:21:07 [INFO] Proj002Step depth 1 updating to 33 blocks...
20250418 16:21:07 [DEBUG] Completed w_pos 7: 736.71 KB [+92.48%], 1.029099327s [+24.52%]
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,0,8]
[1,0,15]
[1,3,7]
[1,3,15]
[1,5,4]
[1,5,8]
[1,8,0]
[1,14,15]
[1,15,14]
[2,1,1]
[2,1,11]
[2,1,14]
[2,10,0]
[2,12,14]
[4,3,7]
[4,5,0]
[4,5,1]
[4,8,5]
[4,8,7]
[4,8,8]
[4,8,11]
[4,8,13]
[8,0,10]
[8,7,15]
[9,6,15]
[9,7,14]
[15,15,0]
[15,15,6]
[15,15,11]
[15,15,13]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A08.blocks' --ends proj002:01:04:03:A09.blocks XX

...
20250418 16:25:32 [INFO] Proj002Step depth 1 updating to 50 blocks...
20250418 16:25:32 [DEBUG] Completed w_pos 4: 43.25 KB, 511.182767ms
...
20250418 16:25:33 [INFO] Proj002Step depth 1 updating to 48 blocks...
20250418 16:25:33 [DEBUG] Completed w_pos 5: 109.34 KB [+86.62%], 896.524025ms [+54.75%]
...
20250418 16:25:33 [INFO] Proj002Step depth 1 updating to 47 blocks...
20250418 16:25:33 [DEBUG] Completed w_pos 6: 285.95 KB [+89.36%], 686.692315ms [-26.51%]
...
20250418 16:25:34 [INFO] Proj002Step depth 1 updating to 46 blocks...
20250418 16:25:34 [DEBUG] Completed w_pos 7: 766.08 KB [+91.28%], 879.472492ms [+24.62%]
...

[1,0,0]
[1,0,3]
[1,0,5]
[1,0,8]
[1,0,15]
[1,3,7]
[1,3,15]
[1,5,4]
[1,5,8]
[1,8,0]
[1,8,11]
[1,14,15]
[1,15,14]
[2,1,1]
[2,1,11]
[2,1,14]
[2,10,0]
[2,10,8]
[2,12,14]
[4,3,7]
[4,5,0]
[4,5,1]
[4,8,5]
[4,8,7]
[4,8,8]
[4,8,11]
[4,8,13]
[8,0,0]
[8,0,1]
[8,0,10]
[8,0,15]
[8,1,0]
[8,1,14]
[8,1,15]
[8,7,15]
[8,10,1]
[8,10,2]
[9,0,0]
[9,0,6]
[9,0,15]
[9,6,15]
[9,7,14]
[15,15,0]
[15,15,6]
[15,15,11]
[15,15,13]

./rlife llsss-recentering p1 --rule 'B25/S157' '@proj002:04:A09.blocks' --ends proj002:01:04:03:A10.blocks XX

...
20250418 16:31:23 [INFO] Proj002Step depth 1 found zero bottom!
thread 'main' panicked at src/llsss/proj/proj002.rs:123:29:
explicit panic
note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace

[amling]

I don't think I can rule out B246/S2478 using proj002 with 3x3 blocks.

I was mostly trying against B24678/S24 which is more restrictive (and thus more likely to be possible to rule out). I have run 3x10 and 4x8 although in both cases I was not pushing super aggressively on waiting for updates and I did not actually wait for both to find a zero bottom but rather saw something in the intermediate output that convinced me they would almost certainly eventually. It is of course possible that more patience on waiting for more updates at each step (like running until memory fills and the search dies) could still work out but I'm skeptical given the various complex parts of still lives I've seen on the way and its (proj002's) limited ability to only trace a fixed depth in from one side.

[LuveelVoom]

Is there any hope of this project being finished? Only 17 rules remain, and it would be quite nice for the OCA community to wrap up the whole OT still-life existence question.

To say something productive, here's an infinite still life in B25/S157:

Code: Select all

x = 19, y = 38, rule = B25/S157
2bo2bo7bo2bo$3b2o9b2o$ob4obo3bob4obo$b6o5b6o$b3obob5obob3o$b2o2b9o2b2o
$b8ob8o$b3obob5obob3o$b2o2b9o2b2o$b8ob8o$b3obob5obob3o$b2o2b9o2b2o$b8o
b8o$b3obob5obob3o$b2o2b9o2b2o$b8ob8o$b3obob5obob3o$b2o2b9o2b2o$b8ob8o
$b3obob5obob3o$b2o2b9o2b2o$b8ob8o$b3obob5obob3o$b2o2b9o2b2o$b8ob8o$b3o
bob5obob3o$b2o2b9o2b2o$b8ob8o$b3obob5obob3o$b2o2b9o2b2o$b8ob8o$b3obob
5obob3o$b2o2b9o2b2o$b8ob8o$b3obob5obob3o$b2o2b9o2b2o$b8ob8o$b3obob5ob
ob3o!