Macbi wrote:We've exhaustively explored 6x6 starting configurations on an infinite grid, so doing all 6x6 tori should be possible. In fact I suspect 8x8 is also in reach because there are two factors that cut down on the search time... I suspect that you'll reach the limit some time before 16x16 will be though.
F_rank wrote:I'd like to get into contact with CGoL fans exploring (or having explored) tori like e.g. 8x8, or 16x16, or ...
I wonder whether an 8 x 8 B3/S23 torus can be or has been fully (exhaustively) explored (2^64 is a pretty large number for a brute-force approach, even if discounting all symmetries). If somebody can point me to software particularly suited for torus exploration (incl. oscillator detection), I would be very grateful.
Yes, you are probably right. But 7x7 is definitely within reach.dvgrn wrote:Macbi wrote:We've exhaustively explored 6x6 starting configurations on an infinite grid, so doing all 6x6 tori should be possible. In fact I suspect 8x8 is also in reach because there are two factors that cut down on the search time... I suspect that you'll reach the limit some time before 16x16 will be though.
Yikes. I think the jump from 6x6 to 8x8 is an awfully big one. If 8x8 is possible, then someone should prove it by doing an exhaustive search on 7x7, which is 2^15 times easier than 8x8... and about eight thousand (2^13) times harder than 6x6, which is as big as we've gone so far.
Macbi wrote:Do you know what the average stabilisation time is for 6x6 soups on an unbounded grid is?
Macbi wrote:Also, since 7x7 and 8x8 tori contain less than 64 cells we can probably do some intricate bit-twiddling to compute each generation a bit faster.
That should get us up to 7x7. To get up to 8x8 I think we would have to do something cleverer than brute force, like perhaps keeping a hash table of some of the generations previously visited.
calcyman wrote:These are square tori, so you can modulo out by translations and rotations...
calcyman wrote:In the 8x8 case, you have just over 2 ** 55 soups, and I fall into Dave's pessimistic camp with regards to that -- it's possible, but might just require four acres of Crays to accomplish in a sensible amount of time.
torus size #cells #states #canonical
1 1 2 2
2 4 16 6
3 9 512 26
4 16 65,536 805
5 25 33,554,432 172,112
6 36 68,719,476,736 ???
Majestas32 wrote:Also for 7x7 it's possible to omit Tori that are found by the evolution of other tori
For circular strings there's an algorithm for generating only the canonical forms: https://en.wikipedia.org/wiki/Lyndon_word. Perhaps this could be adapted to the toroidal case (forgetting about the reflections)? Alternatively we could look at tori which wrap with an offset of 1, so that all the cells are in one long spiral path.dvgrn wrote:The same might even be true of rotations/reflections/translations, unless there's a really quick way of enumerating only the unique 7x7 tori.
Torus Size: 2x2
# of cells: 4
# of states (raw): 16
# of states (canonical): 6
Start torus: 0
Finish torus: 15
[Start] 2018-05-10 16:36:48.478
[Finish] 2018-05-10 16:36:48.479
### ALL PATTERNS analysis: ###
Patterns analyzed:16
Generations analyzed: 11
Canonical patterns found: 6
ashPixCount|0:12|2:4|Total:16
ashPeriodCount|1:16|Total:16
ashGenCount|0:5|1:11|Total:16
Mean # of generations to 'ash': 0.6875
### CANONICAL ONLY analysis: ###
Patterns analyzed:6
Generations analyzed: 4
ashPixCount|0:5|2:1|Total:6
ashPeriodCount|1:6|Total:6
ashGenCount|0:2|1:4|Total:6
Mean # of generations to 'ash': 0.666667
Canonical Ash Patterns (CAP, n=2):
(0|p:1)
00
00
(1|p:1)
10
10
Torus Size: 3x3
# of cells: 9
# of states (raw): 512
# of states (canonical): 26
Start torus: 0
Finish torus: 511
[Start] 2018-05-10 17:31:27.191
[Finish] 2018-05-10 17:31:27.195
### ALL PATTERNS analysis: ###
Patterns analyzed:512
Generations analyzed: 469
Canonical patterns found: 26
ashPixCount|0:386|4:126|Total:512
ashPeriodCount|1:512|Total:512
ashGenCount|0:127|1:301|2:84|Total:512
Mean # of generations to 'ash': 0.916016
### CANONICAL ONLY analysis: ###
Patterns analyzed:26
Generations analyzed: 24
ashPixCount|0:21|4:5|Total:26
ashPeriodCount|1:26|Total:26
ashGenCount|0:6|1:16|2:4|Total:26
Mean # of generations to 'ash': 0.923077
Canonical Ash Patterns (CAP, n=6):
(#0|px:0|period:1)
000
000
000
(#1|px:4|period:1)
010
110
010
(#2|px:4|period:1)
000
110
110
(#3|px:4|period:1)
010
110
100
(#4|px:4|period:1)
010
101
010
(#5|px:4|period:1)
010
011
100
Torus Size: 4x4
# of cells: 16
# of states (raw): 65536
# of states (canonical): 805
Start torus: 0
Finish torus: 65535
[Start] 2018-05-10 16:43:34.346
[Finish] 2018-05-10 16:43:35.105
### ALL PATTERNS analysis: ###
Patterns analyzed:65536
Generations analyzed: 228315
Canonical patterns found: 805
ashPixCount|0:49116|3:1696|4:7464|5:4736|6:320|7:384|8:1820|Total:65536
ashPeriodCount|1:56328|2:3896|4:64|8:5248|Total:65536
ashGenCount|0:53|1:10587|2:17424|3:15168|4:8320|5:2912|6:2816|7:2880|8:1536|9:1280|10:640|11:896|12:896|13:128|Total:65536
Mean # of generations to 'ash': 3.48381
### CANONICAL ONLY analysis: ###
Patterns analyzed:805
Generations analyzed: 2434
ashPixCount|0:617|3:14|4:91|5:40|6:3|7:3|8:37|Total:805
ashPeriodCount|1:714|2:46|4:1|8:44|Total:805
ashGenCount|0:6|1:177|2:227|3:179|4:92|5:31|6:25|7:25|8:13|9:10|10:5|11:7|12:7|13:1|Total:805
Mean # of generations to 'ash': 3.0236
Canonical Ash Patterns (CAP, n=23):
(#0|px:0|period:1)
0000
0000
0000
0000
(#1|px:3|period:2)
0000
0010
0010
0010
(#2|px:4|period:1)
0000
0110
0110
0000
(#3|px:4|period:2)
0100
0000
0011
0100
(#4|px:8|period:2)
0110
0110
0110
0110
(#5|px:6|period:4)
0010
0110
0110
0010
(#6|px:5|period:8)
0000
0110
0010
0110
(#7|px:4|period:1)
0010
0000
0010
0101
(#8|px:4|period:1)
0010
0001
1000
0100
(#9|px:5|period:8)
0101
0101
0010
0000
(#10|px:8|period:1)
0101
0101
0101
0101
(#11|px:4|period:8)
0010
1100
0010
0000
(#12|px:5|period:8)
0010
1110
0010
0000
(#13|px:5|period:8)
0000
1010
0010
0110
(#14|px:5|period:2)
0010
1010
1000
0100
(#15|px:6|period:8)
0010
1000
1010
0110
(#16|px:7|period:8)
0110
1100
1010
0100
(#17|px:7|period:8)
0010
1110
0110
1000
(#18|px:8|period:2)
0011
1001
0011
1001
(#19|px:4|period:2)
0100
0001
1000
0010
(#20|px:7|period:2)
0100
0111
1010
0010
(#21|px:8|period:2)
0100
0111
1110
0010
(#22|px:8|period:1)
0110
1001
0110
1001
x = 12, y = 11, rule = B3/S23:T12,12
3bo3bo3bo$bo3bo3bo$2ob3ob3obo2$3bo3bo3bo$bo3bo3bo$2ob3ob3obo2$3bo3bo3b
o$bo3bo3bo$2ob3ob3obo!
x = 11, y = 10, rule = B3/S23:T12,12
obobobobobo$3ob3ob3o3$obobobobobo$3ob3ob3o3$obobobobobo$3ob3ob3o!
Torus Size: 5x5
# of cells: 25
# of states (raw): 33554432
# of states (canonical): 172112
Start torus: 0
Finish torus: 33554431
[Start] 2018-05-10 17:01:18.401
[Finish] 2018-05-10 17:05:30.620
### ALL PATTERNS analysis: ###
Patterns analyzed:33554432
Generations analyzed: 274631706
Canonical patterns found: 172112
ashPixCount|0:23487902|3:1324600|4:2385825|5:520110|6:3680900|7:11300|8:1338400|9:9500|10:86970|11:108700|12:600025|13:200|Total:33554432
ashPeriodCount|1:31115032|2:1491800|3:5600|4:733400|5:7300|10:30500|20:170800|Total:33554432
ashGenCount|0:3456|1:1135056|2:5484445|3:4038370|4:2280835|5:2164860|6:2242160|7:1990300|8:1749600|9:1677550|10:1444600|11:1402400|12:1035400|13:880100|14:780500|15:688300|16:586900|17:502600|18:477200|19:385700|20:410100|21:407000|22:269500|23:220300|24:181600|25:165200|26:126000|27:146800|28:142000|29:115200|30:91600|31:57800|32:48400|33:40400|34:32800|35:22400|36:27000|37:20400|38:26800|39:11000|40:7600|41:4400|42:3800|43:3000|44:2400|45:2000|46:2400|47:5600|48:6200|49:2400|50:1600|51:400|Total:33554432
Mean # of generations to 'ash': 8.18466
### CANONICAL ONLY analysis: ###
Patterns analyzed:172112
Generations analyzed: 1391774
ashPixCount|0:120630|3:6690|4:12249|5:2634|6:18885|7:60|8:6859|9:48|10:445|11:557|12:3053|13:2|Total:172112
ashPeriodCount|1:159754|2:7552|3:28|4:3723|5:40|10:161|20:854|Total:172112
ashGenCount|0:33|1:6289|2:28519|3:20853|4:11799|5:11183|6:11498|7:10186|8:8936|9:8544|10:7333|11:7089|12:5203|13:4416|14:3927|15:3456|16:2955|17:2526|18:2400|19:1938|20:2056|21:2037|22:1348|23:1102|24:908|25:826|26:630|27:734|28:710|29:576|30:458|31:289|32:242|33:202|34:164|35:112|36:135|37:102|38:134|39:55|40:38|41:22|42:19|43:15|44:12|45:10|46:12|47:28|48:31|49:12|50:8|51:2|Total:172112
Mean # of generations to 'ash': 8.08644
x = 15, y = 14, rule = B3/S23:T15,15
2ob4ob4ob2o$bobo2bobo2bobo$2ob4ob4ob2o$bobo2bobo2bobo2$2ob4ob4ob2o$bob
o2bobo2bobo$2ob4ob4ob2o$bobo2bobo2bobo2$2ob4ob4ob2o$bobo2bobo2bobo$2ob
4ob4ob2o$bobo2bobo2bobo!
x = 15, y = 13, rule = B3/S23:T15,15
3bo4bo4bo$2obob2obob2obo$15o3$3bo4bo4bo$2obob2obob2obo$15o3$3bo4bo4bo$
2obob2obob2obo$15o!
x = 14, y = 15, rule = B3/S23:T15,15
obo2bobo2bobo$2obob2obob2obo2$o4bo4bo$b2o3b2o3b2o$obo2bobo2bobo$2obob
2obob2obo2$o4bo4bo$b2o3b2o3b2o$obo2bobo2bobo$2obob2obob2obo2$o4bo4bo$b
2o3b2o3b2o!
Majestas32 wrote:These are c/2, c/2, c diagonal agar's. Hmm
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