Thanks for the results and detailed explanations. I also began considering minimal single-phase widths, and I worked through the "easy" speeds with WLS and JLS as reported in this post. However, the c/5 orthogonal searches were taking too long, so I decided to try them using LLSSS. I think I set up the asymmetric search correctly, but please let me know if I made a mistake.
Specifically, There are known period-5 c/5 orthogonal spaceship with a single-phase width of 10, such as this one by Josh Ball which is the shortest known with this property:
Code: Select all
#C Single-phase width-10 (1,0)c/5 spaceship
#C By Josh Ball, 13 Oct 2013
x = 10, y = 38, rule = B3/S23
5bobo$3b2o2b2o$3b2o2bo$3b2o2bobo$4b2o3bo$3b5obo$2b4obo$2bobo2b3o$4bobo
bo$4bo2b2o$5bo$2o3bo2bo$2o5bo$2o3bob2o$3bob4o$3b2o$4bo$4bo4bo$3b2obob
2o$4bo$6bobo$2b2o3bo$bo2bo$2bo$5bo$4b2ob2o$b2o4b2o$b2o4b3o$7bo$2bo$bob
o$3bo$bo$b5o$4b2o$3bo$4b3o$5b2o!I figured that for a front-to-back search I would need five different searches corresponding to which phase was restricted to width 9. For this I used the following constraint files:
Code: Select all
$ cat c5o_w9_1.cstr
| ......WWWWWWWWW...... | .....WWWWWWWWWWW..... | ....WWWWWWWWWWWWW.... | ...WWWWWWWWWWWWWWW... | ..WWWWWWWWWWWWWWWWW.. |
$ cat c5o_w9_2.cstr
| ..WWWWWWWWWWWWWWWWW.. | ......WWWWWWWWW...... | .....WWWWWWWWWWW..... | ....WWWWWWWWWWWWW.... | ...WWWWWWWWWWWWWWW... |
$ cat c5o_w9_3.cstr
| ...WWWWWWWWWWWWWWW... | ..WWWWWWWWWWWWWWWWW.. | ......WWWWWWWWW...... | .....WWWWWWWWWWW..... | ....WWWWWWWWWWWWW.... |
$ cat c5o_w9_4.cstr
| ....WWWWWWWWWWWWW.... | ...WWWWWWWWWWWWWWW... | ..WWWWWWWWWWWWWWWWW.. | ......WWWWWWWWW...... | .....WWWWWWWWWWW..... |
$ cat c5o_w9_5.cstr
| .....WWWWWWWWWWW..... | ....WWWWWWWWWWWWW.... | ...WWWWWWWWWWWWWWW... | ..WWWWWWWWWWWWWWWWW.. | ......WWWWWWWWW...... |
Code: Select all
./rlife llsss c5-f2b @bg:21 --constraint grid_loop:c5o_w9_N.cstr --filters bcafCode: Select all
x = 121, y = 78, rule = LifeHistory
F.21B.F.21B.F.21B.F.21B.F.21B.F$F.21B.F.21B.F.21B.F.21B.F.21B.F$F.10B
A10B.F.8BAB2A9B.F.7B2AB2A9B.F.7B2AB2A9B.F.7BAB3A9B.F$F.7B5A9B.F.7B2AB
2A9B.F.7B2ABABA8B.F.6BA3BABA8B.F.6BABABABA8B.F$F.6BABA3BA8B.F.6BA5BA
8B.F.6BABABABA8B.F.6BABABABA8B.F.6BABABABA8B.F$F.6BABABABA8B.F.6BABAB
ABA8B.F.7BA3BA9B.F.7B2AB2A9B.F.7B2AB2A9B.F$F.7B2AB2A9B.F.21B.F.8BABA
10B.F.21B.F.21B.F$F.8B3A10B.F.7B2AB2A9B.F.21B.F.21B.F.9BA11B.F$F.21B.
F.21B.F.11BA9B.F.8B3A10B.F.7BA2BA10B.F$F.8B3A10B.F.7B4A10B.F.7B4A10B.
F.7B3A2BA8B.F.7BA2BA10B.F$F.6B2ABA11B.F.6BA3BA2BA7B.F.6BA3B2ABA7B.F.
6BA14B.F.7B2A4BA7B.F$F.7B2A3B3A6B.F.6B3A3BABA6B.F.6BABAB2ABA7B.F.13B
2A6B.F.12B3A6B.F$F.12B3A6B.F.8B3A10B.F.8BABABABA6B.F.7BA4B2A7B.F.10BA
10B.F$F.9B3ABA7B.F.10B2AB2A6B.F.10B2A9B.F.9B5A7B.F.9B2A10B.F$F.11BA9B
.F.21B.F.13BA7B.F.10BABA8B.F.9B2A10B.F$F.9B3A9B.F.10B3A8B.F.10BABA8B.
F.12B2A7B.F.12B2A7B.F$F.13BA7B.F.11B2A8B.F.13BA7B.F.10BA2BA7B.F.14BA
6B.F$F.11BA2BA6B.F.10B2A2BA6B.F.10B4A7B.F.11B3A7B.F.10B2ABA7B.F$F.10B
5A6B.F.14BA6B.F.21B.F.9BA2BA8B.F.10BA2BA7B.F$F.10B3A8B.F.21B.F.9B2A
10B.F.8BA2BA9B.F.8B2A11B.F$F.8B2A11B.F.8B4A9B.F.8B4A9B.F.8BA12B.F.7BA
13B.F$F.7BA13B.F.7BA2BA10B.F.7BA2B2A9B.F.6BA4BA9B.F.7BAB3A9B.F$F.8B2A
BA9B.F.7B2A12B.F.6B3A12B.F.6BA2B2ABA8B.F.10B2A9B.F$F.7BA4BA8B.F.7BA3B
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6B.F.6B3A2B2A8B.F.7BA13B.F$F.6B2AB2AB2A7B.F.6B2A4B3A6B.F.12BABA6B.F.
14B2A5B.F.7BA3B2AB2A5B.F$F.11B2AB2A5B.F.10BA3BA6B.F.14BA6B.F.12BABA6B
.F.11B2AB2A5B.F$F.12BA8B.F.21B.F.12B2A7B.F.10BAB2A7B.F.9B2A3BA6B.F$F.
9B4AB2A5B.F.8B6A7B.F.9B4A8B.F.9B5A7B.F.9BA3BA7B.F$F.8B2A11B.F.21B.F.
9BA11B.F.9BABA9B.F.9BA11B.F$F.8B3A10B.F.11BA9B.F.21B.F.10B2A9B.F.9BA
2BA8B.F$F.9B3A9B.F.21B.F.10B3A8B.F.10BABA8B.F.10BABA8B.F$F.9BAB3A7B.F
.9BAB2A8B.F.11B2A8B.F.8B2A3BA7B.F.8BA4BA7B.F$F.21B.F.8BA3BA8B.F.7B3AB
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A6B.F$F.8BA12B.F.7B3A4BA6B.F.10BA2B2A6B.F.11B4A6B.F.9BA4BA6B.F$F.9BA
3B3A5B.F.8B3A2B2A6B.F.11B2ABA6B.F.11B2ABA6B.F.10BA3BA6B.F$F.9B2A2BA7B
.F.8B3AB2A7B.F.21B.F.11BA9B.F.10B3A8B.F$F.9BA2BA8B.F.9B2AB2A7B.F.8BAB
A10B.F.10BA10B.F.10B2A9B.F$F.13BA7B.F.12B3A6B.F.9B2A3BA6B.F.10BA2BA7B
.F.11BAB2A6B.F$F.9BA3BABA5B.F.10BABABA6B.F.10BABABA6B.F.12BAB2A5B.F.
9B3AB3A5B.F$F.9BABA9B.F.8B3A2BA7B.F.8BAB5A6B.F.9B2A4BA5B.F.9B2A3B2A5B
.F$F.8BA3B2ABA5B.F.8BA4BA7B.F.11BAB2A6B.F.9BA11B.F.9BABA9B.F$F.8B2AB
2A8B.F.7B3AB3A7B.F.7BA2B2ABA7B.F.10B2ABA7B.F.8BA2B2A8B.F$F.8BA12B.F.
8BABABA8B.F.7BA5BA7B.F.7B2AB2A9B.F.7BA3B2A8B.F$F.10BABA8B.F.9BABA9B.F
.8BA2BA9B.F.7B3A11B.F.10BA10B.F$F.10BA10B.F.9B2A10B.F.8B2A11B.F.8BA
12B.F.10BA10B.F$F.10B2A9B.F.9BA11B.F.9B2A10B.F.8B3A10B.F.8BABA10B.F$F
.10B2A9B.F.12BA8B.F.21B.F.9BA11B.F.8BA2BA9B.F$F.11BA9B.F.9BA2BA8B.F.
10B3A8B.F.10B2A9B.F.10B2A9B.F$F.9B3A9B.F.9BABA9B.F.8B3A10B.F.8BABA10B
.F.10BA10B.F$F.9BA11B.F.8BA12B.F.8BA12B.F.10BA10B.F.10B2A9B.F$F.9B3A
9B.F.8B2ABA9B.F.7B3A2BA8B.F.9BA2BA8B.F.9BA2BA8B.F$F.9BA2BA8B.F.8BA3B
2A7B.F.7B2A2BABA7B.F.10B3A8B.F.10B3A8B.F$F.9B2AB2A7B.F.8BA3B2A7B.F.8B
ABA10B.F.13B2A6B.F.10BA3BA6B.F$F.9B2A10B.F.9B3AB2A6B.F.8B4AB2A6B.F.7B
2A2BAB2A6B.F.7B2A6BA5B.F$F.14B2A5B.F.8BA12B.F.8BA2BAB2A6B.F.8BA2BAB2A
6B.F.11BA2BA6B.F$F.7B2AB3A8B.F.9B2A3BA6B.F.9BA11B.F.8B3ABA8B.F.7BA2B
3A8B.F$F.10B4A7B.F.13BA7B.F.9BA3B2A6B.F.8B2A3B2A6B.F.7BA5BA7B.F$F.7B
3A3BA7B.F.8BA5BA6B.F.9B2ABABA6B.F.8BA2B2A8B.F.8BAB3A8B.F$F.9B5A7B.F.
9B3AB2A6B.F.9B2A2B3A5B.F.9BA2BA8B.F.10BA2BA7B.F$F.13BA7B.F.14BA6B.F.
11BA2B2A5B.F.11B2A8B.F.10B3A8B.F$F.9B2AB2A7B.F.9B2A3BA6B.F.9B3A2BA6B.
F.9BA2BABA6B.F.10BABA8B.F$F.10BAB2A7B.F.9B2AB2A7B.F.9B2ABABA6B.F.9BA
2BA8B.F.13BA7B.F$F.21B.F.12BABA6B.F.11B2A8B.F.21B.F.21B.F$F.13B2A6B.F
.21B.F.11BABA7B.F.13BA7B.F.9BA3B2A6B.F$F.8B2A11B.F.8BABABA8B.F.9B2AB
2A7B.F.8B3A2B2A6B.F.8B2A11B.F$F.8B3AB3A6B.F.7BA2B4A7B.F.7B2ABA2BA7B.F
.8BA3B3A6B.F.7BA3B2A2BA5B.F$F.7BA4BA8B.F.8BABABA8B.F.9B2A3BA6B.F.8B3A
2B2A6B.F.8BAB3A8B.F$F.10BA2B2A6B.F.12B3A6B.F.14BA6B.F.10BA3B2A5B.F.
13BABA5B.F$F.13BA7B.F.11BABA7B.F.11BAB2A6B.F.10B2A3BA5B.F.9B3ABABA5B.
F$F.8B4ABABA5B.F.8BA2BA9B.F.10B2AB2A6B.F.9BA3B2A6B.F.8B2A2BABA6B.F$F.
8B2AB4A6B.F.11BAB2A6B.F.8BAB2A9B.F.7BAB3A9B.F.7BA13B.F$F.6B2A13B.F.6B
3A2BA9B.F.6B2A5B2A6B.F.6BAB2A11B.F.6B2A3BA9B.F$F.5BA6BA8B.F.6BA6BA7B.
F.6BABA12B.F.5BA3BA2BABA6B.F.5B5A2B2A7B.F$F.9BA3B2A6B.F.9BA4BA6B.F.6B
4AB2ABA6B.F.6BA3B3A8B.F.5B2A2B2AB2ABA5B.F$F.9B6A6B.F.6B2AB4ABA6B.F.8B
2A2BABA6B.F.6BA3BA4B2A4B.F.6BA14B.F$F.5B4A12B.F.10BAB2A7B.F23.F23.F
23.F!Edit: I also ran a set of searches for a single-phase width-16 even symmetric c/5 orthogonal ship (width-18 examples are known). My constraint files were the cyclic permutations of the following constraint file:
Code: Select all
$ cat c5o_w8e_1.cstr
| WWWWWWWWW...... | WWWWWWWWWW..... | WWWWWWWWWWW.... | WWWWWWWWWWWW... | WWWWWWWWWWWWW.. |Code: Select all
./rlife llsss c5-f2b @bg:15 --left-edge even --constraint grid_loop:c5o_w8e_N.cstr --filters bcafCode: Select all
x = 16, y = 41, rule = B3/S23
6b4o$4bo6bo$4bo6bo$bo2bo2b2o2bo2bo$2o12b2o$4b3o2b3o$4bob4obo$3b2ob4ob
2o$2o3bob2obo3b2o$obo10bobo$2bo10bo$3o10b3o$obo10bobo$obo10bobo$2o12b
2o$2bo10bo$2bo10bo$b2o10b2o$o14bo$4o8b4o$bobo8bobo2$3obo6bob3o$3b3o4b
3o$ob4o4b4obo$3o10b3o$3o10b3o$2obo8bob2o$3bo2bo2bo2bo$ob2o2bo2bo2b2obo
$bo3b2o2b2o3bo$5b2o2b2o$b2o2bo4bo2b2o$bo3bo4bo3bo$2ob2ob4ob2ob2o$4bo2b
2o2bo$b2obo6bob2o$3o2b2o2b2o2b3o$6b4o$b2o3bo2bo3b2o$o2b3o4b3o2bo!