Snarkperiodicity (and other omniperiodicity tasks w/stable ship turners)
Posted: July 12th, 2024, 11:39 pm
This thread is for exploring the rulespace of the Snark and Snark64 for generalized proofs of omniperiodicity (EDIT: and maybe other things, like cool oscillators). Even so, this thread can also be used to explore similar turners for other spaceships in various CA (e.g. the stable reflector in tflock 2). In general, this thread should aim to tackle Omniperiodicity in a broader space of rules than what is covered by the more well-represented "which life-like cellular automota have been proven Omniperiodic?".
Back to the main topic of discussion this forum thread, the Snark and Snark64 have the dual property of solving oscillators for both an infinite and complete set of periods above the minimum repeat time of each.
The rulespaces are fairly large, and between all evolutionary sequences identical to life cover a space of exactly 160 rules (128 for snark variants and 64 for Snark64, 32 overlap). If differing evolutions which don't change the outcome are included, then there are 128 more for snark and 128 more for Snark64.
Snark & variants under normal evolution - B3/S23 -- B34c8/S234cz5e6n8
Snark64 under normal evolution - B3/S23 -- B34c8/S234cz5e8
Snark & variants with atypical evolution - B34z/S23 -- B34cqz8/S234c5e6n8
Snark64 with atypical evolution - B3/S236e -- B34c8/S234cz5e6e8
However, only a handful of rules covered by all of the rulespaces of each stable turner can actually been proven to be omniperiodic (Namely Life, Eightlife, Pedestrian Life, 4diagonal, Conway++, B34c/S234c, B38/S234c, B3/S234c8, and B34c8/S23. For Snark-only, this also includes B3/S236n and B3/S234c6n), with many others missing a single period (e.g. Honeylife B38/S238) or multiple periods (e.g. zlife B3/S234z).
While it would be nice to have a complete cross-rulespace proof from life to each Snark's end rule of Omniperiodicity for each and every rule, that is not necessary in the least. I will share some of my findings soon.
Back to the main topic of discussion this forum thread, the Snark and Snark64 have the dual property of solving oscillators for both an infinite and complete set of periods above the minimum repeat time of each.
The rulespaces are fairly large, and between all evolutionary sequences identical to life cover a space of exactly 160 rules (128 for snark variants and 64 for Snark64, 32 overlap). If differing evolutions which don't change the outcome are included, then there are 128 more for snark and 128 more for Snark64.
Snark & variants under normal evolution - B3/S23 -- B34c8/S234cz5e6n8
Snark64 under normal evolution - B3/S23 -- B34c8/S234cz5e8
Snark & variants with atypical evolution - B34z/S23 -- B34cqz8/S234c5e6n8
Snark64 with atypical evolution - B3/S236e -- B34c8/S234cz5e6e8
However, only a handful of rules covered by all of the rulespaces of each stable turner can actually been proven to be omniperiodic (Namely Life, Eightlife, Pedestrian Life, 4diagonal, Conway++, B34c/S234c, B38/S234c, B3/S234c8, and B34c8/S23. For Snark-only, this also includes B3/S236n and B3/S234c6n), with many others missing a single period (e.g. Honeylife B38/S238) or multiple periods (e.g. zlife B3/S234z).
Code: Select all
x = 73, y = 97, rule = B3/S23
7$40bo$39bobo$39bob3o$36b2obo4bo$36bobobobobo$38bobob2o4b2o$30b2o5bob
o8bo$30b2o6bo7bobo$46b2o3$35b2o$34bo2bo$35b2o4$23b2o$22bobo$24bo18b2o
$30b2o10bobo$26b2obobo10b2o$26bob2obobo$32b2o3b2o3b4o$37b2o4bo2bo$41b
o3b2o$41b2o4$30b2o$30bobo$32bo4b2o$28b4ob2o2bo2bo$28bo2bobobobob2o$31b
obobobo$32b2obobo$36bo2$22b2o$23bo7b2o$23bobo5b2o$24b2o25bo$49b3o$48b
o$48b2o3$56b2o$34b2o21bo$34bo22bob2o$24b3o8b3o11b2o4b3o2bo$14bo11bo10b
o11b2o3bo3b2o$12b5o8bo5b2o21b4o$11bo5bo13bo8b2o15bo$11bo2b3o12bobo7bo
bo12b3o$10b2obo15b2o8bo13bo$10bo2b4o21b2o14b5o$11b2o3bo3b2o11bo22bo2b
o$13b3o4b2o11b3o22b2o$13bo22bo$10b2obo21b2o$10b2ob2o3$21b2o$22bo$19b3o
$19bo25b2o$38b2o5bobo$38b2o7bo$47b2o2$34bo$33bobob2o4b2o$33bobobobo2b
o2bo$32b2obobobo3b2o$33bo2b2ob4o$33bo4bo3bo$34b3obo2bo$36bobobo$39bo!