Re:Conway's Game of Life Is Omniperiodic
by GolDDranks on Thursday December 07, 2023 @11:33PM
(#38565490)
I don't think that's surprising, because surely there are a lot more possible ways to get larger periods than small periods? The amount of possible interactions / mechanisms in play is more limited with small periods. I think that groups of periods over some theshold numbers would also yield more readily to "constructive" approaches where you can "build up" the period using oscillators of a smaller period as components.
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Re:Conway's Game of Life Is Omniperiodic
by Someone on Friday December 08, 2023 @03:23AM
(#38566600)
for example, search for constellations that send gliders back and forth through empty space.
If you have one of period p, you can make one of period p + 8n for every n in Ν by moving the guns further away from each other. Find a few guns that take longer to ‘reload’ upon getting ‘hit’.
Search on, and hopefully, you can find the 7 other modulos.
And it need not be glider guns. It could also be constellations that send a ‘ripple’ through occupied space back and forth.
I guess such ones can be made with smaller periods, but may require larger constants than 8 because you typically can’t move them further apart by a single cell.
Edit: another comment mentions https://conwaylife.com/wiki/P43_Snark_loop, a single construct that can be tweaked to have any period ≥ 43.