Oscar Cunningham

In Conway's Game of Life there are certain oscillators called 'phoenixes', which have the property that no cell is ever on for more than a single generation consecutively. The only examples known were ones with period 2 (so the cells are just turning on and off repeatedly). It's now been proven that these are the only phoenixes: https://cp4space.hatsya.com/2024/01/20/every-finite-phoenix-has-period-2/

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Every finite phoenix has period 2

A phoenix is an oscillator in Conway’s Life where every cell dies in every generation. The smallest example is Phoenix 1, which oscillates with period 2 and has a constant population of 12: A…

Complex Projective 4-Space
Jan 20, 2024 at 4:27pmWeb
Show threadNon-Euclidean DreamerJan 20, 2024
@OscarCunningham But I could have infinite phoenixes with bigger period? ( E.g spanning a toroidal playfield)
Show threadOscar CunninghamJan 20, 2024
@noneuclideandreamer Yes, the article says that such things are known for period 4 and all multiples of 6, and are known not to exist for period 3 or 5.