Isotropic

A cellular automaton is said to be isotropic if its global transition function is isotropic, i.e. invariant under rotations and reflections. Cellular automata that are not isotropic are called anisotropic or non-isotropic.

There are 2¹⁰² isotropic Life-Like rules, and 2⁵¹² MAP rules. The 2⁵¹² figure includes all outer-totalistic, isotropic, and anisotropic Life-like rules. Totalistic rules are a strict subset of outer-totalistic rules, which in turn are a strict subset of isotropic rules. Isotropic and anisotropic rules together make up the full complement of 2⁵¹² MAP rules.

Isotropic rules are most often represented in Hensel notation, but like any other possible 2-state rule in a range-1 Moore neighbourhood, they can also be encoded as MAP rule strings.

Also see

gollark: https://dragcave.net/teleport/9f1bb72d14f56b7f3982d13568b6b705when it's off cooldown.

gollark: If you want, I have a trade up for a CB thalassa + magma for a gaia one.

gollark: Oh wow.

gollark: Not really.

gollark: It seems that fish has put up a CB silver. I thought fish only liked golds.

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