Isotropic: Difference between revisions
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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'''. | 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 2<sup>102</sup> isotropic Life-Like rules, and 2<sup>512</sup> [[Rule integer|MAP]] rules. The 2<sup>512</sup> 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 2<sup>512</sup> 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== | ==Also see== | ||
* [[Isotropic non-totalistic Life-like cellular automaton]] | * [[Isotropic non-totalistic Life-like cellular automaton]] | ||
* [[Non-totalistic Life-like cellular automaton]] | |||
Revision as of 17:36, 19 April 2018
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.