Isotropic: Difference between revisions
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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. | 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. | ||
[[File:INT Moore R1 4z.png]] [[File:INT Moore R1 4j.png]] | |||
Isotropic cellular automata distinguish between these conditions while Outer-totalistic and totalistic cellular automata do not. | |||
==Amphichiral== | ==Amphichiral== | ||
Revision as of 06:51, 26 May 2024
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 non-totalistic rules (including Life-like rules as a subset), and 2512 MAP rules (including isotropic rules as a subset). 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.
Isotropic cellular automata distinguish between these conditions while Outer-totalistic and totalistic cellular automata do not.
Amphichiral
Equivalently, a one-dimensional cellular automaton is described using amphichiral or chiral. Amphichiral rules are the 1-dimensional version of 2D isotropic rules; they will produce a mirror-image output when given a mirror-image input. Chiral rules are the 1-dimensional version of 2D anisotropic rules, where the left-to-right order matters, so a mirror-image input may produce something radically different from the unmirrored input.
See also
External links
- Isotropy at Wikipedia