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 | There are 2<sup>102</sup> [[isotropic non-totalistic rule]]s (including [[Life-like rule]]s as a subset), and 2<sup>512</sup> [[MAP rule]]s (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 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. | 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. | ||
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==See also== | ==See also== | ||
* [[Isotropic non-totalistic | * [[Isotropic non-totalistic rule]] | ||
* [[Non-totalistic cellular automaton]] | * [[Non-totalistic cellular automaton]] | ||
==External links== | |||
* {{LinkWikipedia|Isotropy|name=Isotropy}} | |||
Revision as of 14:04, 31 March 2023
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.
Amphichiral
Equivalently, a one-dimensional cellular automata is described using amphichiral or chiral.
See also
External links
- Isotropy at Wikipedia