Isotropic: Difference between revisions
m -- oops, the "outer-totalistic" comparison works for range-1 amphichiral rules only because there are so few neighbors; it falls apart for higher-range 1D CA rules |
m -- "isotropic" was coming out as boldface instead of as a link -- because of previous use of the boldface term higher up, maybe? Anyway, the link wasn't needed, since isotropic non-totalistic rule was linked in a previous section. |
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==Amphichiral== | ==Amphichiral== | ||
Equivalently, a [[one-dimensional cellular automaton]] is described using '''amphichiral''' or '''chiral'''. Amphichiral rules are the 1-dimensional version of 2D | 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== | ==See also== | ||
Revision as of 13:10, 25 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.
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