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 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

• Isotropic non-totalistic rule
• Non-totalistic cellular automaton

External links

• Isotropy at Wikipedia