# 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^{102} isotropic non-totalistic rules (including Life-like rules as a subset), and 2^{512} 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 2^{512} 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