Mean dimension of continuous cellular automata
arXiv:2105.09708
Abstract
We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit one-dimensional automata. In higher dimensions, a CA permutative algebraic or having a spaceship has infinite mean dimension. However, building on Meyerovitch's example, we give an example of algebraic surjective cellular automaton with positive finite mean dimension.
21 pages