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 [Mey08], we give an example of an algebraic surjective cellular automaton with positive finite mean dimension.
| Original language | English |
|---|---|
| Pages (from-to) | 311-346 |
| Number of pages | 36 |
| Journal | Israel Journal of Mathematics |
| Volume | 259 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Mar 2024 |