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.
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Burguet, D., Shi, R. Mean dimension of continuous cellular automata. Isr. J. Math. 259, 311–346 (2024). https://doi.org/10.1007/s11856-023-2493-9
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DOI: https://doi.org/10.1007/s11856-023-2493-9