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arXiv · 2105.09708

Mean dimension of continuous cellular automata

David Burguet·Ruxi Shi
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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.

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David Burguet, Ruxi Shi. 2021-05-20. Mean dimension of continuous cellular automata. https://arxiv.org/abs/2105.09708

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