2021/05/20 by David Burguet, Ruxi Shi, Burguet, David +1
Computer Science · Mathematics · #Cellular Automata and Applications #Advanced Operator Algebra Research #Markov Chains and Monte Carlo Methods
paper · doi:10.48550/arxiv.2105.09708
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.