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Entropy of multidimensional cellular automata

  • Automata Theory
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Abstract

Since the topological entropy of a vast class of two-dimensional cellular automata (CA) is infinite, of interest is the possibility to renormalize it so that to obtain a positive finite value. We find the asymptotics of the information function of a multidimensional CA and, accordingly, introduce the renormalized topological entropy as a coefficient of this asymptotics. We describe some properties of the introduced quantity, in particular, its positivity for CA of the type of “The Game of Life.” Also, we give an example of an explicit evaluation of this parameter for a particular cellular automaton.

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Authors and Affiliations

  1. Mathematics Department, Aveiro University, Portugal

    E. L. Lakshtanov

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Russia

    E. S. Langvagen

Authors
  1. E. L. Lakshtanov
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  2. E. S. Langvagen
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Original Russian Text © E.L. Lakshtanov, E.S. Langvagen, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 1, pp. 43–51.

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Lakshtanov, E.L., Langvagen, E.S. Entropy of multidimensional cellular automata. Probl Inf Transm 42, 38–45 (2006). https://doi.org/10.1134/S0032946006010042

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  • DOI: https://doi.org/10.1134/S0032946006010042

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