Classifying elementary cellular automata using compressibility, diversity and sensitivity measures

Shigeru Ninagawa () and Andrew Adamatzky ()
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Shigeru Ninagawa: Kanazawa Institute of Technology, Ishikawa, Japan;
Andrew Adamatzky: University of the West of England, Bristol, UK

International Journal of Modern Physics C (IJMPC), 2014, vol. 25, issue 03, 1-12

Abstract: An elementary cellular automaton (ECA) is a one-dimensional, synchronous, binary automaton, where each cell update depends on its own state and states of its two closest neighbors. We attempt to uncover correlations between the following measures of ECA behavior: compressibility, sensitivity and diversity. The compressibility of ECA configurations is calculated using the Lempel–Ziv (LZ) compression algorithm LZ78. The sensitivity of ECA rules to initial conditions and perturbations is evaluated using Derrida coefficients. The generative morphological diversity shows how many different neighborhood states are produced from a single nonquiescent cell. We found no significant correlation between sensitivity and compressibility. There is a substantial correlation between generative diversity and compressibility. Using sensitivity, compressibility and diversity, we uncover and characterize novel groupings of rules.

Keywords: Cellular automata; compressibility; generative morphological diversity; Derrida coefficients (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0129183113500988

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