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Classifying elementary cellular automata using compressibility, diversity and sensitivity measures

Author

Listed:
  • Shigeru Ninagawa

    (Kanazawa Institute of Technology, Ishikawa, Japan;
    University of the West of England, Bristol, UK)

  • Andrew Adamatzky

    (University of the West of England, Bristol, UK)

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.

Suggested Citation

  • Shigeru Ninagawa & Andrew Adamatzky, 2014. "Classifying elementary cellular automata using compressibility, diversity and sensitivity measures," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(03), pages 1-12.
    • Handle: RePEc:wsi:ijmpcx:v:25:y:2014:i:03:n:s0129183113500988
    DOI: 10.1142/S0129183113500988
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