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Non-uniform Cellular Automata based on Open-ended Rule Evolution

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Abstract

Cellular automata (CAs) are mathematical models of spatially and temporally discrete mathematical systems. Non-uniform CAs are the cellular automata in which each cell may contain a different transition rule and change it with time, while all cells share the same transition rule in regular CAs. Little is still known about the dynamics of open-ended evolution of rules in non-uniform CAs. The purpose of our study is to construct and investigate a model of non-uniform CAs capable of open-ended rule evolution exhibiting a wide variety of behavior across all Wolfram’s classes. For this purpose, we construct 1-dimensional 2-state 3 neighborhood non-uniform CAs with evolving transition rules. In the model, we found an interesting dynamics that Class II (periodical behavior) and III (chaotic behavior) patterns emerged alternately, between which Class IV patterns sometimes emerged.

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Authors and Affiliations

  1. Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan

    Noritsugu Sughimura, Reiji Suzuki & Takaya Arita

Authors
  1. Noritsugu Sughimura
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  2. Reiji Suzuki
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  3. Takaya Arita
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Corresponding author

Correspondence to Noritsugu Sughimura.

Additional information

This work was presented in part at the 18th International Symposium on Artificial Life and Robotics, Daejeon, Korea, January 30–February 1, 2013.

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Sughimura, N., Suzuki, R. & Arita, T. Non-uniform Cellular Automata based on Open-ended Rule Evolution. Artif Life Robotics 19, 120–126 (2014). https://doi.org/10.1007/s10015-014-0145-1

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  • DOI: https://doi.org/10.1007/s10015-014-0145-1

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