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Cellular automata in fractal arrangement

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Abstract

Cellular automata (CAs) have been successfully used to investigate complex phenomena across a broad range of research fields. Standard CAs can be extended by applying a novel algorithm known as the recursive estimation of neighbors. This process allows the construction of non-uniform CAs that are composed of cells with different perception areas parameterized by an extra radius. This paper proposes a non-uniform CA called Fractal CA (F-CA), which is composed of cells with self-similar fractal arrangement. By focusing on the extension of 1D elementary CAs, certain characteristics of standard CAs are carried over into F-CAs, including time reversibility of the linear rules. F-CAs based on 2D outer-totalistic CAs are also mentioned briefly.

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Notes

  1. Other options are beyond the scope of this paper.

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Acknowledgements

The author wishes to thank all the anonymous reviewers for valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Media and Information, BAIKA Women’s University, 2-19-5 Shukuno-sho, Osaka, Ibaraki, 567-8578, Japan

    Yoshihiko Kayama

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  1. Yoshihiko Kayama
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Correspondence to Yoshihiko Kayama.

Additional information

This work was presented in part at the 23rd International Symposium on Artificial Life and Robotics, Beppu, Oita, January 18–20, 2018.

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Kayama, Y. Cellular automata in fractal arrangement. Artif Life Robotics 23, 395–401 (2018). https://doi.org/10.1007/s10015-018-0448-8

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  • DOI: https://doi.org/10.1007/s10015-018-0448-8

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