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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.

References

  1. von Neumann J (1966) The theory of self-reproducing automata. In: Burks AW (ed) Essays on cellular automata. University of Illinois Press, Illinois

    Google Scholar 

  2. Reynolds CW (1987) Flocks, herds and schools: a distributed behavioral model. ACM Siggraph Comput Gr 21(4):25–34

    Article  Google Scholar 

  3. Kayama Y (2016) Extension of cellular automata by introducing an algorithm of recursive estimation of neighbors. In: Proceedings of the 21st international symposium on artificial life and robotics, pp 73–77

  4. Kayama Y (2016) Expansion of perception area in cellular automata using recursive algorithm. In: Proceeding of the fifteenth international conference on the simulation and synthesis of living systems, pp 92–99

  5. Wolfram S (1983) Statistical mechanics of cellular automata. Rev Mod Phys 55:601–644

    Article  MathSciNet  MATH  Google Scholar 

  6. Wolfram S (2002) A new kind of science. Wolfram Media Inc, Champaign

    MATH  Google Scholar 

  7. Li W, Packard N (1990) The structure of the elementary cellular automata rule space. Complex Syst 4:281–297

    MathSciNet  MATH  Google Scholar 

  8. Chaudhuri PP (1997) Additive cellular automata: theory and applications, vol 1. Wiley, Oxford

    MATH  Google Scholar 

  9. Encinas LH, del Rey AM (2007) Inverse rules of eca with rule number 150. Appl Math Comput 189(2):1782–1786

    MathSciNet  MATH  Google Scholar 

  10. Mandelbrot BB, Pignoni R (1983) The fractal geometry of nature, vol 173. WH freeman, New York

    Google Scholar 

  11. Gardner M (1970) Mathematical games. Sci Am 223:102–123

    Article  Google Scholar 

  12. Berlekamp ER, Conway JH, Guy RK (1982) Winning ways for your mathematical plays. Academic Press, New York

    MATH  Google Scholar 

  13. Adamatzky A (ed) (2010) Game of life cellular automata. Springer, London

    MATH  Google Scholar 

  14. Eppstein D (2010) Growth and decay in life-like cellular automata. In: Adamatzky A (ed) Game of life cellular automata. Springer, Berlin, pp 71–98

    Chapter  Google Scholar 

  15. Wang X, Luan D (2013) A novel image encryption algorithm using chaos and reversible cellular automata. Commun Nonlinear Sci Numer Simul 18(11):3075–3085

    Article  MathSciNet  MATH  Google Scholar 

Download references

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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