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Symmetric cellular automata

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Abstract

A class of cellular automata with permutation-invariant local rules acting on symmetric lattices is considered. In the case of two states, we show that these local rules are nothing else than a generalization of the rules of the game of Life. In view of the symmetry relative to the state renaming, we can further reduce the number of possible automata. For automata with symmetric rules acting on highly symmetric lattices, we can develop efficient algorithms to study their dynamics. Relevant examples are presented.

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References

  1. http://psoup.math.wisc.edu/mcell/rullex_life.html.

  2. Harari, F., Graph Theory, Reading, Mass.: Addison-Wesley, 1969. Translated under the title Teoriya grafov, Moscow: Mir, 1973.

    Google Scholar 

  3. Hilbert, D. and Cohn-Vossen, S., Geometry and the Imagination, New York: Chelsea, 1952. Translated under the title Naglyadnaya geometriya, Moscow: Nauka, 1981.

    MATH  Google Scholar 

  4. Kostant, B., The Graph of the Truncated Icosahedron and the Last Letter of Galois, Notices AMS, 1995, vol. 42, no. 9, pp. 959–968.

    MATH  MathSciNet  Google Scholar 

  5. Klein, F., Vorlesungen über das Ikosaeder Leipzig: Teubner, 1884. Translated under the title Lektsii ob ikosaedre i reshenii uravnenii pyatoi stepeni, Moscow: Nauka, 1989.

    Google Scholar 

  6. Atiyah, M.F. and Sutcliffe, P.M., Polyhedra in Physics, Chemistry and Geometry, Milan J. Math., 2003, vol. 71, pp. 33–58, http://arxiv.org/abs/math-ph/0303071.

    Article  MATH  MathSciNet  Google Scholar 

  7. McKay, B.D., Practical Graph Isomporphism, Congressus Numerantium, 1981, vol. 30, pp. 45–87, http://cs.anu.edu.au/:_bdm/nauty/PGI/.

    MathSciNet  Google Scholar 

  8. Lidl, R. and Niederreiter, H., Finite Fields, Reading, Mass.: Addison-Wesley, 1983. Translated under the title Konechnye polya, Moscow: Mir, 1988.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980, Russia

    V. V. Kornyak

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  1. V. V. Kornyak
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Original Russian Text © V.V. Kornyak, 2007, published in Programmirovanie, 2007, Vol. 33, No. 2.

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Kornyak, V.V. Symmetric cellular automata. Program Comput Soft 33, 87–93 (2007). https://doi.org/10.1134/S0361768807020065

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  • DOI: https://doi.org/10.1134/S0361768807020065

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