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Rotators, periodicity, and absence of diffusion in cyclic cellular automata

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Abstract

Cyclic cellular automata are two-dimensional cellular automata which generalize lattice versions of the Lorentz gas and certain biochemistry models of artificial life. We show that rotators and time reversibility play a special role in the creation of closed orbits in cyclic cellular automata. We also prove that almost every orbit is closed (periodic) and the absence of diffusion for the flipping rotator model (also known as the ant).

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia

    L. A. Bunimovich

  2. Forschungszentrum BiBoS, Universität Bielefeld, 33615, Bielefeld, Germany

    S. E. Troubetzkoy

Authors
  1. L. A. Bunimovich
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  2. S. E. Troubetzkoy
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Bunimovich, L.A., Troubetzkoy, S.E. Rotators, periodicity, and absence of diffusion in cyclic cellular automata. J Stat Phys 74, 1–10 (1994). https://doi.org/10.1007/BF02186804

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  • DOI: https://doi.org/10.1007/BF02186804

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