Journal of Statistical Physics

, Volume 74, Issue 1, pp 1–10

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

  • L. A. Bunimovich
  • S. E. Troubetzkoy

DOI: 10.1007/BF02186804

Cite this article as:
Bunimovich, L.A. & Troubetzkoy, S.E. J Stat Phys (1994) 74: 1. doi:10.1007/BF02186804


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).

Key Words

Cellular automata closed orbit periodic point rotators time reversibility Lorentz lattice gas 

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • L. A. Bunimovich
    • 1
  • S. E. Troubetzkoy
    • 2
  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlanta
  2. 2.Forschungszentrum BiBoSUniversität BielefeldBielefeldGermany

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