Cellular Automata, Dynamics and Complexity

  • E. Goles
Part of the Springer Proceedings in Physics book series (SPPHY, volume 46)

Abstract

In this paper we study some dynamical aspects of Cellular Automata. Essentially we characterize the steady state behavior for a class of local rules in the context of Potts and Bounded Threshold Automata. For Potts automata we exhibit a class that has a complex dynamics, i.e. the automaton simulates any logical function by coding binary information as gliders in a one-dimensional cellular space. On the other hand, we characterize another class which has a simple dynamical behavior: fixed points or two-cycles in the steady state. In the context of Bounded Threshold Automata with arbitrary interactions (not necessarily symmetric) we characterize its dynamics for one-dimensional cellular arrays: the only admissible cycles have period T ≤ 4. Furthermore, we give sufficient conditions to obtain a period-2 behavior in high dimensional lattices.

Keywords

Wolfram Olivos 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • E. Goles
    • 1
  1. 1.Departamento de Matematicas, Escuela de IngenieriaU. de ChileSantiagoChile

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