Global properties of cellular automata

Abstract

Cellular automata are discrete mathematical systems that generate diverse, often complicated, behavior using simple deterministic rules. Analysis of the local structure of these rules makes possible a description of the global properties of the associated automata. A class of cellular automata that generate infinitely many aperiodic temporal sequences is defined, as is the set of rules for which inverses exist. Necessary and sufficient conditions are derived characterizing the classes of “nearest-neighbor” rules for which arbitrary finite initial conditions (i) evolve to a homogeneous state; (ii) generate at least one constant temporal sequence.

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Jen, E. Global properties of cellular automata. J Stat Phys 43, 219–242 (1986). https://doi.org/10.1007/BF01010579

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Key words

  • Cellular automata
  • discrete dynamical systems
  • local interactions
  • deterministic structures