Journal of Statistical Physics

, Volume 78, Issue 5, pp 1325–1335

Two applications of percolation to cellular automata

  • Jeffrey E. Steif

DOI: 10.1007/BF02180134

Cite this article as:
Steif, J.E. J Stat Phys (1995) 78: 1325. doi:10.1007/BF02180134


The point of this paper is to show how ideas from percolation can be used to study the asymptotic behavior of some cellular automata systems. In particular, using these ideas, we prove that the Greenberg-Hastings and cyclic cellular automata models with three colors, threshold 2, and theL neighborhood are uniformly asymptotically locally periodic ind≥2 dimensions. We also show that every lattice point is eventually “controlled by a finite clock” in the standard Greenberg-Hastings and cyclic cellular automata models in two dimensions, which is a stronger description than the already known asymptotic behavior.

Key Words

Cellular automatapercolation

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Jeffrey E. Steif
    • 1
  1. 1.Department of MathematicsChalmers University of TechnologyGothenbergSweden