Journal of Statistical Physics

, Volume 38, Issue 5, pp 901–946

Two-dimensional cellular automata

  • Norman H. Packard
  • Stephen Wolfram

DOI: 10.1007/BF01010423

Cite this article as:
Packard, N.H. & Wolfram, S. J Stat Phys (1985) 38: 901. doi:10.1007/BF01010423


A largely phenomenological study of two-dimensional cellular automata is reported. Qualitative classes of behavior similar to those in one-dimensional cellular automata are found. Growth from simple seeds in two-dimensiona! cellular automata can produce patterns with complicated boundaries, characterized by a variety of growth dimensions. Evolution from disordered states can give domains with boundaries that execute effectively continuous motions. Some global properties of cellular automata can be described by entropies and Lyapunov exponents. Others are undecidable.

Key words

Discrete modelsdynamical systemspattern formationcomputation theory

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Norman H. Packard
    • 1
  • Stephen Wolfram
    • 1
  1. 1.The Institute for Advanced StudyPrinceton