Journal of Statistical Physics

, Volume 38, Issue 5–6, pp 901–946 | Cite as

Two-dimensional cellular automata

  • Norman H. Packard
  • Stephen Wolfram


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 models dynamical systems pattern formation computation theory 


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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

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

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