Communications in Mathematical Physics

, Volume 93, Issue 2, pp 219–258 | Cite as

Algebraic properties of cellular automata

  • Olivier Martin
  • Andrew M. Odlyzko
  • Stephen Wolfram


Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations.


Neural Network Dynamical System Statistical Physic State Transition Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Olivier Martin
    • 1
  • Andrew M. Odlyzko
    • 2
  • Stephen Wolfram
    • 2
    • 3
  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Bell LaboratoriesMurray HillUSA
  3. 3.The Institute for Advanced StudyPrincetonUSA

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