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Computational Mechanics of Cellular Automata: An Example

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  • James E. Hanson
  • James P. Crutchfield

Abstract

We illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space-time behavior of elementary one-dimensional cellular automaton rule 54. The CA's dominant regular domain filter is constructed to locate and classify defects in the domain. The primary particles are identified and a range of interparticle interactions is studied. The deterministic equation of motion of the filtered space-time behavior is derived. Filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher-level defects, particle interactions, and secondary domains. We define the emergence time at which the space-time behavior condenses into configurations consisting only of domains, particles, and particle interactions. Taken together, these techniques serve as the basis for the investigation of pattern evolution and self-organization in this representative system.

Suggested Citation

  • James E. Hanson & James P. Crutchfield, 1995. "Computational Mechanics of Cellular Automata: An Example," Working Papers 95-10-095, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:95-10-095
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    References listed on IDEAS

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    1. Rajarshi Das & James P. Crutchfield & Melanie Mitchell & James E. Hanson, 1995. "Evolving Globally Synchronized Cellular Automata," Working Papers 95-01-005, Santa Fe Institute.
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