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A Group Interpretation Of Particles Generated By One-Dimensional Cellular Automaton, Wolfram'S Rule 54

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  • BRUNO MARTIN

    (LIP, École Normale Supérieure de Lyon, 46, allée d'Italie, 69 364 Lyon Cedex 07, France)

Abstract

One-dimensional cellular automata are known to be able to present complex behaviors. In some cases, their evolution may be understood as movings, collisions, or creations of particles. In the case of the special Wolfram's rule 54, Boccara has previously pointed out basic particles. In this paper, we introduce a group which allows the formal study of interactions between these particles. Coming back to the complexity of rule 54 and using the new algebraic classification of Rapaport, we prove that rule 54 is not simple.

Suggested Citation

  • Bruno Martin, 2000. "A Group Interpretation Of Particles Generated By One-Dimensional Cellular Automaton, Wolfram'S Rule 54," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 101-123.
    • Handle: RePEc:wsi:ijmpcx:v:11:y:2000:i:01:n:s0129183100000109
    DOI: 10.1142/S0129183100000109
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    Cited by:

    1. Martínez, Genaro Juárez & Adamatzky, Andrew & McIntosh, Harold V., 2006. "Phenomenology of glider collisions in cellular automaton Rule 54 and associated logical gates," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 100-111.

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