A GROUP INTERPRETATION OF PARTICLES GENERATED BY ONE-DIMENSIONAL CELLULAR AUTOMATON, WOLFRAM'S RULE 54

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

International Journal of Modern Physics C (IJMPC), 2000, vol. 11, issue 01, 101-123

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.

Keywords: Cellular Automaton; Particle; Tiling; Filter (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1142/S0129183100000109

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