A Group Interpretation of Particles Generated by One Dimensional Cellular Automaton, 54 Wolfram's rule

B. Martin
Int. Journ. of Mod. Phys. C, 11(1):101-123, 2000.
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  • One dimensional cellular automata are known to be able to present complex behaviors. In some cases, their evolution may be understood as movings, collisions, creations of particles. In the case of the special Wolfram 54 rule, N. Boccara has previously pointed out basic particles. In this paper, we introduce a group which allows to formally study interactions between these particles. Coming back on the complexity of the rule 54, using a new algebraic classification due to I. Rapaport, we give sense to, and prove, the fact that the rule 54 is not simple.

  • Keywords: Cellular Automaton, Particle, Tiling.

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             author = {B. Martin},
             title = {A group interpretation of particles generated by one
             dimensional cellular automaton, 54 Wolfram's rule},
             journal = {Int. Journ. of Mod. Phys. C},
             volume = {11}
             number = {1}
             pages = {101-123}
             year = {2000}