Directed percolation phenomena in asynchronous elementary cellular automata

  • Authors:
  • Nazim Fatès

  • Affiliations:
  • LORIA, University Nancy, Vandoeuvre-lès-Nancy, France

  • Venue:
  • ACRI'06 Proceedings of the 7th international conference on Cellular Automata for Research and Industry
  • Year:
  • 2006

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Abstract

Cellular automata are discrete dynamical systems that are widely used to model natural systems Classically they are run with perfect synchrony ; i.e., the local rule is applied to each cell at each time step A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate It has been shown in a previous work that varying the synchrony rate continuously could produce a discontinuity in the behaviour of the cellular automaton This works aims at investigating the nature of this change of behaviour using intensive numerical simulations We apply a two-step protocol to show that the phenomenon is a phase transition whose critical exponents are in good agreement with the predicted values of directed percolation.