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Directed Percolation Phenomena in Asynchronous Elementary Cellular Automata

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Cellular Automata (ACRI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4173))

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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.

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Author information

Authors and Affiliations

  1. LORIA, University Nancy, 1, Campus Scientifique, B.P. 239, 54506, Vandoeuvre-lès-Nancy, France

    Nazim Fatès

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  1. Nazim Fatès
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Editors and Affiliations

  1. Laboratory of Mathematics, Physics and Systems, University of Perpignan, 52, Paul Alduy Avenue, 66860, Perpignan, Cedex, France

    Samira El Yacoubi

  2. Computer Science Department, University of Geneva, Switzerland

    Bastien Chopard

  3. Research Center on Complex Systems and Artificial Intelligence (CSAI) Department of Computer Science, Systems and Communication (DISCo), University of Milan, Bicocca viale Sarca, 336, 20126, Milan, (Italy)

    Stefania Bandini

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Fatès, N. (2006). Directed Percolation Phenomena in Asynchronous Elementary Cellular Automata. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds) Cellular Automata. ACRI 2006. Lecture Notes in Computer Science, vol 4173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11861201_77

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  • DOI: https://doi.org/10.1007/11861201_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40929-8

  • Online ISBN: 978-3-540-40932-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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