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Qualitative and Quantitative Cellular Automata from Differential Equations

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Book cover Cellular Automata (ACRI 2006)

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

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Abstract

We give a synthetic and formalized account of relationships between cellular automata (CA) and differential equations (DE): Numerical schemes and phase portraits analysis (via cell-to-cell mappings) can be translated into CA, and compositions of differential operators and phase portraits induce CA compositions. Based on DE, CA can be tuned according to discretization parameters so that faithful CA sequences can be built describing qualitative as well as quantitative solutions.

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Author information

Authors and Affiliations

  1. LaBRI, University of Bordeaux 1, France

    Philippe Narbel

Authors
  1. Philippe Narbel
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Editor information

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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© 2006 Springer-Verlag Berlin Heidelberg

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Narbel, P. (2006). Qualitative and Quantitative Cellular Automata from Differential Equations. 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_16

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  • DOI: https://doi.org/10.1007/11861201_16

  • 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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