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Constructing Continuous Systems from Discrete Cellular Automata

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The Nature of Computation. Logic, Algorithms, Applications (CiE 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7921))

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Abstract

This paper studies a way of transforming discrete time and discrete space cellular automata into systems described by partial differential equations with a similar behavior. The goal is to find new kinds of chaotic behaviors for systems ruled by partial differential equations.

This work is supported by projects EQINOCS (ANR 11 BS02 004 03) and TARMAC (ANR 12 BS02 007 01).

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References

  1. Kari, J.: Universal pattern generation by cellular automata. Theor. Comput. Sci. 429, 180–184 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kurka, P.: Topological and symbolic dynamics. Société Mathématique de France (2003)

    Google Scholar 

  3. Masi, A.D., Ferrari, P., Lebowitz, J.: Reaction-diffusion equations for interacting particle systems. Journal of Statistical Physics 44, 589–644 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Durret, R., Neuhauser, C.: Particle systems and reaction-diffusion equations. Annals of Probability 22, 289–333 (1994)

    Article  MathSciNet  Google Scholar 

  5. Dobrushin, R., Kriukov, V., Toom, A.: Stochastic Cellular Systems: Ergodicity, Memory, Morphogenesis. Nonlinear science. Manchester University Press (1990)

    Google Scholar 

  6. Durrett, R.: Stochastic spatial models. SIAM Review 41(4), 677–718 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Thomas, J.: Numerical Partial Differential Equations: Finite Difference Methods. Texts in Applied Mathematics. Springer (2010)

    Google Scholar 

  8. Cattaneo, G., Flocchini, P., Mauri, G., Quaranta Vogliotti, C., Santoro, N.: Cellular automata in fuzzy backgrounds. Physica D: Nonlinear Phenomena 105, 105–120 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire d’Algorithmique, Complexité et Logique (LACL), University Paris-Est, 94010, Créteil cedex, France

    Julien Cervelle

Authors
  1. Julien Cervelle
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Editor information

Editors and Affiliations

  1. Dipartimento die Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Piazza dell’Ateneo Nuovo 1, 20126, Milan, Italy

    Paola Bonizzoni

  2. Institute for Theoretical Computer Science, Mathematics and Operations Research, Faculty of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Vasco Brattka

  3. Institute for Logic, Language and Computation, University of Amsterdam, Postbus 94242, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

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Cervelle, J. (2013). Constructing Continuous Systems from Discrete Cellular Automata. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_7

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  • DOI: https://doi.org/10.1007/978-3-642-39053-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39052-4

  • Online ISBN: 978-3-642-39053-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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