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Topological Dynamics of 2D Cellular Automata

  • Mathieu Sablik
  • Guillaume Theyssier
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5028)

Abstract

Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more complex. The main results are the existence of non sensitive CA without equicontinuous points, the non-recursivity of sensitivity constants and the existence of CA having only non-recursive equicontinuous points. They all show a difference between the 1D and the 2D case. Thanks to these new constructions, we also extend undecidability results concerning topological classification previously obtained in the 1D case.

Keywords

Cellular Automaton Turing Machine Cellular Automaton Recursive Function Topological Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mathieu Sablik
    • 1
  • Guillaume Theyssier
    • 2
  1. 1.UMPA, (UMR 5669 — CNRS, ENS Lyon), 46, allée d’Italie 69364 Lyon cedex 07, France and LATP, (UMR 6632 — CNRS, Université de Provence), CMI, Université de Provence, Technopôle Château-Gombert, 39, rue F. Joliot Curie, 13453 Marseille Cedex 13France
  2. 2.LAMA(UMR 5127 — CNRS, Université de Savoie)Le Bourget-du-lac cedexFrance

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