Elementary Probabilistic Cellular Automata with Memory in Cells

  • Ramón Alonso-Sanz
  • Margarita Martín
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3305)

Abstract

Standard Cellular Automata (CA) are memoryless: i.e., the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article considers an extension to the standard framework of CA by implementing memory capabilities in cells. Thus in CA with memory : while the update rules remain unaltered, historic memory of past iterations is retained by featuring each cell by a summary of all its past states. A study is made of the effect of historic memory on two given sides of the hypercube of elementary probabilistic CA.

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References

  1. 1.
    Ilachinski, A.: Cellular Automata. A Discrete Universe. World Scientific, Singapore (2000)Google Scholar
  2. 2.
    Alonso-Sanz, R.: One-dimensional, r=2 cellular automata with memory. Int. J. Bifurcation and Chaos 14 (in press)Google Scholar
  3. 3.
    Alonso-Sanz, R., Martin, M.: Three-state one-dimensional cellular automata with memory. Chaos, Solitons and Fractals 21, 809–834 (2004)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Alonso-Sanz, R.: Reversible CA with Memory. Physica D 175, 1–30 (2003)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Alonso-Sanz, R., Martin, M.: Elementary cellular automata with memory. Complex Systems 14, 99–126 (2003)MATHMathSciNetGoogle Scholar
  6. 6.
    Alonso-Sanz, R., Martin, M.: Cellular automata with accumulative memory. Int. J. Modern Physics C 14, 695–719 (2003)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Alonso-Sanz, R., Martin, M.C., Martin, M.: One-dimensional cellular automata with memory. Int. J. Bifurcation and Chaos 12, 205–226 (2002)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Alonso-Sanz, R., Martin, M.C., Martin, M.: Two-dimensional cellular automata with memory. Int. J. Modern Physics C 13, 49–65 (2002); and the references thereinMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Adamatzky, A.: Identification of Cellular Automata. Taylor & Francis, Abington (1994)MATHGoogle Scholar
  10. 10.
    Kinzel, W.: Phase Transitions of CA. Z. für Physics B 58, 229–244 (1985)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Domany, E., Kinzel, W.: Equivalence of Cellular Automata to Ising Models and Directed Percolation. Physical Review Letters 53, 311–314 (1984)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Lebowitz, J.L., Maes, C., Speer, E.: Statistical Methods of Probabilistic Cellular Automata. J. Statistical Physics 59, 117–170 (1990)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ramón Alonso-Sanz
    • 1
  • Margarita Martín
    • 2
  1. 1.ETSI Agrónomos (Estadística)C.UniversitariaMadridSpain
  2. 2.Bioquímica y Biología Molecular IVUCM. C.UniversitariaMadridSpain

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