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Cellular Automata With Accumulative Memory: Legal Rules Starting From A Single Site Seed

Author

Listed:
  • RAMÓN ALONSO-SANZ

    (ETSI Agrónomos (Estadística), C. Universitaria. 28040, Madrid, Spain)

  • MARGARITA MARTÍN

    (F. Veterinaria (Bioquímica y Biologí a Molecular IV, UCM), C. Universitaria. 28040, Madrid, Spain)

Abstract

Standard Cellular Automata (CA) are ahistoric (memoryless), i.e., the new state of a cell depends only on the neighborhood configuration at the preceding time step. This article introduces an extension of the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remains the same, each site remembers a weighted mean of all its past states, with a decreasing weight of states farther back in the past. The historic weighting is defined by a potential series of coefficients,tk,kacting as a forgetting factor. This paper considers the time evolution of one-dimensional, legal CA rules with accumulative memory.

Suggested Citation

  • Ramón Alonso-Sanz & Margarita Martín, 2003. "Cellular Automata With Accumulative Memory: Legal Rules Starting From A Single Site Seed," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 695-719.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:05:n:s0129183103004863
    DOI: 10.1142/S0129183103004863
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    Cited by:

    1. Alonso-Sanz, Ramón, 2007. "A structurally dynamic cellular automaton with memory," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1285-1295.

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    Keywords

    Cellular automata; memory;

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