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Eventually Number-Conserving Cellular Automata

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  • NINO BOCCARA

    (Department of Physics, University of Illinois at Chicago, USA)

Abstract

Although it is undecidable whether a one-dimensional cellular automaton obeys a given conservation law over its limit set, it is however possible to obtain sufficient conditions to be satisfied by a one-dimensional cellular automaton to be eventually number-conserving. We present a preliminary study of two-input one-dimensional cellular automaton rules calledeventually number-conserving cellular automaton ruleswhose limit sets, reached after a number of time steps of the order of the cellular automaton size, consist of states having a constant number of active sites. In particular, we show how to find rules having given limit sets satisfying a conservation rule. Viewed as models of systems of interacting particles, these rules obey a kind of Darwinian principle by either annihilating unnecessary particles or creating necessary ones.

Suggested Citation

  • Nino Boccara, 2007. "Eventually Number-Conserving Cellular Automata," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 35-42.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:01:n:s0129183107010310
    DOI: 10.1142/S0129183107010310
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    Keywords

    Number-conserving; cellular automata;

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