EVENTUALLY NUMBER-CONSERVING CELLULAR AUTOMATA

Nino Boccara ()
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Nino Boccara: Department of Physics, University of Illinois at Chicago, USA

International Journal of Modern Physics C (IJMPC), 2007, vol. 18, issue 01, 35-42

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.

Keywords: Number-conserving; cellular automata (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S0129183107010310

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