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Journal Articles Journal of Cellular Automata Year : 2009

Examples of Fast and Slow Convergence of 2D Asynchronous Cellular Systems

Nazim A. Fatès
Lucas Gerin
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Abstract

This article studies the convergence properties of some 2D cellular automata, when a single cell is updated at random at each time step. We tackle this question for a particular set of rules, namely, the totalistic rules with nearest neighbours. We focus on a few examples that represent, in our view, the diversity of behaviours found in dimension two. These behaviours are analysed quantitatively with an estimation of the time needed to converge to a fixed point.
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Dates and versions

hal-00260184 , version 1 (03-03-2008)
hal-00260184 , version 2 (16-05-2008)
hal-00260184 , version 3 (23-10-2008)
hal-00260184 , version 4 (31-10-2008)

Identifiers

  • HAL Id : hal-00260184 , version 4

Cite

Nazim A. Fatès, Lucas Gerin. Examples of Fast and Slow Convergence of 2D Asynchronous Cellular Systems. Journal of Cellular Automata, 2009, 4 (4), pp.323-337. ⟨hal-00260184v4⟩
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