On the analysis of ”simple” 2D stochastic cellular automata
TLDR
In this paper, the dynamics of a two-dimensional cellular automaton for the Moore neighborhood (eight closest neighbors of each cell) under fully asynchronous dynamics (where one single random cell updates at each time step).Abstract:
Cellular automata are usually associated with synchronous deterministic dynamics, and their asynchronous or stochastic versions have been far less studied although significant for modeling purposes. This paper analyzes the dynamics of a two-dimensional cellular automaton, 2D Minority, for the Moore neighborhood (eight closest neighbors of each cell) under fully asynchronous dynamics (where one single random cell updates at each time step). 2D Minority may appear as a simple rule, but It is known from the experience of Ising models and Hopfield nets that 2D models with negative feedback are hard to study. This automaton actually presents a rich variety of behaviors, even more complex that what has been observed and analyzed in a previous work on 2D Minority for the von Neumann neighborhood (four neighbors to each cell) (2007) This paper confirms the relevance of the later approach (definition of energy functions and identification of competing regions) Switching to the Moot e neighborhood however strongly complicates the description of intermediate configurations. New phenomena appear (particles, wider range of stable configurations) Nevertheless our methods allow to analyze different stages of the dynamics It suggests that predicting the behavior of this automaton although difficult is possible, opening the way to the analysis of the whole class of totalistic automataread more
Citations
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Journal ArticleDOI
Progresses in the analysis of stochastic 2D cellular automata: A study of asynchronous 2D minority
TL;DR: This paper addresses the problem of analyzing an apparently simple 2D asynchronous cellular automaton: 2D Minority where each cell, when fired, updates to the minority state of its neighborhood and reveals that in spite of its simplicity, the minority rule exhibits a quite complex response to asynchronism.
Book ChapterDOI
Does Life Resist Asynchrony
TL;DR: This chapter analyses how the Game of Life is affected by the presence of two structural pertubations: a change in the synchrony of the updates and a modification of the links between the cells.
Journal ArticleDOI
Stochastic minority on graphs
TL;DR: In this paper, the authors study how the asynchronism and the graph act upon the dynamics of the classical minority rule and show that the worst case convergence time is strongly dependent on the topology.
Posted Content
Stochastic Minority on Graphs
TL;DR: This paper studies how the asynchronism and the graph act upon the dynamics of the classical Minority rule and shows that the worst case convergence time is, in fact, strongly dependent on the topology.
Book ChapterDOI
Asynchronous Cellular Automata
TL;DR: This text is intended as an introduction to the topic of asynchronous cellular automata and starts from the simple example of the Game of Life and examines what happens to this model when it is made asynchronous.
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T.E. Ingerson,R.L. Buvel +1 more
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