Topology-induced phase transitions in totalistic cellular automata
type: Item
instance of: scholarly article
title: Topology-induced phase transitions in totalistic cellular automata
zbMATH Open document ID: 1279.37014
published in: Physica D
publication date: 2013-04-30T00:00:00Z
review text: This article deals with totalistic cellular automata (CA) over random tesselations: each cell of the plane holds a binary state that evolves according to a local rule which only depends on the number of neighboring cells with state 1. It responds to other results attributing the property of sensitivity (to initial conditions) to some of these CA without emphasizing the tesselation over which it is considered, though it plays a crucial role. Indeed, the authors show the results of their numerical experiments computing the maximal Lyapunov exponent (which basically corresponds to the maximal long-range communication speed) of many CA over random tesselations with prescribed mean connectivity (average number of neighbors): 89 so-called intrinsically complex CA have a positive exponent which always remains the same or evolves smoothly with respect to the connectivity, while 124 so-called topology-mediated complex CA involve a phase transition: a slight change in the mean connectivity can suddenly bring a positive Lyapunov exponent to 0.
Mathematics Subject Classification ID: 37B15
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 6159599
zbMATH Keywords: cellular automata
zbMATH Keywords: random graph
zbMATH Keywords: topological phase transition
zbMATH Keywords: Lyapunov exponent
author: J. M. Baetens
author: B. De Baets
MaRDI profile type: Publication
full work available at URL: j.physd.2013.01.004
OpenAlex ID: W2128474631
Wikidata QID: Q60256569
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DOI: 10.1016/J.PHYSD.2013.01.004
description: scientific article; zbMATH DE number 6159599