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Marr, C.* ; Hütt, M.-T.*

Topology regulates pattern formation capacity of binary cellular automata on graphs.

Physica A 354, 641-662 (2005)
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We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent rules, each containing a single parameter. We observe that changes in graph topology induce transitions between different dynamic domains (Wolfram classes) without a formal change in the update rule. Along with topological variations, we study the pattern formation capacities of regular, random, small-world and scale-free graphs. Pattern formation capacity is quantified in terms of two entropy measures, which for standard cellular automata allow a qualitative distinction between the four Wolfram classes. A mean-field model explains the dynamic behavior of random graphs. Implications for our understanding of information transport through complex, network-based systems are discussed.
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Publication type Article: Journal article
Document type Scientific Article
ISSN (print) / ISBN 0378-4371
Journal Physica A
Quellenangaben Volume: 354, Issue: , Pages: 641-662 Article Number: , Supplement: ,
Publisher North-Holland Publ.
Publishing Place Amsterdam
Reviewing status Peer reviewed