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Topology regulates pattern formation capacity of binary cellular automata on graphs | | Carsten Marr
; Marc-Thorsten Huett
; | | Date: |
21 Feb 2005 | | Subject: | Statistical Mechanics; Cellular Automata and Lattice Gases | cond-mat.stat-mech nlin.CG | | Abstract: | 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. | | Source: | arXiv, cond-mat/0502509 | | Services: | Forum | Review | PDF | Favorites | |
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