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Topology regulates pattern formation capacity of binary cellular automata on graphs

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  • Marr, Carsten
  • Hütt, Marc-Thorsten

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.

Suggested Citation

  • Marr, Carsten & Hütt, Marc-Thorsten, 2005. "Topology regulates pattern formation capacity of binary cellular automata on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 641-662.
    • Handle: RePEc:eee:phsmap:v:354:y:2005:i:c:p:641-662
    DOI: 10.1016/j.physa.2005.02.019
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    Cited by:

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    2. Beck, Gary L. & Matache, Mihaela T., 2008. "Dynamical behavior and influence of stochastic noise on certain generalized Boolean networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4947-4958.
    3. Carvunis, Anne-Ruxandra & Latapy, Matthieu & Lesne, Annick & Magnien, Clémence & Pezard, Laurent, 2006. "Dynamics of three-state excitable units on Poisson vs. power-law random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 595-612.

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