Outer-totalistic cellular automata on graphs |
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Authors: | Carsten Marr Marc-Thorsten Hütt |
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Institution: | a Institute for Bioinformatics and Systems Biology, Helmholtz Zentrum München - German Research Center for Environmental Health, D-85764 Neuherberg, Germany b Computational Systems Biology, School of Engineering and Science, Jacobs University Bremen, D-28759 Bremen, Germany |
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Abstract: | We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive elementary cellular automata and find that the overall number of complex patterns decreases under increasing neighborhood size in regular graphs. As exemplary applications, we apply the formalism to complex networks and compare the potential of scale-free graphs and metabolic networks to generate complex dynamics. |
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