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Outer-totalistic cellular automata on graphs.

Phys. Lett. A 373, 546-549 (2009)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
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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Publication type Article: Journal article
Document type Scientific Article
Keywords complex networks; statistical-mechanics; pattern-formation; topology; computation; robustness; stability; emergence; model
Reviewing status