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The Dynamics of Cellular Automata on 2-Manifolds is Affected by Topology
David J. Warne and Ross F. Hayward

In this paper, we demonstrate that the distribution of Wolfram classes within a cellular automata rule space in the triangular tessellation is not consistent across different topological general. Using a statistical mechanics approach, cellular automata dynamical classes were approximated for cellular automata defined on genus-0, genus-1 and genus-2 2-manifolds. A distribution-free equality test for empirical distributions was applied to identify cases in which Wolfram classes were distributed differently across topologies. This result implies that global structure and local dynamics contribute to the long term evolution of cellular automata.

Keywords: Dynamical class changes, topology, 2-manifold, triangular tessellation, topological genus, 3-regular graphs

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