Outer Median and Probabilistic Cellular Automata on Network Topologies

Oneand two-dimensional cellular automata have traditionally modeled systems with an underlying regular lattice well. However, for other systems, such as those with nonlocal phenomena, running cellular automata over different topologies could result in a simpler, more natural model. The creation of so-called “outer median” rules, and the use of modified probabilistic rules, make it possible to run cellular automata over network topologies. In this way, the rules themselves remain simple while more complicated nonlocal information is encoded in the topology. In this manner we can model systems with nonlocal elements, and briefly consider two examples of such systems: country border relationships and forest fire spread.