On patterns and dynamics of Rule 22 cellular automaton
arXiv:2005.01480 · doi:10.25088/ComplexSystems.28.2.125
Abstract
Rule 22 elementary cellular automaton (ECA) has a 3--cell neighborhood, binary cell states, where a cell takes state `1' if there is exactly one neighbor, including the cell itself, in state `1'. In Boolean terms the cell-state transition is a XOR function of three cell states. In physico--chemical terms the rule might be seen as describing propagation of self-inhibiting quantities/species. Space-time dynamics of Rule 22 demonstrates non-trivial patterns and quasi-chaotic behavior. We characterize the phenomena observed in this rule using mean field theory, attractors, de Bruijn diagrams, subset diagrams, filters, fractals and memory.
arXiv comment50 pages, 28 figures, 7 tables
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