On Patterns and Dynamics of Rule 22 Cellular Automaton

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 cellstate 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 nontrivial 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.

On complexity of colloid cellular automata

“…The use of xor gates in modern circuit design offers several advantages, such as reduced representation size and improved testability, and optimal power consumption [35]. CA governed by xor gate exhibit unpredictable dynamics, similar to that of that randomly generated patterns [36] and, when evolve from single non-zero state configurations produced fractal patterns -Sierpenski gasket [37]. An evolution of rule f 7 CA started from a single cell in state '1' is shown in (Fig.…”