Describing complex dynamics in life-like rules with de Bruijn diagrams on complex and chaotic cellular automata

De Bruijn diagrams are useful tools for a systematic analysis of onedimensional cellular automata (CA), i.e. calculating particular kinds of configurations, ancestors, complex patterns, cycles, Garden of Eden configurations, and formal languages. The de Brujin diagrams are barely employed in two-dimensions because complexity of their calculation increases exponentially.We apply de Bruijn diagrams for analysis of two evolution rules in two dimensions: the Conway’s Game of Life and the quasi-chaotic Diffusion Rule.