Complex dynamics in life-like rules described with de Bruijn diagrams: Complex and chaotic cellular automata

De Bruijn diagrams have been used as a useful tool for the systematic analysis of one-dimensional cellular automata (CA). They can be used to calculate particular kind of configurations, ancestors, complex patterns, cycles, Garden of Eden configurations and formal languages. However, there is few progress in two dimensions because its complexity increases exponentially. In this paper, we will offer a way to explore systematically such patterns by de Bruijn diagrams from initial configurations. Such analysis is concentrated mainly in two evolution rules: the famous Game of Life (complex CA) and the Diffusion Rule (chaotic CA). We will display some preliminary results and benefits to use de Bruijn diagrams in these CA.