A New Parameter $F$ to Classify Cellular Automata Rule Table Space and a Phase Diagram in $\lambda-F$ Plane

Abstract

It is shown that for the N-neighbor and K-state cellular automata, the class II, class III and class IV patterns coexist at least in the range $\frac{1}{K} \le \lambda \le 1-\frac{1}{K} $. The mechanism which determines the difference between the pattern classes at a fixed $\lambda$ is found, and it is studied quantitatively by introducing a new parameter $F$. Using the parameter F and $\lambda$, the phase diagram of cellular automata is obtained for 5-neighbor and 4-state cellular automata. PACS: 89.75.-k Complex Systems