Structure of Rule Table and Phase Diagram of One Dimensional Cellular Automata

Abstract

In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$. With this parameter, the phase diagram for an one dimensional cellular automata is obtained. Our result explains why the edge of chaos(class IV) is scattered rather wide range in $\lambda$ around 0.5, and presents an effective way to control the pattern classes. \noindent PACS: 89.75.-k Complex Systems