Transition Phenomena in Cellular Automata Rule Space

We define several qualitative classes of cellular automata (CA) behavior, based on various statistical measures, and describe how the space of all cellular automata is organized. As a cellular automaton is changed by varying entries in its rule table, abrupt changes in qualitative behavior may occur. These abrupt changes have the character of bifurcations in smooth dynamical systems, or of phase transitions in statistical mechanical systems. The most complex CA rules exhibit many of the characteristics of second-order transitions.