Operator Representation and Class Transitions in Elementary Cellular Automata

We exploit the mirror and complementary symmetries of elementary cellular automata (ECAs) to rewrite their rules in terms logical operators. The operator representation based on these fundamental enables us construct a periodic table ECAs that maps all unique clusters similar asymptotic behavior. also expand automaton (ECA) dynamics by introducing parameter scales pace with which operators iterate system. While tuning this continuously, further emergent behavior is unveiled as several undergo multiple phase transitions between periodic, chaotic complex (class 4) This extension provides an environment for studying class ECAs. Moreover, emergence 4 structures can potentially enlarge capacity many ECA universal computation.