Phase Transitions in Cellular Automata

In many systems in nature and elsewhere, we find discrete structures — even when the underlying system is seemingly continuous. One origin of such discreteness is the phenomenon of phase transitions.

In this minimal example of a phase transition, we examine a particular three-color cellular automaton initialized with varying densities of black cells. Although we can continuously vary the initial density from all white to all black, the computation the cellular automaton performs changes in a discrete way.