# Global Recurrence Plot of Cellular Automaton Dynamic

Global Recurrence Plot of Cellular Automaton Dynamic

A global recurrence plot defined by the expression , where is a function of the step, shows the recurrence of states in the space of all possible states (phase space). Instances of indicate two steps at which the same state occurs.

R(x,y)=|f(x)-f(y)|

f(n)

th

n

R(x,y)=0

Recurrence plots can be used to analyze cellular automaton (CA) evolution. Calculating the mean, total, or binary-to-decimal of each step in an elementary CA's evolution illustrates its behavior. This Demonstration uses random finite initial conditions.