# Poincaré recurrence time

tags
Dynamical systems

The Poincaré recurrence time for a finite dynamical system is the maximal theoretical time after which the system will return to its initial state and the trajectory will repeat.

In the case of a cellular automaton on a grid of size $$n$$ with $$k$$ possible states per cell, the recurrence time is $$t_P = k^n$$.

← Back to Notes