Poincaré recurrence time

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 \(t_P = k^n\).

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