Fundamental to finite automata is eventually periodic evolution, prolonged to the full number of states in the exceedingly rare event that their sequence is cyclic. The number of ``states'' of a cellular automaton is the number of configurations (not states per cell), providing an exponentially large bound relative to the automaton's length. In practice, many short cycles usually predominate over a few long ones, almost always reached through transients.

Longer automata admit longer cycles and longer transients too; the infinite limit may lack cycles. Cyclic boundary conditions locate behavior repeating over a finite range, leaving truly aperiodic configurations for a separate study.

- Cycles in Life
- Evolution for Rule 22 - one dimensional Life
- Evolutionary diagrams and matrices
- Evolution of a seven-cell ring
- Cycles for a sixteen-member ring
- Cycles for Rule 22
- The evolution matrix
- The reduced evolution matrix

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