From (Hanson, Crutchfield 1997):

Finite state machines are appropriate for investigating pattern dynamics of CAs for a number of reasons, among which we may note the following:

- FAs encompass the full range of behavior types from periodic to complex to random;
- Characterization of patterns using FAs makes possible a definition of pattern complexity which is both natural and computable in practice;
- Ensemble evolution in the space of regular languages is closed under the CA rule;
- The CA update rule is itself an FST;
- Automated inference techniques exist for reconstructing FAs from experimental data

## Bibliography

- James E. Hanson, James P. Crutchfield. . "Computational Mechanics of Cellular Automata: An Example".
*Physica D: Nonlinear Phenomena*, Lattice Dynamics, 103 (1):169–89. DOI.