Reversibility, Simulation and Dynamical Behaviour

A cellular automaton (CA) is reversible if it repeats its configuration in a cycle.Reversible one-dimensional CA are studied as automorphisms of the shift dynamicalsystem, and analyses using graph-theoretical approaches and with block permutations. Reversible CA are dynamical systems which conserve their initial information.This is why they pose a particular interest in mathematics, coding and cryptography.