Dynamics is the study of time-dependent phenomena.
The work here concentrates mostly on symbolic and measurable dynamics. One-dimensional symbolic dynamics has a well developed theory but the higher dimensional case is considerably more subtle and its theory still in infancy. The systems have close relations to certain tiling systems and as a consequence of this the undecidability, NP-completeness etc. Through the last strong connections to Statistical Mechanics come around. Cellular automata are a special case of multidimensional Markov-shifts but because of their importance in physics and elsewhere in natural sciences their study warrants an extra set of questions to be asked.