  We consider discrete dynamical systems and lattice models in statistical
mechanics from the point of view of their symmetry groups. We describe a C
program for symmetry analysis of discrete systems. Among other features, the
program constructs and investigates phase portraits of discrete dynamical
systems modulo groups of their symmetries, searches dynamical systems
possessing specific properties, e.g., reversibility, computes microcanonical
partition functions and searches phase transitions in mesoscopic systems. Some
computational results and observations are presented. In particular, we explain
formation of moving soliton-like structures similar to ``spaceships'' in
cellular automata.
