In paper are spend analysis of two classes of operations on geometric images of automaton models of discrete dynamical systems. The operations of combining and regularization of geometrical images of automaton mappings are investigated. As a means of regularization of the partially defined automaton mappings are used both the classical interpolation methods of the numerical graphs and their new modifications. Various operations of combining of geometrical images are investigated. For the selected class of combining opera-tions is made an analysis of the dependence of the number of states of the automaton, the geometric image of which is obtained as a result of the juxtaposition of geometric images of basic automatons, from the powers of the sets of states of basic automatons. The effectiveness of various methods of interpolation is investigated for regularization of partially defined geometric images of automatons.