Presumable applications of cellular automates with strong anticipation in quantum physics

The paper discusses the use of models with discrete geometry in field theory problems. Approaches of cellular automata in problems of quantum field theory are considered. The equations of the model of cellular automata are given taking into account the property of strong anticipation (according Daniel M. Dubois) for such objects and the possible consequences in the interpretation of such solutions are discussed. The illustrations of the behavior of such systems and the possible directions of subsequent research are given. (paper)