Construction and Study of the Mathematical Model for the System Using Three-Dimensional Cellular Automata

The paper considers a three-dimensional mathematical model for a system created using cellular automata. The mathematical model of the system (MMS) is constructed using a cellular automata implements a single methodological approach to the study of systems with a different nature; the analysis of the motion for such a system is described using certain objective laws. The behavior and state of the mathematical model described by the game “Life” under certain rules are studied. The model is based on such rules of automata generation as prolongation of life in the presence of 4.5 and 9 living neighbors and revival with 7,8,3,2 living cells around. The generation was considered in the field 5x5 and 10x10., It is established that the mathematical model comes to a stable state in the first case regardless of the initial state. The transition time for the automata into a stable state increases significantly when the number of living cells reaches more than 28. The problem of determining 4th class automata in a chaotic structure with a long evolution requires further research.