Matrix Model of Deterministic Synchronous Cellular Automata

The paper presents an approach for modeling deterministic synchronous cellular automata by matrices and operations on them. It is proposed to renumber the states of the automaton and write down a matrix, the elements of which are the current states (numbers associated with them) of the cells of the automaton. It is proposed to calculate the matrix of cell states in the next cycle in two stages: find the convolution of the current matrix with a special core, and map the resulting convolution matrix into the matrix of cell states in the next cycle. The convolution core is determined by the cell neighborhood pattern, and the convolution mapping to the matrix of the following states is based on the transition function of the automaton.