Classification of 2D Cellular Automata Nongroup Rules

Cellular automata (CA) are self-organizing lattices consisting of cell grids, and the state of each cell can be updated according to the neighboring cell states. The updating rules depend on the neighbors involved in updating a particular cell. In a two-dimensional CA (2DCA) structure, each cell has nine neighbors, including the cell itself. The CA characteristics may change depending on the nature of the operations and the set of neighbors used. Accordingly, researchers have used the 2DCA group rules as a tool to model complex systems in various applications, including artificial intelligence, genomics, computer architecture, graphics, image processing, engineering, and physics. However, nongroup 2DCA rules contain a large number of rules, and the general behavior of all these rules has not yet been studied. In this study, the behavior of 2DCA nongroup rules with null boundary conditions was investigated, and the rules were classified into three categories based on their cycle length and depth. In addition, we applied these classifications to propose a cellular automata-based pseudo-random number generator (PRNG). Statistical tests were performed to validate the suitability of the nongroup CA rules for PRNGs.