Matrix characteristics for two dimensional nongroup Cellular Automata

In this paper we explore the properties of two dimensional Cellular Automata based on its matrix characteristics. In general, Cellular Automata is divided into two classes: group and nongroup Cellular Automata, each of which has its own matrix characteristics with the different properties. In this paper we restrict our study to nongroup Cellular Automata because of its uniqueness properties. The nongroup Cellular Automata will evolve unpredictably when its matrix characteristics is not uniform, as a consequence it yields a tree structure with cycles and/or loops, or none. Two Dimensional Cellular Automata is more complex than that of one dimensional CA, so we need to simplify this model by reducing the number of its neighbourhoods and use a particular type of CA, i.e. Additive Cellular Automata.