DOI: 10.1142/s0218127427500192 ISSN: 0218-1274
Convergence of Finite Cellular Automata Over Cayley Tree
Bipul Patra, Subrata Paul, Sukanta DasThis work studies the convergence of Cellular Automata (CA) over Cayley tree of order 2. Each node of the Cayley tree is considered as a cell and its adjacent nodes are the neighbors of the cell. This work considers finite CAs that have two-state and four-neighborhood dependency. The fixed point configurations of such a CA are investigated by introducing the fixed point graph. This work further introduces [Formula: see text]-coefficient for the CA to investigate its dynamical behavior. A statistical technique is developed to precisely find D-coefficient of a given CA. It is observed experimentally that the [Formula: see text]-coefficient can satisfactorily predict the convergence of such a CA.