Garden of eden configurations for 2-D cellular automata with rule 2460N
An important problem in cellular automata theory is the reversibility of a cellular automaton which is related to the existence of Garden of Eden configurations in cellular automata. In this paper, we study new local rules for two-dimensional cellular automata over the ternary field Z3 Z 3 (the set of integers modulo three) with some of their important characteristics. We obtain necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional ternary cellular automata. Also by making use of the matrix representation of two-dimensional cellular automata, we provide an algorithm to obtain the number of Garden of Eden configurations for two-dimensional cellular automata defined by rule 2460N. We present an application of the reversible two-dimensional ternary cellular automata to cryptography.
garden of eden cellular automata matrix algebra