2D Linear CA with Mixing Boundary Conditions and Reversibility

In this paper, we consider two-dimensional cellular automata (CA) with the von Neumann neighborhood. We study the characterization of 2D linear cellular automata defined by the von Neumann neighborhood with new type of boundary conditions over the field [Formula: see text]. Furthermore, we investigate the rule matrices of 2D von Neumann CA by applying the group of permutations [Formula: see text]. Moreover, the algorithm for computing the rank of rule matrices is given. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for considered two-dimensional cellular automata are obtained.