In cellular automata, the von Neumann neighborhood comprises the four cells orthogonally surrounding a central cell on a two-dimensional square lattice. The neighborhood is named after John von Neumann, who used it for his pioneering cellular automata including the Universal Constructor. It is one of the two most commonly used neighborhood types, the other one being the 8-cell Moore neighborhood.
The concept can be extended to higher dimensions, for example forming a 6-cell octahedral neighborhood for a cellular automaton in three dimensions.
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