MooreNeighbour

Moore neighbourhood, also spelled Moore neighborhood in British English, is a concept used in cellular automata and image processing to describe the set of grid cells surrounding a central cell on a two-dimensional square lattice that are considered its neighbors. For radius 1, the Moore neighbourhood consists of the eight surrounding cells: north, northeast, east, southeast, south, southwest, west, and northwest. The central cell itself is not included. It is named after Edward F. Moore, who introduced the idea in theoretical computer science.

Generalization and contrast: The radius parameter r expands the neighbourhood to all cells with Chebyshev distance at most r, resulting in (2r+1)^2 − 1 neighbors. For r = 1, eight neighbors; for r = 2, twenty-four neighbors. By contrast, the von Neumann neighbourhood (the four-neighborhood) includes only the orthogonally adjacent cells (north, south, east, west).

Applications and relevance: In cellular automata, many rule sets use the Moore neighbourhood to determine a cell’s next state based on the states of the surrounding eight cells, as seen in variants of the Game of Life. In image processing, the Moore neighbourhood corresponds to 8-connectedness and is used in morphological operations, local filtering, and neighborhood-based feature analysis.

Edge cases and general remarks: On finite grids, edge handling schemes such as toroidal wrapping, reflection, or clipping affect which neighbors are counted at borders. In theoretical discussions, an infinite lattice is often assumed. In three dimensions, the Moore neighbourhood generalizes to all cells with Chebyshev distance 1, totaling 26 neighboring cells.