Eightcells

Eightcells is a term used in grid-based modeling to describe the set of eight cells surrounding a central cell on a two-dimensional square lattice. This configuration is commonly associated with the Moore neighborhood of radius 1, excluding the central cell. The eight surrounding locations are the eight compass directions: north, northeast, east, southeast, south, southwest, west, and northwest.

Although commonly called the eight-neighborhood, there is overlap with the Moore neighborhood concept. In some texts the phrase eightcells emphasizes the exclusion of the central cell, whereas others treat it as synonymous with the Moore 8-neighborhood. The term is not formalized in a single standard, but it is widely understood in discussions of local interactions in grid-based models.

Uses include cellular automata, where update rules depend on the states of the eight neighboring cells, and image processing or spatial statistics that apply filters over a 3x3 window centered on a pixel or cell. In such contexts, the eightcells set is the input neighborhood for convolution, smoothing, edge-detection, or pattern recognition tasks.

Implementation notes: on a discrete grid, the eightcells coordinates relative to the center are (-1,-1), (0,-1), (1,-1), (-1,0), (1,0), (-1,1), (0,1), (1,1). Handling grid edges requires padding, wrap-around, or truncation depending on boundary conditions. Performance considerations include avoiding double counting and ensuring consistent ordering of neighbors.

See also: Moore neighborhood; von Neumann neighborhood; 3x3 kernel; cellular automata; image processing.