A square-shaped neighborhood that can be used to define a set of cells surrounding a given cell (x_0, y_0) that may affect the evolution of a two-dimensional cellular automaton on a square grid. The Moore neighborhood of range r is defined by N_(x_0, y_0)^M = {(x, y): left bracketing bar x - x_0 right bracketing bar <=r, left bracketing bar y - y_0 right bracketing bar <=r}. Moore neighborhoods for ranges r = 0, 1, 2, and 3 are illustrated above. The number of cells in the Moore neighborhood of range r is the odd squares (2r + 1)^2, the first few of which are 1, 9, 25, 49, 81, ... (OEIS A016754).
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