A square-shaped neighborhood that can be used to define a set of cells surrounding a given cell
that may affect the evolution of a two-dimensional cellular
automaton on a square grid. The Moore neighborhood
of range
is defined by
Moore neighborhoods for ranges , 1, 2, and 3 are illustrated above. The number of cells
in the Moore neighborhood of range is the odd squares , the first few of which are 1, 9, 25, 49, 81, ... (OEIS
A016754).
Gray, L. "A Mathematician Looks at Wolfram's New Kind of Science." Not. Amer. Math. Soc.50, 200-211, 2003.Sloane,
N. J. A. Sequence A016754 in "The
On-Line Encyclopedia of Integer Sequences."