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Moore Neighborhood

المؤلف:  Gray, L

المصدر:  "A Mathematician Looks at Wolfram,s New Kind of Science." Not. Amer. Math. Soc. 50

الجزء والصفحة:  ...

22-8-2021

2030

Moore Neighborhood

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

{(x,y):|x-x_0|<=r,|y-y_0|<=r}. " src="https://mathworld.wolfram.com/images/equations/MooreNeighborhood/NumberedEquation1.gif" style="height:22px; width:244px" />

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).

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REFERENCES:

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."