k-neighborhood for Cellular Automata
arXiv:1605.08870
Abstract
A neighborhood for d-dimensional cellular automata is introduced that spans the range from von Neumann to Moore neighborhood using a parameter which represents the dimension of hypercubes connecting neighboring cells. The neighborhood is extended to include a concept of radius. The number of neighbors is calculated. For diamond-shaped neighborhoods, a sequence is obtained whose partial sums equal Delannoy numbers.
8 pages, 3 figures, 12 references, OEIS: A265014, A266213