k-neighborhood for Cellular Automata
Discrete Mathematics
2016-05-31 v1
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.
Cite
@article{arxiv.1605.08870,
title = {k-neighborhood for Cellular Automata},
author = {Dmitry A. Zaitsev},
journal= {arXiv preprint arXiv:1605.08870},
year = {2016}
}
Comments
8 pages, 3 figures, 12 references, OEIS: A265014, A266213