Table 1.

Multiplicity and Euclidian distances of n^th-nearest neighbors for 2D square and hexagonal lattices. The number of n^th neighbors and their distances from the central pixel differ in a 3D lattice. CompuCell3D calculates distance between neighbors by setting the volume of a single pixel (whether in 2D or 3D) to 1.

Neighbor Order	Number of Neighbors	Euclidian Distance	Number of Neighbors	Euclidian Distance
1	4	1	6	$\sqrt{2}$
2	4	$\sqrt{2}+\sqrt{2}$	6	$\sqrt{6∕\sqrt{3}}$
3	4	2	6	$\sqrt{8∕\sqrt{3}}$
4	8	$\sqrt{5}$	12	$\sqrt{14∕\sqrt{3}}$