Networks cells are indexed and arranged in a regular space with periodic boundary conditions as shown below (where ``x'' represents a cell). A 1d space forms a ring of cells. A 2d space forms a regular orthogonal grid on the torus (except when the neighbourhood is 7, in this case the grid is hexagonal, though shown as orthogonal). The diagrams below illustrate the geometry of 1d and 2d networks .
1d network, (size n) 2d network (size n, i x j)
n-1 n-2 n-3 ... 2 1 0 (column=j-1) (column=0)
x x x ... x x x | |
cell n-1- x x x x x x -(row i-1)
x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x -cell 0 (row=0)