The wiring options define how each ``target`` cell is connected to other cells with respect to its notional or ``pseudo-neighbourhood'' of nearest neighbours. In cellular automata (regular 1d or 2d) the actual (local) neighbourhood is identical to the pseudo-neighbourhood. In a ``non-local`` network the set of cells that influence a given cell (its actual ``neighbourhood'' to use the term loosely) may be scattered arbitrarily within the network. Each scattered cell is mapped back (or wired) to one position in the target cell's pseudo-neighbourhood. This allows a CA rule to be applied equally to regular CA and to networks with non-local connections (see ``Rules`` #13).
In 1d networks the pseudo-neighbourhood (size k=1-9) is centred on the target cell (odd neighbourhoods have an extra cell on the right) as shown below, where ``o'' represents the target cell and ``x'' its pseudo-neighbours. Cells in the pseudo-neighbourhood are indexed k-1, k-2, ....0.
1 2 3 4 5 6 7 8 9
o ox xox xoxx xxoxx xx0xxx xxxoxxx xxxoxxxx xxxxoxxxx
In 2d networks, the pseudo-neighbourhoods (size 1-9) are defined and indexed as shown below (again, ``o`` represents the target cell and ``x'' its pseudo-neighbours).
1 2 3 4 5 6 7(odd) 7(ev) 8 9
x x x xxx xx xx xxx xxx
o o xox xox xox xox xox xox xox xox
x xx xx X X xxx
1 3 3 543 65 65 765 876
0 0 210 210 421 210 432 432 432 543
0 10 10 1 0 210