On a square grid of 1 ohm resistors, the effective resistance between the node at (0,0) and the node at (p,q) is given by the following expression. R[p,q] = (1/(4 pi^2)) int (F(x,y), x=-pi..pi, y=-pi..pi), F(x,y) = [1 - cos(p x + q y)] / [2 - (cos x + cos y)]. This can be generalized to the cubic array in d dimensions. R[p[1], ... , p[d]] is (2 pi)^(-d) times the integral over [-pi, pi]^d of the fraction whose numerator is 1 - cos(p[1] x[1] + ... + p[d] x[d]), and whose denominator is d - (cos x[1] + ... + cos x[d]). Gene ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ