We introduce two new types of random field. The cross correlation field R(s, t) is the usual sample correlation coefficient for a set of pairs of Gaussian random fields, one sampled at point s ∈ <M , the other sampled at point t ∈ <N . The homologous correlation field is defined as R(t) = R(t, t), that is, the ‘diagonal’ of the cross correlation field restricted to the same location s = t. Alth...