Non-homogeneous fractal-like colonization processes, where the cluster of visited sites has large voids and grows slowly, could explain the negative results of Search for Extraterrestrial Intelligence (SETI) preserving the possibility of a galactic spanning civilization. Here we present a generalized invasion percolation model to illustrate a minimal colonization process with large voids and delayed colonization. Spatial correlation between unvisited sites, in the form of large empty regions, suggests that to search civilizations in the Sun neighbourhood may be a misdirected SETI strategy. A weaker form of the Fermi Paradox also suggests this last conclusion.