Gradient percolation in three dimensions and relation to diffusion fronts

Percolation in a concentration gradient has been carried out for the cubic lattice. In contradistinction with the two-dimensional case, the frontier of the infinite cluster extends over a macroscopic range of concentrations. In that range almost all occupied sites belong to the frontier which has dimension three. This defines an ideally porous material. The ratio of the local concentrations of the frontier and its external perimeter is equal to the ratio of the local overall concentrations of occupied and empty sites.