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We investigate invasion percolation fingers in'a quenched medium in which the randomness has a gradient following a power law both in the direction of the flow and perpendicular to it. The first gradient corresponds to a pressure gradient, the second one to the density of microcracks that arises in a self-organized way around a large crack. We, give an argument for the value of the fractal dimension as found in previous simulations. We calculate the roughness exponent of the fingers and find adoi:10.1088/0305-4470/26/22/003 fatcat:3rlnrxswcjgktfwysgsh4dciou