In this letter, a theoretical method for the analysis of diffusive flux/current to limited scale selfaffine random fractals is presented and compared with experimentally measured electrochemical current for such roughness. The theory explains the several experimental findings of the temporal scale invariance as well as deviation from this of current transients in terms of three dominant fractal parameters for the limited-length scales of roughness. This theoretical method is based on limited scale power-law characterization of the interfacial roughness spectrum and the solution