The criteria for surface reproducibility during erosion or growth

The general theory of erosion and growth of a surface, treated as an advancing (or retreating) wavefront, is applied to evaluate the conditions necessary to ensure time-independent surface reproducibility. It is shown that homogeneous and heterogeneous systems must be analysed separately and that, in the former case, surface reproducibility only occurs for well-defined variations in the surface normal velocity with surface orientations. In the latter case, spatial variations in the surface normal velocity can compensate for the orientational variations.