  Surface roughness emerges naturally during mechanical removal of material,
fracture, chemical deposition, plastic deformation, indentation, and other
processes. Here, we use continuum simulations to show how roughness which is
neither Gaussian nor self-affine emerges from repeated elastic-plastic contact
of rough and rigid surfaces on a flat elastic-plastic substrate. Roughness
profiles change with each contact cycle, but appear to approach a steady-state
long before the substrate stops deforming plastically and has hence
"shaken-down" elastically. We propose a simple dynamic collapse for the
emerging power-spectral density, which shows that the multi-scale nature of the
roughness is encoded in the first few indentations. In contrast to macroscopic
roughness parameters, roughness at small scales and the skewness of the height
distribution of the resulting roughness do not show a steady-state, with the
latter vanishing asymptotically with contact cycle.
