Nonstandard roughness of terraced surfaces

We present a class of surfaces which are simultaneously Bat and rough over the same range of lengths. They are self-affine, have well-defined roughness exponents, and consist of terraces of all sizes. The coexistence of flat and rough makes them respond to different external interactions with variable roughness. We demonstrate this for optical scattering (including x rays), two wetting situations, diffusion currents, and catalysis. A terraced Cu surface is a "self-assembled" experimental example, and designs For nano- and micromachined examples are presented.