Fractal approach to two-dimensional and three-dimensional surface roughness

Our aim is to show that a fractal number D can be associated with any profile or cartography. Its interest lies in the fact that it conveys in a most concise form all the basic information otherwise provided by numerous parameters or criteria. Our approach, based on Mandelbrot's work, consists in processing a z(x) profile as would be done with a random motion x(t). An original approach, the “reticular cell counting” method, has been successfully applied to simulated or sampled surfaces.