A Monte Carlo method for simulating fractal surfaces

A Monte Carlo method is presented for simulating rough surfaces with the fractal behavior. The simulation is based on power-law size distribution of asperity diameter and self-affine property of roughness on surfaces. A probability model based on random number for asperity sizes is developed to generate the surfaces. By iteration, this method can be used to simulate surfaces that exhibit the aforementioned properties. The results indicate that the variation of the surface topography is related to the effects of scaling constant G and the fractal dimension D of the profile of rough surface. The larger value of D or smaller value of G signifies the smoother surface topography. This method may have the potential in prediction of the transport properties (such as friction, wear, lubrication, permeability and thermal or electrical conductivity, etc.) on rough surfaces.