Roughness exponents to calculate multi-affine fractal exponents

Abstract

We propose a new method to determine the multi-affine fractal exponents based on a generalization of the roughness concept. For synthetic multi-attine fractal profiles with exactly known exponents, we show that the results obtained in this method are more accurate than the results obtained with the height-height correlation function method. Also in the present method, scaling is observed using profiles with a number of points more than one order of magnitude smaller.