PROJECTED MEASURES - A SIMPLE WAY TO CHARACTERIZE FRACTAL STRUCTURES AND INTERFACES

The properties of projected measures of fractal objects are investigat ed in detail. In general, projected measures display multifractal feat ures which play a role in the evolution of dynamic phenomena on/throug h fractal structures. Closed-form results are obtained for the moment hierarchy of model fractal interfaces. The distinction between self-si milar and self-affine interfaces is discussed by considering the prope rties of multifractal spectra, the orientational effects in the behavi or of the moment hierarchies, and the scaling of the corresponding Fou rier transforms. The implications of the properties of projected measu res in the characterization of transfer phenomena across fractal inter faces are briefly analyzed.