title: Models for correlated multifractal hypersurfaces.
abstract: We discuss and implement computer approximations of fractal and multifractal hypersurfaces. These hypersurfaces consist of reconstructions of a stochastic process in the real space from randomly distributed variables in the discrete wavelet domain. The synthetic surfaces have the usual fractional Brownian motion as a particular case, and inherit the correlation structure of these fractals. We first introduce the one-dimensional version of these surfaces that obey a weak self-affine symmetry. This symmetry appears in the wavelet domain as a condition on the second moments of the probability distributions of the wavelet coefficients. Then we use these relations to define the fractals and multifractals in d dimensions. Finally, we concentrate on the generation of samples of these hypersurfaces.
authors.affiliation: International Center for Complex Systems and Departamento de Física Teórica e Experimental-UFRN, Natal-RN 59078-970, Brazil.
authors.forename: D M
authors.initials: DM
authors.lastname: Tavares
authors.forename: L S
authors.initials: LS
authors.lastname: Lucena