Models for correlated multifractal hypersurfaces

Details Models for correlated multifractal hypersurfaces Models for correlated multifractal hypersurfaces

Mar 2003

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003phrve..67c6702t&link_type=abstract

Physical Review E, vol. 67, Issue 3, id. 036702

Mathematics

Probability

Mathematical Procedures And Computer Techniques, Fluctuation Phenomena, Random Processes, Noise, And Brownian Motion, Probability Theory, Stochastic Processes, And Statistics, Porous Materials, Granular Materials

Scientific paper

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.

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