Stochastic Models That Separate Fractal Dimension and the Hurst Effect
Abstract
Fractal behavior and longrange dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by selfsimilar random functions, thereby implying a linear relationship between fractal dimension, a measure of roughness, and Hurst coefficient, a measure of longmemory dependence. This letter introduces simple stochastic models which allow for any combination of fractal dimension and Hurst exponent. We synthesize images from these models, with arbitrary fractal properties and powerlaw correlations, and propose a test for selfsimilarity.
 Publication:

SIAM Review
 Pub Date:
 January 2004
 DOI:
 10.1137/S0036144501394387
 arXiv:
 arXiv:physics/0109031
 Bibcode:
 2004SIAMR..46..269G
 Keywords:

 Cauchy class;
 fractal dimension;
 fractional Brownian motion;
 Hausdorff dimension;
 Hurst coefficient;
 longrange dependence;
 powerlaw covariance;
 selfsimilar;
 simulation;
 Physics  Data Analysis;
 Statistics and Probability;
 Mathematics  Probability;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 8 pages, 2 figures