On the fractal dimension of self-affine profiles
- 21 December 1994
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 27 (24) , 8079-8089
- https://doi.org/10.1088/0305-4470/27/24/018
Abstract
One-dimensional profiles f(x) can be characterized by a Minkowski-Bouligand dimension D and by a scale-dependent generalized roughness W(f, epsilon ). This roughness can be defined as the dispersion around a chosen fit to f(x) in an epsilon -scale. It is shown that D=limepsilon to 0(2-In W(f, epsilon )/In epsilon ) holds for profiles nowhere differentiable. This establishes a close connection between the roughness and the fractal dimension and proves that D=2-H for self-affine profiles (H is the roughness or Hurst exponent). Two numerical algorithms based on the roughness, one around the local average (f(x))epsilon (usual roughness) and the other around the local RMS straight line (a generalized roughness), are discussed. The estimates of D for standard self-affine profiles are reliable and robust, especially for the last method.Keywords
This publication has 8 references indexed in Scilit:
- Experimental measurements of the roughness of brittle cracksPhysical Review Letters, 1992
- Dynamic scaling and phase transitions in interface growthPhysica A: Statistical Mechanics and its Applications, 1990
- The effects of attractive and repulsive interactions on three-dimensional reaction-limited aggregationJournal of Colloid and Interface Science, 1990
- Self-affine fractal interfaces from immiscible displacement in porous mediaPhysical Review Letters, 1989
- Random fractals: Self-affinity in noise, music, mountains, and cloudsPhysica D: Nonlinear Phenomena, 1989
- Evaluating the fractal dimension of profilesPhysical Review A, 1989
- Evaluation de la dimension fractale d'un grapheRevue de Physique Appliquée, 1988
- Self-Affine Fractals and Fractal DimensionPhysica Scripta, 1985