Detecting self-similarity in surface microstructures

Abstract

The relative configurational entropy per cell as a function of length scale is a sensitive detector of spatial self-similarity. For Sierpinski carpets the equally separated peaks of the above function appear at the length scales that depend on the kind of the carpet. These peaks point to the presence of self-similarity even for randomly perturbed initial fractal sets. This is also demonstrated for the model population of particles diffusing over the surface considered by Van Siclen, Phys. Rev. E 56 (1997) 5211. These results allow the subtle self-similarity traces to be explored.

9 pages, 4 figures, presented at ECOSS18 (Vienna) Sept. 1999

References in corpus (3)

• Microstructure analysis of reconstructed porous media
• Entropic measure of spatial disorder for systems of finite-sized objects
• What is a physical measure of spatial inhomogeneity comparable to the mathematical approach?

Cited by in corpus (11)

• Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy
• Microstructure reconstruction using entropic descriptors
• Entropic descriptor of a complex behaviour
• Inhomogeneity and complexity measures for spatial patterns
• Versatile entropic measure of grey level inhomogeneity
• Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands
• Statistical Reconstruction of Microstructures Using Entropic Descriptors
• Decomposable multiphase entropic descriptor
• A generalization of the inhomogeneity measure for point distributions to the case of finite size objects
• Effective conductivity in a lattice model for binary disordered media with complex distributions of grain sizes
• Duality and spatial inhomogeneity