Claude Tricot

Fractals in Engineering

Pattern Formation in Metal on Metal Epitaxy, P 0 Hwang and P J Behm Scaling in the Frequency-Dependent Admittance of Electrodeposited Fractal Electrodes, A E Larsen et al. Resonant Optics of Fractals, V Shalaev et al. Fractal Surfaces in Engineering: Applications of Dynamic Scaling, F Family Fractals in Fluid Mechanics, K R Sreenivasan Diffusional Analysis of Intermittent Two-Phase Flow Transitions, M Giona et al. Anomalous Relaxation in Noise-Driven Bistable Systems, S J Fraser & R Kaptal Complexity Maps Reveal Clusters in Neuronal Arborizations, B Dubuc et al. Infrared Scene Modeling and Interpolation Using Fractional Levy Stable Motion, S M Kogon & D G Manolakis Solving the Inverse Problem for Function/Image Approximation Using Iterated Function Systems: 1. Theoretical Basis, B Forte & E R Vrscay Solving the Inverse Problem for Function/Image Approximation Using Iterated Function Systems: 11. Algorithm and Computations, B Forte & E R Vrscay Fractal Image Compression, Y Fisher Utilization of Fractal Image Models in Medical Image Processing, W S Kuklinski Universal Multifractals in Seismicity, C Hooge et al. Determination of Fractal Scales on Trabecular Bone X-Ray Images, R Harba et al. Developing a New Method for the Identification of Microorganisms for the Food Industry Using the Fractal Dimension, O Castillo & P Melin. (Part contents).

On Various Multifractal Spectra

We introduce two classes of multifractal spectra, called respectively dimension and continuous spectra. Dimension spectra offer an interesting alternative to the classical Hausdorff spectrum: They are much easier to estimate yet still give relevant information about the geometry of the Holder function. Continuous spectra are a generalization of the large deviation spectrum that allow to obtain partition free results. Both classes of spectra allow to perform efficient multifractal analysis in an experimental framework.

A model for rough surfaces

Data obtained from sized road tracks or rubber samples do not show a self-affinity behavior, and the usual fractal models such as the Fractional Brownian Motion are not in order. We propose here a much simpler model called the Random Bumps Functions, which allow to describe such surfaces with a good accuracy and a very few parameters. The validity of the model is checked using q-structure functions. Applications are made to experimental sets of data.