Dekking M. Fractals. Theory and Applications in Engineering 1999

Textbook in PDF format

Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications inEngineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.
Front Matter
Front Matter
From Self-Similarity to Local Self-Similarity: the Estimation Problem
Generalized Multifractional Brownian Motion: Definition and Preliminary Results
Elliptic Self Similar Stochastic Processes
Wavelets for Scaling Processes
Front Matter
Classification of Natural Texture Images from Shape Analysis of the Legendre Multifractal Spectrum
A Generalization of Multifractal Analysis Based on Polynomial Expansions of the Generating Function
Local Effective Hölder Exponent Estimation on the Wavelet Transform Maxima Tree
Easy and Natural Generation of Multifractals: Multiplying Harmonics of Periodic Functions
Front Matter
IFS-Type Operators on Integral Transforms
Comparison of Dimensions of a Self-Similar Attractor
Front Matter
Vector Analysis on Fractal Curves
Local Fractional Calculus: a Calculus for Fractal Space-Time
Front Matter
Conformal Multifractality of Random Walks, Polymers, and Percolation in Two Dimensions
Fractal Pores and Fractal Tunnels: Traps for “Particles” or “Sound Particles”
Fractal Pores and the Degradation of Shales
Continuous Wavelet Transform Analysis of Fractal Superlattices
Front Matter
Mixing in Laminar Chaotic Flows: Differentiable Structures and Multifractal Features
Adhesion AFM Applied to Lipid Monolayers. A Fractal Analysis
Front Matter
Faster Fractal Image Coding Using Similarity Search in a KL-transformed Feature Space
Can One Break the “Collage Barrier” in Fractal Image Coding?
Front Matter
Two Algorithms for Non-Separable Wavelet Transforms and Applications to Image Compression