BEYOND CLASSICAL MULTIFRACTAL ANALYSIS USING WAVELETS: UNCOVERING A MULTIPLICATIVE PROCESS HIDDEN IN THE GEOMETRICAL COMPLEXITY OF DIFFUSION LIMITED AGGREGATES
Autor: | Françoise Argoul, J. F. Muzy, Emmanuel Bacry, M. Tabard, Alain Arneodo |
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Přispěvatelé: | Centre de recherches Paul Pascal (CRPP), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées (CMAP), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS) |
Jazyk: | angličtina |
Rok vydání: | 1993 |
Předmět: |
Dynamical systems theory
Applied Mathematics [PHYS.PHYS.PHYS-BIO-PH]Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph] Mathematical analysis Wavelet transform Multifractal system Invariant (physics) 01 natural sciences Fractal analysis 010305 fluids & plasmas Fractal Wavelet Modeling and Simulation 0103 physical sciences Geometry and Topology Invariant measure Statistical physics 010306 general physics ComputingMilieux_MISCELLANEOUS Mathematics |
Zdroj: | Fractals Fractals, World Scientific Publishing, 1993, 1 (3), pp.629-649. ⟨10.1142/s0218348x93000666⟩ |
ISSN: | 0218-348X |
DOI: | 10.1142/s0218348x93000666⟩ |
Popis: | We emphasize the wavelet transform as a very promising tool for solving the inverse fractal problem. We show that a dynamical system which leaves invariant a fractal object can be Uncovered from the space-scale arrangement of its wavelet transform modulus maxima. We illustrate our theoretical considerations on pedagogical examples including Bernoulli invariant measures of linear and nonlinear expanding Markov maps as well as the invariant measure of period-doubling dynamical systems at the onset of chaos. We apply this wavelet based technique to analyze the fractal properties of DLA azimuthal Cantor sets defined by intersecting the inner frozen region of large mass off-lattice DLA clusters with a circle. This study clearly reveals the existence of an underlying multiplicative process that is likely to account for the Fibonacci structural ordering recently discovered in the apparently disordered arborescent DLA morphology. The statistical relevance of the golden mean arithmetic to the fractal hierarchy of the DLA azimuthal Cantor sets is demonstrated. |
Databáze: | OpenAIRE |
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