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Generalized Binomial Multiplicative Cascade Processes and Asymmetrical Multifractal Distributions : Volume 21, Issue 2 (04/04/2014)

By Cheng, Q.

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Book Id: WPLBN0003992444
Format Type: PDF Article :
File Size: Pages 11
Reproduction Date: 2015

Title: Generalized Binomial Multiplicative Cascade Processes and Asymmetrical Multifractal Distributions : Volume 21, Issue 2 (04/04/2014)  
Author: Cheng, Q.
Volume: Vol. 21, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Cheng, Q. (2014). Generalized Binomial Multiplicative Cascade Processes and Asymmetrical Multifractal Distributions : Volume 21, Issue 2 (04/04/2014). Retrieved from

Description: State Key Lab of Geological Processes and Mineral Resources, China University of Geosciences, Beijing and Wuhan, China. The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a five-parameter binomial multiplicative cascade model is proposed based on the anisotropic partition processes. Each partition divides the unit set (1-D length or 2-D area) into h equal subsets (segments or subareas) and m1 of them receive d1 (> 0) and m2 receive d2 (> 0) proportion of the mass in the previous subset, respectively, where m1+m2 ≤ h. The model is demonstrated via several examples published in the literature with asymmetrical fractal dimension spectra. This model demonstrates the various properties of asymmetrical multifractal distributions and multifractal indices with explicit functions, thus providing insight into and an understanding of the properties of asymmetrical binomial multifractal distributions.

Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions

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