Detrended fluctuation analysis for fractals and multifractals in higher dimensions

Gao-Feng Gu and Wei-Xing Zhou

Phys. Rev. E 74, 061104 – Published 7 December 2006

Abstract

One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MFDFA) are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MFDFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces including fractional Brownian surfaces and multifractal surfaces. The two-dimensional MFDFA is also adopted to analyze two images from nature and experiment, and nice scaling laws are unraveled.

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Received 8 August 2006

DOI:https://doi.org/10.1103/PhysRevE.74.061104

Authors & Affiliations

Gao-Feng Gu^1,2 and Wei-Xing Zhou^1,2,3,*

¹School of Business, East China University of Science and Technology, Shanghai 200237, China
²Research Center of Systems Engineering, East China University of Science and Technology, Shanghai 200237, China
³School of Science, East China University of Science and Technology, Shanghai 200237, China

^*Electronic address: wxzhou@moho.ess.ucla.edu

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Issue

Vol. 74, Iss. 6 — December 2006

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics