Detrended fluctuation analysis for fractals and multifractals in higher dimensions

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...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2006-12, Vol.74 (6 Pt 1), p.061104-061104, Article 061104
Main Authors: Gu, Gao-Feng, Zhou, Wei-Xing
Format: Article
Language:English
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Summary: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.
ISSN:1539-3755
1550-2376
DOI:10.1103/physreve.74.061104