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Preprint . 2006
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Detrended fluctuation analysis for fractals and multifractals in higher dimensions

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 07 Dec 2006Embargo end date: 01 Jan 2006 English Publisher:American Physical Society (APS)Journal:Physical Review E, volume 74 (issn: 1539-3755, eissn: 1550-2376, Copyright policy )
Authors: Gu, Gao-Feng; Zhou, Wei-Xing;

doi: 10.1103/physreve.74.061104 , 10.48550/arxiv.physics/0607194

pmid: 17280035

arXiv: physics/0607194

Detrended fluctuation analysis for fractals and multifractals in higher dimensions

Abstract

One-dimensional detrended fluctuation analysis (1D DFA) and multifractal detrended fluctuation analysis (1D MF-DFA) are widely used in the scaling analysis of fractal and multifractal time series because of being accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MF-DFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces including fractional Brownian surfaces and multifractal surfaces. The two-dimensional MF-DFA is also adopted to analyze two images from nature and experiment and nice scaling laws are unraveled.

7 Revtex pages inluding 11 eps figures

Related Organizations
Keywords

Physics - General Physics, General Physics (physics.gen-ph), Physics - Data Analysis, Statistics and Probability, FOS: Physical sciences, Data Analysis, Statistics and Probability (physics.data-an)

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 188
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 1%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
188
Top 1%
Top 1%
Top 10%
Green
bronze