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Detrended fluctuation analysis for fractals and multifractals in higher dimensions

Gao-Feng Gu·Wei-Xing Zhou
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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.

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Gao-Feng Gu, Wei-Xing Zhou. 2006-08-08. Detrended fluctuation analysis for fractals and multifractals in higher dimensions. https://doi.org/10.1103/physreve.74.061104

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