Detrended fluctuation analysis for fractals and multifractals in higher dimensions

Details Detrended fluctuation analysis for fractals and multifractals in higher dimensions Detrended fluctuation analysis for fractals and multifractals in higher dimensions

2006-07-23

arxiv.org/abs/physics/0607194v2

Physical Review E 74, 061104 (2006)

Physics

General Physics

7 Revtex pages inluding 11 eps figures

Scientific paper

10.1103/PhysRevE.74.061104

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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