Detrended fluctuation analysis for fractals and multifractals in higher dimensions
Authors:
- 7 December 2006
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 74 (6) , 061104
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.Keywords
All Related Versions
This publication has 53 references indexed in Scilit:
- Fast and Exact Simulation of Fractional Brownian SurfacesJournal of Computational and Graphical Statistics, 2002
- A wavelet-based method for multifractal image analysis. III. Applications to high-resolution satellite images of cloud structureThe European Physical Journal B, 2000
- A wavelet-based method for multifractal image analysis. II. Applications to synthetic multifractal rough surfacesThe European Physical Journal B, 2000
- A wavelet-based method for multifractal image analysis. I. Methodology and test applications on isotropic and anisotropic random rough surfacesThe European Physical Journal B, 2000
- An Algorithm for Simulating Stationary Gaussian Random FieldsJournal of the Royal Statistical Society Series C: Applied Statistics, 1997
- Simulation of Stationary Gaussian Processes in [0,1] dJournal of Computational and Graphical Statistics, 1994
- Mosaic organization of DNA nucleotidesPhysical Review E, 1994
- Singularity spectrum of fractal signals from wavelet analysis: Exact resultsJournal of Statistical Physics, 1993
- Fast Generation and Surface Structuring Methods for Terrain and Other Natural PhenomenaComputer Graphics Forum, 1992
- On the wavelet transformation of fractal objectsJournal of Statistical Physics, 1988