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Discrete wavelet approach to multifractality

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  • Kantelhardt, Jan W
  • Eduardo Roman, H
  • Greiner, Martin

Abstract

A new and simple method is presented to study local scaling properties of measures defined on regular and fractal supports. The method, based on a discrete wavelet analysis (WA), complements the well-known multifractal analysis (MA) extensively used in many physical problems. The present wavelet approach is particularly suitable for problems where the multifractal analysis does not provide conclusive results, as e.g. in the case of measures corresponding to Anderson localized wave-functions in one-dimension. Examples of different types of measures are also discussed which illustrate the usefulness of the WA to classify non-multifractal measures according to additional characteristic exponents, which can not be obtained within the MA.

Suggested Citation

  • Kantelhardt, Jan W & Eduardo Roman, H & Greiner, Martin, 1995. "Discrete wavelet approach to multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 219-238.
    • Handle: RePEc:eee:phsmap:v:220:y:1995:i:3:p:219-238
    DOI: 10.1016/0378-4371(95)00267-B
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    References listed on IDEAS

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    1. Grussbach, Heiko & Schreiber, Michael, 1992. "Multifractality of wave functions and wave packets at the metal-insulator transition in the Anderson model of localization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 394-400.
    2. Carruthers, Bruce G., 1995. "Accounting, ambiguity, and the new institutionalism," Accounting, Organizations and Society, Elsevier, vol. 20(4), pages 313-328, May.
    3. Pietronero, L., 1987. "The fractal structure of the universe: Correlations of galaxies and clusters and the average mass density," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 144(2), pages 257-284.
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    1. Beretta, Alessandro & Roman, H. Eduardo & Raicich, Fabio & Crisciani, Fulvio, 2005. "Long-time correlations of sea-level and local atmospheric pressure fluctuations at Trieste," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 695-703.
    2. Wang, Fang & Wang, Lin & Chen, Yuming, 2022. "Multi-affine visible height correlation analysis for revealing rich structures of fractal time series," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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