4 December 2000 Discrete wavelet approach to multifractality
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The use of wavelet techniques for the multifractal analysis generalizes the box counting approach, and in addition provides information on eventual deviations of multifractal behavior. By the introduction of a wavelet partition function Wq and its corresponding free energy (beta) (q), the discrepancies between (beta) (q) and the multifractal free energy r(q) are shown to be indicative of these deviations. We study with Daubechies wavelets (D4) some 1D examples previously treated with Haar wavelets, and we apply the same ideas to some 2D Monte Carlo configurations, that simulate a solution under the action of an attractive potential. In this last case, we study the influence in the multifractal spectra and partition functions of four physical parameters: the intensity of the pairwise potential, the temperature, the range of the model potential, and the concentration of the solution. The wavelet partition function Wq carries more information about the cluster statistics than the multifractal partition function Zq, and the location of its peaks contributes to the determination of characteristic sales of the measure. In our experiences, the information provided by Daubechies wavelet sis slightly more accurate than the one obtained by Haar wavelets.
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Susana I. Isaacson, Susana I. Isaacson, Susana C. Gabbanelli, Susana C. Gabbanelli, Jorge R. Busch, Jorge R. Busch, } "Discrete wavelet approach to multifractality", Proc. SPIE 4119, Wavelet Applications in Signal and Image Processing VIII, (4 December 2000); doi: 10.1117/12.408593; https://doi.org/10.1117/12.408593

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