Thermodynamics of fractal signals based on wavelet analysis: application to fully developed turbulence data and DNA sequences

We use the continuous wavelet transform to generalize the multifractal formalism to fractal functions. We report the results of recent applications of the so-called wavelet transform modulus maxima (WTMM) method to fully developed turbulence data and DNA sequences. We conclude by briefly describing some works currently under progress, which are likely to be the guidelines for future research.