Comparison of multifractal and thermodynamical properties of fractal and natural spectra

In this paper, we explain the multifractal and thermodynamical properties of deterministic fractal spectra, and compare the most relevant behaviors with those obtained for some natural spectra with multifractal properties. In particular, we compare the heat capacity, C(T), derived from Cantor-set-type spectra with the ones obtained from several atomic spectra. We find that, although many of the properties of deterministic fractals, previously reported, are also reproduced in natural fractals (oscillations of C(T) in log scale), new features appear in the natural case: the mean value of C(T) is not always related to the multifractal properties, and the oscillations are present in cases for which they disappear in deterministic fractals.