Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have
been found to describe and model many systems in nature, in particular fluid
mechanics and geophysical related geometrical objects, like the convective
boundary layer of cumulus cloud fields, topographic landscapes, solar
granulation patterns, and observational astrophysical time series, like light
curves of pulsating stars. The main interest in the study of fractal properties
in such physical phenomena lies in the close relationships they have with
chaotic and turbulent dynamic. In this work we introduce some statistical tools
for fractal analysis of light curves: Rescaled Range Analysis (R/S),
Multifractal Spectra Analysis, and Coarse Graining Spectral Analysis (CGSA), an
FFT based algorithm, which can discriminate in a time series the stochastic
fractal power spectra from the harmonic one. An interesting application of
fractal analysis in asteroseismology concerns the joint use of all these tools
in order to develop classification criteria and algorithms for {\delta}-Scuti
pulsating stars. In fact from the fractal and multi-fractal fingerprints in
background noise of light curves we could infer on different mechanism of
stellar dynamic, among them rotation, modes excitation and magnetic activity.Comment: 13 pages, 10 figure