  In this work, we have studied the temporal evolution of some properties of a
sample of superactive regions with the aim to single out the most significant
for flare activity forecasting. We have investigated properties of 14
superactive regions, observed between January 1st 2000 and December 31st 2006
with MDI/SOHO instrument and characterized by a particularly intense flare
activity during their passage on the solar disk. We have analyzed the temporal
evolution of fractal and multifractal properties of photospheric magnetic
fields, namely the generalized fractal dimension and the cntribution and
dimensionality diversities, as well as the potential unstable volumes of
magnetic discontinuities above the studied ARs. Correlations of these
quantities with the flare index, which provides information about the flare
activity of a region, have also been estimated. We found that in 50 % of our
sample the generalized fractal dimension is correlated with the flare index
computed over windows of 50 hours, while the contribution diversity and the
dimensional diversity are anticorrelated with the same index. An increase of
the potential unstable volume of magnetic discontinuities in the corona is
observed before the phases characterized by more frequent and intense flares.
We also found that the free energy distribution functions of unstable volumes
of the analyzed superactive regions can be fitted with straight lines whose
slope is larger than the values found in previous works for less active
magnetic regions. The generalized fractal dimension and the potential unstable
volume of magnetic discontinuities are the most suitable for statistical
investigations of relations with flare activity over longer (50 hours) and
shorter (few hours) time intervals, respectively.
