The famous
sunspots on the surface of the Earth's star result from the dynamics of strong
magnetic fields, and their numbers are an important indicator of the state of
activity on the Sun. At the Institute of Nuclear Physics of the Polish Academy
of Sciences in Kraków, Poland, researchers have been conducting multifractal
analysis into the changes in the numbers of sunspots. The resulting graphs were
surprisingly asymmetrical in shape, suggesting that sunspots may be involved in
hitherto unknown physical processes. Mathematical analysis of multifractals
provides invaluable information on the dynamic phenomena, as they occur to
varying degrees of complexity. The results are useful in a number of ways, but
most importantly, they can allow us to discard the influence of current,
longstanding trends. Researchers have shown for the first time that certain
overlooked features of the graphs of multifractals, known as singularity
spectra of the time series, have in fact a close relationship with the nature
of the analyzed phenomena.
The graphs
generated by the analysis of multifractals reveal a certain asymmetry, and
we've turned our attention towards that. Until now, the asymmetry was treated
as a by product of the computational method. We have proven that the asymmetry
might carry valuable information about the nature of the analyzed processes.
Using this approach, looking at some of the graphs, for example those regarding
the number of sunspots on the face of the Sun, we come to some very interesting
conclusions. Tests carried out using multifractals disclose the properties
encoded in the data relating to the relationships on different scales. The
basic graphic tools here are known as multifractal spectra or spectra of
singularity. If the data take the structure of a simple fractal, the
multifractal graphs are reduced to a point. If the structure of a multifractal
is homogenous, then the graph takes the ideal symmetrical form, that of a neat
hill -- an inverted parabola. The thing is, with many graphs we've seen on the
actual data, there is no ideal symmetry. As a rule, the left side is dominant.
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