Abstract
The existence of the universal fractal spectra was demonstrated in a number of studies. The article considers a general approach demonstrating the occurrence of such spectra for various nature systems. It is based on two extremely general concepts: resonance and roughness of real physical systems. Application of the algorithm developed in the study causes the occurrence of two complementary fractals on the sets of rational and irrational numbers accordingly. Besides, it was shown that the power of equivalence classes of rational numbers is connected with well-known fact that resonance appears more easily for pairs of frequencies, which are small natural numbers. The results are used for the analysis of the spectrum of the periods of various nature systems.
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