The paper discusses the role of the Mach principle as a theoretical basis for the universal spectra of periods obtained experimentally. The connection following from this principle according to the “all-to-all” principle can be used as the basis for the model of complementary fractal distributions or R-fractal. It is shown that the irrational fractal sequences following from the R-fractal can serve as a model of the universal spectra of periods, which act as the temporal aspect of the R-fractal. Examples of phenomena that represent the spatial aspect of the R-fractal are given, in particular, the icosahedral-dodecahedral model of the Earth’s structure.