We have recently argued that a simple nonlinear law could be important for the origin of the Universe resulting in fractal or multifractal features [1]. Various fractal scaling models of the large-scale mass distribution have already been proposed. The expected universal multifractal function for galaxies is similar to that identified by NASA's Voyager mission in the Solar System [2]. Now we apply the similar method to determine a reliable multifractal spectrum of distribution of galaxies on cosmological scales, based on selected observations from a million of galaxies in the Redshift Catalog (June 2008) [3]. We show that the observed spectrum is consistent with the weighted oneor two-scale Cantor set models characteristic for turbulence in laboratory and inside the Sun's heliosphere immersed in the very local interstellar medium. However, the total degree of multifractality ∆ ≈ 0.2 is much smaller then that inside the heliosphere. This would be characteristic for a simple linear fractal scaling of galaxy distribution, but somewhat varying for nearby (∆ ≈ 0.1) and the most remote galaxies (∆ ≈ 0.2) receding from our Solar System. The parameters p ≈ 0.45 and λ ≤ 1/2 for one-scale model are apparently related to some voids in the large-scale distribution of matter. A possible asymmetry (A ≈ 0.75) of the total spectrum for two-scale weighted Cantor set (A ̸ = 1) could admittedly be attributed to some deviations from the Hubble's law for the ideal uniform expansion of the Universe.

We show that the solar wind turbulence exhibits features characteristic for Markov processes. We have presented statistical analysis of magnetic field fluctuations in the Earth's magnetosheath using data from the Magnetospheric Multiscale (MMS) mission on very small kinetic scales [1; 2]. We have verified that the Chapman-Kolmogorov necessary condition for Markov processes is well satisfied. Here we are testing for local transfer of energy between the magnetic and velocity fields at various regions in Earth's space environment: behind the bow shock, inside the magnetosheath, and near the magnetopause [3]. Interestingly, magnetic turbulence is consistent with a generalized Ornstein-Uhlenbeck process. Solutions of the Fokker-Planck equation agree with experimental Probability Density Functions (PDFs), from the Kappa to normal Gaussian distributions for larger scales, which exhibit a universal global scale invariance with a linear (mono-fractal) scaling. For the velocity fluctuations higher order coefficients in Kramers-Moyal expansion should be considered hence scale invariance is not observed, suggesting rather nonlinear (multi-fractal) turbulence. Obtained results could be important to better understand the physical mechanism governing turbulent systems in space plasmas.