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An abstract mathematical concept of fractal organization of certain complex objects received significant attention in astrophysics during last decades. The concept evolved into a broad field including multi-fractality and intermittency, percolation theory, self-organized criticality, theory of catastrophes, etc. Such a strong mathematical and physical approach provide new possibilities for exploring various aspects of astrophysics. In particular, in the solar and stellar magnetism, multi-fractal properties of magnetized plasma turned to be useful for understanding burst-like dynamics of energy release events, conditions for turbulent dynamo action, nature of turbulent magnetic diffusivity, and even the dual nature of solar dynamo. In this review, I will briefly outline how the ideas of multi-fractality are used to explore the above mentioned aspects of solar magnetism.
Recent space based observations of the Sun revealed that magnetic reconnection is ubiquitous in the solar atmosphere, ranging from small scale reconnection (observed as nanoflares) to large scale one (observed as long duration flares or giant arcades
We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen
The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free path
The heating of coronal loops is investigated to understand the observational consequences in terms of the thermodynamics and radiative losses from the Sun as well as the magnetized coronae of stars with an outer convective envelope. The dynamics of t
Finding solar-analog stars with fundamental properties as close as possible to the Sun and studying the characteristics of their surface magnetic activity is a very promising way to understand the solar variability and its associated dynamo process.