The solar dynamo generates a toroidal magnetic field that, forms active regions (ARs) on the surface of the Sun. The toroidal magnetic field lines rise through the turbulent convection zone, where distortions, deformation of already formed regular toroidal magnetic flux bundles and the formation of irregular, complex magnetic structures are possible. At the minimum of solar activity, the toroidal magnetic field of the old cycle disappears and the magnetic field of the new cycle is still very weak. During this period, it is possible to assess the role of the turbulence in the formation of an AR. In this paper, we analyzed ARs of two solar activity minima (between cycles 23-24 and between cycles 24-25). We analyzed ARs located within 60 degrees from central meridian and exhibiting magnetic flux at the maximum development of at least 10(21) Mx. Bipolar and multipolar ARs were divided into regular ones (consistent with the mean-field dynamo theory) and irregular ones, the formation of which was influenced by the turbulence of the convection zone (unipolar spots were considered separately). It was found that regular ARs significantly predominate during solar minima, their magnetic flux is a half or more of the total magnetic flux (0.6 for the first period, 0.5 for the second period). Irregular ARs are fewer in number than regular ones, and in terms of magnetic flux they make up about one-third of the total magnetic flux (0.3 and 0.2 in the first and second periods, respectively). Irregular ARs are predominantly represented by bipolar structures of improper orientation, while very complex multipolar ARs are extremely rare. It is concluded that the generation of ARs with the magnetic flux exceeding 10(21) Mx occurs due to the global dynamo action, while the turbulence of the convection zone causes deformation of the magnetic flux bundles without significant magnetic flux generation.