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The origin and dynamics of magnetic patterns in the solar photosphere are considered in the framework of Parker’s spaghetti" model , as the process of diffuse aggregation of filaments-like magnetic field imposed by convection to the photospheres level. The processes of aggregation of magnetic flux tubes (MFT) into patterns of different types, including spot structures of solar active regions, are regarded with help of numerical solutions of equations of motion MFT under the influence of hydrodynamic forces, the forces of the magnetic interaction, and random forces. The following results were received: 1. Rate and nature of changes in the structure of the MFT ensemble fundamentally depends on the twist factor k. Small torsion match Slowly evolving "loose" structures, consisting of sparsely populated clusters (from two to several MFT) correspond to small twist. . For moderate values of k the rapidly evolving diverse and complex structures arise. 2. The model quite acceptably describes the known from observations common traits of kinematics of sunspot groups: the discrepancy of polarity centers at the phase of growth, the formation of spots of different size and their travel. 3. The model reproduces the morphological asymmetry of the leading and complementary polarities. The cause of asymmetry is small (only a few per cent) differences in the average value the twist factor k. 4. Obtained from the model averages of the values of the active regions parameters (N ~ 500 – number of MFT, a ~ 150 km – average radius of MFT cross-section; l~ 30a – effective length of MPT, k ~ 0.08, d ~ 80 m/sec – average speed of MFT random moving) are in good agreement with their known estimates of the model of «spaghetti», as well as with the last of helio-tomography data.