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We report the results of numerical simulations of nonisothermal dendritic flux penetration in type-II superconductors. We propose a generic mechanism of dynamic branching of a propagating hot spot of a flux flow/normal state triggered by a local heat pulse. The branching occurs when the flux hot spot reflects from inhomogeneities or the boundary on which magnetization currents either vanish, or change direction. The hot spot then undergoes a cascade of successive splittings, giving rise to a dissipative dendritic-type flux structure. This dynamic state eventually cools down, turning into a frozen multifilamentary pattern of magnetization currents.