Nonlinear dynamics of the formation of mixing fields was investigated at low Reynolds numbers (Re < 100) in a disk-turbine stirred vessel with no baffle plates by means of now-visualization. The fine structures of isolated mixing regions (IMRs) were successfully observed. It has been found that a limited number of filament structures are formed and move around the torus with a certain period depending on the rotation of the impeller and the number of turbine blades and that the number of island-shaped filaments can be determined from the number of turbine blades and the rotation number of the impeller. It has also been elucidated that the isolated filament structure can be formed, only when and where the time-period ratio of the circulating filaments to the impeller rotation becomes a certain definite integer, which is determined from the number of turbine blades and the rotation number of the impeller. As the Reynolds number is raised, the isolated mixing regions become small and finally disappear. A physical rule of bifurcation for predicting the nonlinear-dynamic mixing structure has successfully been presented in a low Reynolds number region.