The present study examined the pattern formation In complex bimanual coordination at a self-paced tempo. 10 subjects performed two motor tasks in a self-paced situation, a single-rhythmic rapping with the preferred hand and a 3:2 polyrhythmic tapping with the right hand taking the Easter Lcat. To clarify the process of polyrhythmic pattern formation, the transition route of frequency ratios were analyzed. analysis showed that a 3:2 pattern was formed by transition repeatedly shifting among 1:1, 2:1, and 3:1 patterns. Consequently, transitions were induced from a simple dissipative structure to a more complex dissipative structure. This process could be represented as a shift from lower- to higher-order ratios in the Farey tree. Furthermore, dose relationships were indicated between personal tempo in the polyrhythmic tapping with the faster hand and in the single-rhythmic tapping.