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 tapping with the preferred hand and a 3:2 polyrhythmic tapping with the right hand taking the faster beat. To clarify the process of polyrhythmic pattern formation, the transition routes 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, close relationships were indicated between personal tempo in the polyrhythmic tapping with the faster hand and in the single-rhythmic tapping.