Point vortices and pensive billiards

Point vortex dipole pairs on a disk domain. In the case of a single dipole pair, the center moves as a “pensive billiard”. Namely a variant of classical billiards which preserves the rule of equality of the angles of incidence and reflection, but differs in that the "billiard ball” travels along the boundary for some distance depending on the incidence angle before reflecting back into the domain. Multiple dipole pairs obey similar fusions/fission rules, but may exchange partners dynamically over time.