The roll-up of an initially spherical vortex sheet into a vortex ring is computed using the vortex blob method. The ring sheds about 30% of its circulation into a tail which, in turn, rolls up into a ring that sheds circulation. The process repeats itself at smaller and smaller scales in a self-similar manner. The relation between the vortex shedding and the energy of the vortices is investigated. In contrast, an initially cylindrical vortex sheet rolls up into a vortex pair that sheds essentially no circulation.