How does one make a rippled sheet terminate at a straight edge? If the sheet is sufficiently thin, such as a piece of paper or fabric, then the obvious solution of stretching it out flat will induce large stresses near the edge, possibly even tearing the sheet apart. One solution to this problem is suggested by the series of ever-smaller sharp folds of fabric generated near a curtain rod. Menon and Russell, working at the UMass Materials Research Science and Engineering Center, studied wrinkling patterns on an ultrathin floating raft of polystyrene, and discovered a new mechanism by which nature resolves such a conflict. In the middle of the film, a competition between gravity (which prefers shallow, frequent ripples) and the energy cost of bending the film (which favors longer, higher folds) determines the height and frequency of the folds. Near the edge, however, surface tension forces the film to lie flat. This refinement of structure occurred not by a hierarchy of pleats, but by a smooth cascade of ever-smaller wrinkles emerging as the edge is approached. This kind of hierarchical geometry is explained theoretically by the action of the surface tension of water that tends to “iron out” sharp features in the sheet. Similar types of smooth cascades may appear in other problems in materials science where a patterned surface hits an edge that is incompatible with the pattern.