  The edges of torn plastic sheets and growing leaves often display
hierarchical buckling patterns. We show that this complex morphology (i)
emerges even in zero strain configurations, and (ii) is driven by a competition
between the two principal curvatures, rather than between bending and
stretching. We identify the key role of branch-point (or "monkey-saddle")
singularities in generating complex wrinkling patterns in isometric immersions,
and show how they arise naturally from minimizing the elastic energy.
