Singularities of an Ellipsoidal Wave Front
This Demonstration shows the appearance of singularities on an elliptical wave front. The singularities are semicubical cusp edges and swallowtails.
A "wave front" begins with a smooth, closed surface in space (or a curve in the plane) that propagates inward so that each point moves with the same speed in the direction of the inward normal to the initial surface. The position of the front at time is the equidistant surface of the initial surface. For a generic initial surface, singularities of the semicubical cusp and swallowtail type appear.
 V. I. Arnold, The Theory of Singularities and Its Applications, Cambridge, UK: Cambridge University Press, 1993.