"Because of its intermediate nature the parabola occupies a middle position [between the ellipse and the hyperbola]. As it is produced it does not spread out its arms like the hyperbola but contracts them and brings them nearer to parallel, always encompassing more, yet always striving for less – whereas the hyperbola, the more it encompasses, the more it tries to obtain." -Johannes Kepler
view from inside a parabolic dune (click to enlarge)
Parabolic dunes in Provincetown are formed when the prevailing west wind blows out the middle of an existing dune.- Geologic History of Cape Cod
Smudge's past forays with the parabolic dunes of Ptown.