The Swallow's Tail — Series on Catastrophes
Salvator Dali

When a wave transverses a media it produces characteristic patterns,
places where its intensity is extremely large. Each pattern is
associated with a discontinuity of a certain polynomial, called catastrophe.
There are only seven such polynomials, catastrophes, but for the two
dimensional patterns there are only three. Patterns that are produced
from an interplay of light and sea ripples on the shallow sea floor is indefinite
interchange of these.

 

Basic one dimensional catastrophes

fold, cusp, swallowtail (see the Dali painting), butterfly

 

Basic two dimensional catastrophes

hyperbolic umbilic, elliptic umbilic, and parabolic umbilic