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