In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.
Swallowtail catastrophe surface
The edge of the rainbow is a fold catastrophe, and so it has a diffraction pattern described by the Airy function. This is generic and stable for any shape of the water droplet.
René Frédéric Thom was a French mathematician, who received the Fields Medal in 1958.
Thom in 1970