There are 7 types of catastrophes: fold, cusp, swallowtail, butterfly, hyperbolic umbilic, eliptic umbilic and parabolic umbilic.
This is "The Swallow's Tail"
Nowadays (perhaps more accurately, ten years ago), the public seems to be enamored with fractals. Fractals are far less interesting and philosophically important than some would have you think, but fractal art can be very beautiful.
Johan Andersson's "'St Anthony and The Temptation of the Fractalic Mystical Daliphan" is an obvious pastiche of Salvador Dali's "The temptation of St. Anthony"

An obvious mathematical-artist is M.C. Escher. Here are a few of his lesser known pieces:

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