The Swallow's Tail - Series on Catastrophes (1983) by Salvador Dali and the Golden Rectangle

Successive Golden Rectangles dividing a Golden Rectangle into squares (The Swallow's Tail - Series on Catastrophes by Salvador Dali).

Salvador Dali (1904 - 1989) was a Spanish Catalan surrealist painter born in Figueres. Dali was a skilled draftsman, best known for the striking and bizarre images in his surrealist work. His painterly skills are often attributed to the influence of Renaissance masters.

The Swallow's Tail - Series on Catastrophes was the last painting of Salvador Dali, done in May 1983. It is the final work in a series based on René Thom's catastrophe theory.

The shape of Dali’s Swallow's Tail is taken directly from Thom's 4-dimensional graph of the same title, combined with a second catastrophe graph, the s-curve that Thom dubbed, "the cusp". Thom’s model is presented alongside the elegant curves of a cello and the instrument’s f-holes, which, especially as they lack the small pointed side-cuts of a traditional f-hole, equally connote the mathematical symbol for an integral in calculus.

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A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden or Fibonacci spiral.
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