The Mandelbrot set is the most famous object in the branch of mathematics known as fractals and chaos theory. It was discovered in 1980 by the mathematician Benoit Mandelbrot, who pioneered this relatively new field.

A picture of the Mandelbrot set is reminiscent of a beetle with two main segments: a large circular bulb adjoining the left end of an even larger cartioid shaped central region. While these two segments visually dominate the Mandelbrot set, the geometric intricacies of its border truly define it.

A glance at that border reveals a number of bulbs of varying sizes attached to the two main regions of the set. Each of these bulbs, no matter the size, has a number of antennae protruding from it. Like the main region of the Mandelbrot set, the border of these antennae are decorated with a series of bulbs, which in turn have antennae...