This is the top view of a three-dimensional fractal set obtained by using different colors (and a nice rendering method) for points that end up in different regions after iterating a particular map from 3-space to itself.
Fractal sets are used extensively in computer graphics, to build interesting, "natural-looking" clouds, plants, landscapes, sea surfaces, .. They are also used in medical applications, to model organs (lungs) or blood vessel networks.
Figure credit: Paul Carlson.
URL for this and many other fractal sets: http://sprott.physics.wisc.edu/carlson.htm