Chaoscope is a visualization toy. It draws beautiful pictures of strange attractors, which are a bizarre fractal-like mathematical construct from the field of chaos theory. Whatever, they look really nice:

The interface is really well done, letting you randomly find interesting attractors, but then drag them in three dimensions and fiddle with their parameters. You can get a good intuitive sense of the chaos in chaos theory by making small changes in the parameters, and seeing sometimes small changes in the output, and sometimes huge changes. There are a number of nice options for the rendering phase too.

This is definitely going in my list of mesmerizing desktop toys...