Lissajous Curves are a family of parametric functions that define X and Y in terms of a pair of sinusoids. By varing the frequency of each sine wave as well as the phase difference between them a variety of harmonic shapes can be created. The appearance of the curve is largely tied to the ratio between the two frequencies and works best when the ratio is a rational number. For these videos I am automatically varying the phase offset between the X and Y curves which makes it seem like it is rotating in 3D.

Lissajous I from Pehr Hovey on Vimeo.

Lissajous II from Pehr Hovey on Vimeo.

See Wikipedia for more information on Lissajous curves:
http://en.wikipedia.org/wiki/Lissajous_curve

Since this program can plot arbitrary curves it is pretty easy to do parametric function plotting. I am going to continue experimenting with other parametric curve families, starting with Rose Curves.

Along similar lines, I am also interested in working with Spirographs: http://en.wikipedia.org/wiki/Spirograph