Below you will see an animation showing Lissajous curves. A and B each represent a speed that a dot moves around a circle. In one curve, the A dot represents the X axis movement, and the B dot represents the Y axis. In the other, the inverse is true; B ~ X and A ~ Y.

Similar to spirographs, but not to be confused with spirographs, a Lissajous curve is the graph of a system of parametric equations, which describe complex harmonic motion. Here, you can tweak the parameters of the lissajous curve drawing animation.

A B