Besides software development, one of my hobbies is poi spinning. If you don't know what that is, here are some YouTube video links of folks doing it:
One kind of thing we can do with poi is called a compound circle or flower pattern, in which the arm makes a circular motion while the ball makes a circular motion around the hand. Depending on the relative direction of the arm and poi and the ratio of rotations between the two, different kinds of Spirograph-like patterns are formed.
This page is sort of a scribble I wrote up in a few hours over a couple of days to simulate these kinds of patterns using Canvas and JavaScript. Note that this will only work in a Canvas-capable browser.