There are lots of sites referencing "spirograph". Below is a short list of some that looked interesting to me. Suggestions for other links are welcome.

- Anu Garg's Spirograph, announced Feb 23, 1996.
- David Little's Spirograph, including a long discussion of trochoids and cycloids. Animated.
- Math.com spirograph, with a brief description of the math.

- Roulettes (Spirograph Curves), a mathematical treatment from The Geometry Center at the University of Minnesota.