I was noodling around the net and stumbled upon this. I then proceeded to create my own spirograph.
Click anywhere to create another pattern and press and hold any key to freeze the image. Colors are randomly chosen and the numbers are some of the variables that control the shape being drawn. Nothing really interesting however a way for me to see what was going on in terms of changing things. You will notice that k is exactly one half of b. One thing that I would have liked to have done was to be able to stop the drawing after it had completed a cycle of 360 degrees. After a trivial number of rotations, it automatically restarts.