Spirograph Circles with math from Wikipedia
This sheet lets you build three different spirographs by controlling three to four parameters for each spirograph.
The display of three separate spirographs lets you see how the different shapes interact. You determine the shape of each spirograph by setting the radius of the enclosing circle, the ratio of the inner to the outer circle and the ratio of the pen position to the inner circle radius. You may also rotate the spirographs relative to each other by specifying a value for phase. An explanation of the math used can be found on http://en.wikipedia.org/wiki/Spirograph