Magic Designer Emulator will help you to create interesting and complex shapes right from your desktop.
You may remember the Magic Designer toy from years ago, it was a fun way to make some pretty cool designs. This little app is more of a fun walk down nostalgia lane than anything else but it works nicely and has numerous available adjustments to choose from.
This program uses trigonometry to figure out how to draw these intricate designs. Without getting overly technical this is how it works:
To draw a design, the paper is rotated a full circle. The position of the pen moves around due to the motion of the gears. The program takes many samples and asks, where is the pen at this point? Because the number of pixels is not infinite a finite number of samples is all that is needed to get the maximum possible accurate drawing. The length of the two arms is known and the position of the pegs (which are those pins standing on the gears) is calculated relative to a common center. Then, one of the possible two points where the circles made by those two arms swinging around their pegs (imagine that the arms were not connected to one another) intersect, is where the pen is located at that moment. This becomes a colored pixel.
Magic Designer Emulator is much more than a simple Spirograph because it is capable of so much more complexity. There are a number of help pages available at the author's site if needed.