I am trying to make a Spirograph drawing program using the formulas found here:
I am pretty sure I copied the formulas correctly, but all my program does is draw a circle. Anyone have any ideas? Thanks!
Here is the project.
May I see what you have so far in your project?
EDIT- Here is the project.
It works for me.
It also works for me, but sometimes it doesn't finish. Maybe you can improve that... 
The results you get depend critically on the ratios between those three slider values. Here's the best I've done so far, just putzing around:
(I'm too lazy to read the Wikipedia article to see what values they used for that animated gif.)
But anyway, a more Snap!ly way would be to use nested sprites:
All of the sprites are forever-TURNing, some clockwise and some counterclockwise. The one named "dot" has its rotation center at the black-dot end. The green dot at its outer end is the one whose pen is down.
The problem with doing it by drawing costumes, as I did, is that it's hard to get precise control of the (relative) sizes of the circles and the black rod. So one could argue for drawing a circle of a precise size and turning the picture into a costume.
I forgot to mention that I already solved the problem, it was just a plus were there should be a minus.
About your idea of making circles and nested sprites, If you look in the List section, there is a block labeled "old ideas" that is my attempt to draw costumes with a pen. Drawing them worked fine, and the rotation centers looked correct, but when I tried to animate it, the circles did not move correctly. My plan was to have one sprite move the circle and another on just draw them.
I have the red and blue circles turning ccw, but the black rod turning cw. But I think more important is that I clicked the little gray circle in the sprite corral icon for the blue circle.