I don't have the education to be educated by mathworld, but it looks (as
best I can tell) like they did the opposite of what I did.

You've got a big cirle of radius RAD that spins around 1 time in one
unit of TIME. So the POSITION on the big circle is:
(multiply by 2*pi to get radians from TIME)
POSITION = <cos(TIME*pi*2) , sin(TIME*pi*2), 0> * RAD;

Then put a smaller wheel whever that wheel is at. Make the small wheel
spin around something like 3.5 SPINS per one unit of TIME:
SMALLPOS = <cos(TIME*pi*2*SPINS) , sin(TIME*pi*2*SPINS), 0> * SMALLRAD;

Add POSITION and SMALLPOSITION together (or subtract, like Mathworld
did), and you're at the point for whatever TIME is on the graph. Connect
several TIME positions together, and you've got a spirograph.

Of course, That formula on Mathworld is just the beginning. <see attached>

   -Shay

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