This applet allows you to create all the SpiroGraphs your heart desires by varying the radii of the circles and the position of the drawing point, as well as any of the other controls. Here are the key definitions:

Radius1 (a)

Radius of Circle 1, centered at the origin.

Radius2 (b)

Radius of Circle 2, centered at (a + b, 0)

Position (c)

Distance of the drawing point from the center of Circle 2, the circle of radius b.