This is my attempt to recreate the "Turntable Spirograph" seen on Geogebra's Facebook page on 3/24/12. Moving Circles A and C and changing their diameters changes the figure that's being created. Also, the speed at which the sliders are moving will vary the output. The sliders' speeds are currently set at 0.5 and pi/2 so that they will not coincide. I've also put some dynamic color into the points.
What happens if you change the center or radius of the circles? What happens if the speeds (the sliders) are the same? What if they are multiples of each other?