I created a spirograph inside of After Effects, with some sliders for customizing the visuals. Project File for download:
I saw this tweet on my timeline and wondered how I could recreate it in After Effects. I created three shapelayers - once for each circle - with the inner two having lines. The small, outer circle is the indicator and most important null for drawing the spirographs. The way I visualized the spirograph was by parenting a point light to the outer circle, and using the light as an emitter in Trapcode Particular.
checkbox that toggles the visibility of the shapelayers
specifices the number of points or vertices you want the spirograph to have
indiciated the number of revolutions per second. Setting it to 1 would make the object do one complete rotation every second. Each of these values are keyframe-able but numPoints creates interesting results when keyframed.