These are really fun shapes to play with -- here's another little python script to draw animated hypotrochoid frames that can be stitched together with ffmpeg: https://github.com/hecanjog/hypotrochoid.py/blob/master/hypo...

I stole the relevant bit from here: https://stackoverflow.com/questions/22894942/plotting-hypotr...

Here's one video example: https://vimeo.com/99493389