I was perusing Thingiverse and came across "Spirograph Sharpie Art By CNC" (http://www.thingiverse.com/thing:77581) which reminded me that there's an extension for rendering spirograph style "Epitrochoids and Hypotrochoids" (to quote the Inkscape wiki). It's been a while since I poked through all the extensions, and back in my pre-polargraph days this extension probably seemed somewhat frivolous, but thanks to Thingiverse user andyseubert I'm giving it another look.

Check out the Thingiverse link and see if it sparks any creative ideas. To try it out, open Inkscape and go to "Extensions/Render/Spirograph..." and play with the settings. Fun stuff.