The Hilbert curve

This video actually started when a student who had gotten interested in doodling Hilbert curves asked if I could animate him one.  Fractals are a fun thing to program, and I actually went a little crazy trying out what different space-filling curves look like, hence the supplemental "Fractal charm".  

As I was creating it, I thought about how it's very rare for people presenting space-filling curves to mention that the hard part is ensuring these things are well-defined.  That is to say, to define what it means for a family of curves to actually have a limit.  It also reminded me of a thought I had a while back about how translating visual data to audio data would benefit from using space-filling curve approximations.  In short, I realized there was some good fodder for a story there, so the animation for my student turned into a full-blown video.