In a complete coincidence, two different coworkers today sent me links to two different works of 3Blue1Brown on YouTube. I loved both of them, and I wanted to share them with you.
The first one demonstrates how Fourier series can be used to trace out two-dimensional shapes on a plane. I've seen animations like this before, but this one might be the most beautifully done.
The second is an exploration of Hilbert curves, including a connection to image processing.
For some related material, see my 25-Jan-2012 post on generating Hilbert curves.
I hope you enjoy these videos.