Looping with Noise
This is a trick I’ve known for ages from VFX work, so I really like this through explanation by Etienne Jacob (who has an excellent Tumblr blog of generative stuff). The post also explores a bunch of different things that you can draw with noise. Perlin (and Simplex) noise is useful for more than just the heightfield maps you may be used to!
Golan Leven has made an animation that demonstrates the basic idea behind the looping animations even more directly. (And provided source code for that too.) Like I said, this is one of my favorite noise tricks, and it works with any application of noise, so long as you have noise that’s at least 1 dimension higher than your output. And while circles are easiest (just rotate around a point) you can use any closed figure or repeating loop.
https://gist.github.com/golanlevin/46a8fd29114f7a9f41345a9f0ccfd059