Saw a beautiful piece of art by Valerie Jaudon that made me want to tile. (http://mathhombre.tumblr.com/post/158486835629/art-mysecondname-valerie-jaudon-this-has-me)
I went with an infinity tile type approach. First I had piecewise lines, but then when there was a (now fixed) GeoGebra bug with them, I tried Bezier curves. I had only done those as a parameterized locus, which wouldn't allow transformations. So I tried as parameterized curves, which almost worked. They were attracted to the origin, so... something was wrong. Looking it up, finally, I saw that I needed the symmetric polynomials. Of course!
If you download the sketch, there are Bezier tools you can use to make your own curvy designs.
