This closed curve looks a bit like a lateral slice of a cerebral cortex, and has a very simple parametric formula:
If you let
n = 0, the curve is a circle, for
n = 1, you get an
epicycloid, and for n around 4 you start to get something that looks like the brain slice. I think that there is a small copy of the whole curve on the left, giving the curve some
self-similarity.
I first saw this curve, and some other neat ones that have very similar formulas, when looking at the scrambler amusement park ride (see
here, and
here).
Update: A very nice Mathematica animation that traces out this curve can be found at Curiosa Mathematica.