Wednesday, December 18, 2013

brain curve

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.