# The Polar Super-Formula

- Author:
- David Richeson

Johan Gielis devised a polar coordinates function that produces a wide variety of interesting shapes. We present the following simplified version:

Note that in Gielis's more versatile formula, users can choose different values for the two *n*-variables and the two *c*-variables. Also, I added the multiplicative factor at the beginning just to keep the radius of the final product constant. For more information, see https://en.wikipedia.org/wiki/Superformula.
Here are a few values you may want to try:

- circle:
*c*= 2 (*b*and*n*can be any values) - square:
*b*= c = 1,*n*= 4 - star 1:
*b*= 8 and c = 20 - star 2:
*b*=*c*= 0.5 - an almost-triangle:
*b*= 0.55,*c*= 0.9,*n*= 3