The Polar Super-Formula

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