This question is about a physical phenomenon and so I would like to actually know the derivation of the shape as well as the formula.
I was playing around with powder pillow packets, and regardless of shape seem to have these classes of shapes:
I was curious if there is a known formula with a closed analytic expression to describe this family of shapes like there is for the Superformula.
The lemon-shaped image on the top left looks like two joined images of the superformula for: 2 0.5 0.5 0.5. The image on the top right looks like two joined images of the superformula for: 1 0.5 0.5 0.5. I didn't see a shape that would give the shape with the 'S'-like walls. I looked at the Original Paper for the Superformula But it doesn't seem like it gives a reason to describe it's presence in nature other than that it does. And I highly doubt it is related even though two of the shapes look similar. It is just a weak hypothesis.
I really appreciate a closed-form analytical solution though if possible.
