Curves of Lamé

These are curves of Lamé, generalizations of the circle given by the formula xⁿ + yⁿ = 1. When n = 2, you get a circle; when n is a bit greater than 2, you get Piet Hein’s “supercircles”. He liked the effect you got when n was roughly e, which is the default here, but you can change the exponent in the drop-down box to see the different kinds of curves you can get.