Superellipse (Lamé Curve)

The superellipse, also known as a Lamé curve, is a geometric shape that generalizes the ellipse. It was discovered by the French mathematician Gabriel Lamé in 1818.

The parameter n controls the shape's curvature:

• When n = 2, it becomes a circle or ellipse
• When n > 2, it gradually transforms into a rectangle with rounded corners
• When n < 2, it becomes star-shaped with concave sides
• When n = 1, it becomes a diamond (rhombus) shape
• When n = 4, it creates the famous 'squircle' used in iOS icon design

The superellipse has been widely used in design and architecture, most notably by Danish architect Piet Hein who used it to create superelliptical traffic circles, tables, and even the Sergels Torg plaza in Stockholm.