A superellipse is a planar, closed curve in the rectangle x \in [-R_x,R_x] , y \in [-R_y,R_y]. It can be viewed as a generalization of the ellipse as it retains the symmetry properties about the semi-major and semi-minor axes. All points on the curve satisfy the following equation

\Big\vert \frac{x}{R_x} \Big\vert^n  +   \Big\vert \frac{y}{R_y} \Big\vert^n  = 1

The ellipse is a special case of this equation with n=2. For n>=1 convex curves are obtained. Examples are the rhombus (n=1) or a curve resembling a rounded rectangle (n=4) shown below. Concave curves, like the four armed star shown below, are a result of exponents n<1.