Enneper's surface is a well-known minimal surface. Though it has a fairly uncomplicated parameterization (first equations below), it is somewhat hard to visualize because of its self-intersections. The plot above suggests the self-intersections exhibited by the surface, but the plot range has been kept small enough that the structure of the surface's center is also visible. Note that the self-intersection curves are subsets of the planes y = 0 and x = 0. The surface above is a special case of the more general Enneper's surface of degree n (second equations below). These surfaces tend to be even more complicated and difficult to visualize. Below is an animation for the case n = 2 of Enneper's surface of degree n, as radius increases. Note how the self-intersections become more complicated as the surface grows.
Enneper's minimal surface is parameterized by:
The more general Enneper's surface of degree n is parameterized in polar coordinates by:
Note: The exponent on r is 1+2n.