Enneper's Surface 

Introduction:Enneper's surface is a wellknown minimal surface. Though it has a fairly uncomplicated parameterization (first equations below), it is somewhat hard to visualize because of its selfintersections. The plot above suggests the selfintersections 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 selfintersection 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 selfintersections become more complicated as the surface grows. Definition: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. Properties:
