Enneper surface, order 3

Higher-order Enneper surface with n = 3, built from the Weierstrass representation with g(w) = w³ and f(w) = 1. Every member of the family is minimal — its mean curvature is zero everywhere.

X = r·cos θ − r⁷/7·cos 7θ
Y = −r·sin θ − r⁷/7·sin 7θ
Z = 2r⁴/4·cos 4θ

Parameters sweep the disc 0 ≤ r ≤ R, 0 ≤ θ < 2π. The order changes the surface itself; R only crops it. Order n has (n+1)-fold rotational symmetry about the Z axis — four-fold here. Setting n = 1 recovers the classical Enneper surface.