Enneper surface, order 2

Higher-order Enneper surface with n = 2, built from the Weierstrass representation with g(w) = w² and f(w) = 1. Every member of the family is minimal — its mean curvature is zero everywhere.

X = r·cos θ − r⁵/5·cos 5θ
Y = −r·sin θ − r⁵/5·sin 5θ
Z = 2r³/3·cos 3θ

Parameters sweep the disc 0 ≤ r ≤ R, 0 ≤ θ < 2π. The order changes the surface itself; R only crops it. Setting n = 1 recovers the classical Enneper surface.