Enneper surface, order 4

Higher-order Enneper surface with n = 4, built from the Weierstrass representation with g(w) = w⁴ and f(w) = 1. Every member of the family is minimal — its mean curvature is zero everywhere.

X = r·cos θ − r⁹/9·cos 9θ
Y = −r·sin θ − r⁹/9·sin 9θ
Z = 2r⁵/5·cos 5θ

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 — five-fold here. Setting n = 1 recovers the classical Enneper surface.