Enneper's Minimal Surface

Mathematica code

(* The Global Enneper - Weierstrass representation of minimal surfaces *)
phi[f_, g_, eta_] := {(1 - g^2) f, I (1 + g^2) f, 2 f g} eta ;
X[z0_, f_, g_, eta_] :=  X[z0, f, g, eta] =
         Re[Integrate[phi[f, g, eta], {z, z0, Z}]] /. Z -> r Exp[I th] ;
Xeval = X[0, 1, z, 1] ; 
     

     ParametricPlot3D[Xeval, {th, 0, 2 Pi}, {r, 0, 2.0},
             Boxed -> False, PlotPoints -> {100, 20}]