$$f(u,v) =u^3 - 3 uv^2$$
Here $f$ is a harmonic function.
If $u=r\cos\ t,\ v= r\sin\ t$, then $f(u,v)=r^3\cos\ (3t)$
Then we have a parametrization \begin{align*} z(u,v)&:=(u-\frac{1}{3}f(u,v),v-\frac{1}{3} f(v,u),u^2-v^2) \\&= - \frac{1}{3}(f(u,v),v,u) -\frac{1}{ 3} (u,f(v,u),v) +(u,v,u^2-v^2) + \frac{1}{ 3} (u,v,u+v) \\&=(r\cos\ t- \frac{r^3}{3}\cos\ 3t,r\sin\ t+ \frac{r^3}{3}\sin\ 3t,r^2\cos\ 2t) \end{align*} for Enneper's surface. (Here $(u,v,f(u,v))$ is a parametrization for Monkey-saddle surface)
I think that Enneper surface is a slight perturbation of saddle $(u,v,u^2-v^2)$.
Since saddle surface is not minimal, then we have a minimal surface, Enneper, which is a slight pertubation. How can we find Ennper surface ?