Oh.  Yeah.

My intuition was correct, and this looked very much like an Enneper surface of
order 3.

So after much dabbling with the parametric equations, I got rid of some
"twisting", split up the function, add the "curl" to the "wings", and managed to
work out a way to at least get a good look at it with Paul Nylander's
ParametricPlot3D macro.

Then I tweaked it a bit more, and I'd say that I'm _almost_ there.   :)

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