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$\begingroup$ IIRC, the behaviour of the function x y/(x^2 + y^2) was considered by Cameron Smith back in 1989 in the Preview issue of The Mathematica Journal as the cover image (I have hard copy, but I cannot find this issue anywhere on line though). His approach was to use polar coordinates, essentially, ParametricPlot3D[{r Cos[t], r Sin[t], Sin[2 t]/2}, {r, 0, 1}, {t, 0, 2 Pi}, Mesh -> None, PlotPoints -> {40, 15}] $\endgroup$

TheDoctor
– TheDoctor

2018-08-08 13:56:16 +00:00
Commented Aug 8, 2018 at 13:56
$\begingroup$ @TheDoctor Wow, I think I didn't even know about Mathematica in 1989... $\endgroup$

Jens
– Jens

2018-08-08 14:50:00 +00:00
Commented Aug 8, 2018 at 14:50

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