Looks like it could lend itself to Math Functions XYZ or perhaps Math Nodes.
The closest I’ve seen to something comparable (code wise) is this from Instructables (using Blender):
(It’s regarding Mandelbulb, so, not sure how closely or if it correlates):
These are the parametric equations:
X: a * cos(u) - 0.5 * a2 * cos(2*u)
Y: -a * sin(u) - 0.5 * a2 * sin(2u)
Y: -a * sin(u) * (a * cos(u) + 1) # both Y equations yield similar results
Z: 4/3 * a**1.5 * cos(1.5u)
I’m noticing that the equation I type in isn’t the same as what shows up when I hit the reply button.
I’m guessing the same is happening with the equations you entered, which would explain the problems.
If you look at the image of the Bour’s surface though, compared to yours, yours has the Center vertex sitting low.
The example at the top has the Center vertex centered on the circle.
Yours is off center. Other than that, pretty darned close.
I’m also not sure, maybe I screwed up the equations, it seems like there are a lot of unnecessary edge lines in the finished result compared to the example.