I am a beginner with Rhino and Grasshopper. Some years ago I went to an exhibition (can’t remember what was about, nor who the author was), this exhibition had on display, various models that were generated from mathematic equations. I only took this two photographs, one i was lucky to include the equation.

So, how do I even start to model this one with Rhino? I guess I must use Grasshopper.
I also believe that the model is composed of two intersecting parts, hence the break in the equation. I wasn’t that great with mathematics, but I can see it’s composed with parabolic equations, giving the U shapes, I just don’t understand how the cubic exponent influences the model.

Thank you.

I want to learn how to make other model from equations so I am grateful if you provide links or tutorials on how to start with the basics.

for version 4 and 5 there is a plugin which lets you produce equational shapes i believe even based on nurbs. i have no idea if that works with rhino 6, also i never got it to run on the mac version of rhino. but i believe it should be exactly what you are after.

Thank you @pascal and @encephalon. I will read your suggestions carefully and see what I can do for now. I will post feedback later.

Meanwhile, I found the authors of those shapes, which are very interesting to take a look at. All shapes and model come from algebraic geometry like Kummer Surface, Togliatti Surface.

But I was, specifically, more interested in the Swallowtail surface, which can be seen in 3D here:

In addition to @pascal’s link to Mathematica, Wolfram have an online solver, Alpha. This will solve your equation for Z:

Taking the result on trust , in Grasshopper you can use the two resulting equations to plot points for domains in X and Y and then fit curves through them.

Regards
Jeremy

p.s. Your typed equation does include an error: there are two consecutive + signs