Superformula

The superformula depends of four parameters and is able to model many different curves. I wonder if that superformula would be useful to learn to generalize the form of a curve given few points. It could be that, in same way, the four parameters of that curve are a orthogonal bases in the hypothesis space, in the sense that each parameters add a lot the information. If this intuition has any meaning, it could be the start of a new theory for constructing bases of the hypothesis space, that is models with few parameters but great expressive power.

Edited: (1) The following link explains expressivity and generalization power in machine learning: https://blog.evjang.com/2017/11/exp-train-gen.html

So my question is whether the superformula constitute an example of great expressivity and powerful generalization for curve fitting by using machine learning models.

Edited: (2) In the following link they use the superformula, Automatic Generation of Smooth Curves from Interpretable Low-Dimensional Parameters.

So the intuition seems fruitful. https://arxiv.org/pdf/1808.08871.pdf