How can i get an attractor to shape something I want?

As an initial problem: how can i make an attractor forming a sphere, or sphere-like object?

I've considered trial and error by simply designing and using equations which sort of work, and going from there and iteratively shaping it to something which resembles a sphere. That would work. But maybe you smarter people can help me, it's mathy stuff in the background after all.

The end goal is entering some sort of 3d-format and then having an attractor created, which then will be animated by my javascript particle engine. It'll look cash as f