There are many math formulas that create rather interesting forms when explored in 3D in unusual ways.
I love to start out with something totally abstract like a three-dimensional Hilbert curve and then work it into much more physical realms and see what happens.
I was lucky to have a math and physics teacher in school who was very hands on and somehow managed to make this often very dry field into a place of wonder and beauty by showing us for instance how conic sections occur in nature and in how many ways they can be constructed.
This left me wide open to not think of math so much as something tedious and "somehow related to adding numbers", but as a language and a realm to use and go to for a stroll.
This gallery shows some of the findings.