Superformula

One equation to rule them all — Johan Gielis' Superformula (2003) is a single mathematical formula that can describe an almost infinite range of natural shapes: flowers, shells, starfish, crystals, and things that don't even exist in nature yet.

I built a fully parametric 3D implementation in Blender Geometry Nodes — entirely procedural, no sculpting, no modelling. Just pure math turned into geometry in real time. (Superhivemarket)

The setup includes: 

🔵 Two independent superformulas combined via a spherical product 

🟠 Sphere ↔ Torus topology switch for ring-based forms 

🟤 Shell mode with Archimedes and Logarithmic spirals 

🐚 Shell_Turns parameter to control how many revolutions the shell grows 

🎨 Natural UV mapping that follows the shape's own coordinate space

Every parameter is live-editable — tweak a number, the shape transforms instantly. From a perfect sphere to a nautilus shell to something completely alien, all within the same node graph. Based on the original work of Johan Gielis and the brilliant reference pages of Paul Bourke (paulbourke.net) — highly recommended if you want to go deep into the math.