Playing with the Gielis Superformula in Blender

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.

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.

What does the WEB say: The superformula, introduced by Johan Gielis in 2003, is a flexible polar equation that can sketch everything from starfish to lily petals by adjusting just a handful of parameters. Think of it as a mathematical brush: the *m* parameter sets the rotational symmetry while *n₁*, *n₂*, and *n₃* gently tune how rounded or pointed the curves become. Because it builds shapes by iterating angles around a circle and computing radius with a blend of cosine, sine, and power terms, artists can explore organic forms without modeling every contour by hand. In creative practice, it's valued for producing elegant, nature-adjacent geometry—ideal for generative illustrations, parametric patterns, or subtle 3D surfaces that feel grown rather than constructed. You don't need deep calculus to use it; just experiment with the sliders, watch the form unfold, and let the math suggest the next artistic move.

⚠️ please notice: the version for Blender 3.6 does not contain the presets, for this feature you need Blender 4++