Superformula Shape Morphing Screensaver
The superformula is a real single polar equation, published by Johan Gielis in 2003, that generalizes circles, polygons, stars and countless organic shapes from just a handful of parameters. This screensaver slowly drifts those real parameters over time, continuously morphing the outline between flowers, gears, stars and blob-like forms.
How the Superformula Shape Morphing screensaver works
For every angle around a circle, the real superformula computes a radius from six parameters — a symmetry count and five shape exponents.
Small changes to those parameters produce dramatically different real outlines: circles and ellipses, n-pointed stars, gear-like polygons, and smooth organic blobs are all genuinely the same formula.
This screensaver slowly and continuously drifts the parameters over time using gentle sine waves, so the outline is always genuinely mid-transition between recognizable shape families.
The same real formula, discovered by botanist Johan Gielis, was originally created to describe shapes found throughout nature — from starfish to diatoms to flower petals.
A worked example
Watch a 5-pointed star gradually round its points into a smooth flower shape, then keep drifting into an asymmetric organic blob — all from the exact same underlying real equation, just with its parameters slowly sliding.
Settings & tips
- Shape color recolours the drawn outline.
- The shape's symmetry count changes periodically for variety.
- Watch a full morph cycle — it typically takes under a minute to cross several distinct shape families.
Frequently asked questions
- Is this a real mathematical/botanical formula?
- Yes — the superformula was published by botanist Johan Gielis in 2003 and genuinely describes a wide range of natural and geometric shapes with one equation.
- Is a key needed?
- No — it's a pure local computation.
- Is it free?
- Yes — free, no download, in your browser.
- What real shapes can the formula produce?
- Circles, ellipses, regular polygons, n-pointed stars, gear shapes and many organic, flower-like or starfish-like outlines, all from one formula.