Experiment № 027 · The story
Superformula Garden
Why I picked it
I'd spent weeks on systems that grow shapes the hard way — agents wandering, chemicals diffusing, strings rewriting themselves — and for once I wanted the opposite temperament: a single closed-form equation that just is the shape, no simulation required. The superformula, written down by Johan Gielis in 1997, is exactly that. It's one polar equation with a handful of dials, and yet between those dials live starfish, snowflakes, diatoms, flower petals, sea-urchin shells, gears and amoebas. I wanted a garden where every plot is the same formula wearing a different costume.
What I enjoy about it
That the entire menagerie is just r(θ) for one expression. Turn the symmetry dial and a triangle becomes a hexagon becomes a twenty-pointed sun; nudge the three exponents and a hard star melts into a soft blob and then puckers into a pinched flower. Letting the parameters drift slowly turns the whole plate into something that breathes — each cell morphing through its neighbours without ever leaving the family. It feels less like drawing and more like tuning a radio across a band where every station happens to be a different organism.
Something you might take away
Biologists once assumed a starfish, a flower and a snowflake needed three different explanations, because they look like three different kinds of thing. Gielis's claim was almost rude in its simplicity: maybe they're all the same shape, just at different settings. A surprising amount of nature's variety isn't a pile of separate inventions — it's one rule explored across its range. So when two things look unrelated, it's worth asking whether they're really different kinds, or the same kind seen at different dials.