A line that outgrows its space
Start with a smooth ring of points. Now let it add material — new points, slipped in along its length — while a soft boundary holds it in. The ring lengthens, runs out of room, and has no choice but to wrinkle.
That tension — growth against confinement — is the entire idea. Watch it fold.
Three local rules
Every point obeys three simple urges. Attraction keeps it near its two neighbours, so the curve stays whole. Repulsion pushes it off any point that drifts too close, carving out space and preventing crossings. Smoothing eases it toward the average of its neighbours, keeping the line graceful.
Switch each off and watch what breaks — that's how you learn what each one was holding together.
How fast it grows
The single most expressive knob is the growth rate — how quickly new material is inserted. Grow slowly and the curve has time to relax into broad, smooth lobes. Grow fast and length piles up faster than it can settle, packing the space with tight, restless folds.
Same rules, same boundary — only the pace changes. Slide it.
How much space each point keeps
Growth rate sets how dense the folding is; the repulsion radius sets its scale. A large radius means each point demands a wide berth, so the curve sweeps into big, lazy waves. A small one lets points pack tight, and the folds turn fine and intricate — coral to coastline.
One number choosing the wavelength of the whole form.
The growth studio
Now hold all the dials at once. There's no target shape anywhere in here — only a loop, three forces, and the steady pressure of new material. Yet what emerges is unmistakably alive: the gyri of a brain, the frill of a sea slug, the rumpled edge of a leaf. Tune the growth, the spacing, the smoothing; recolour; and watch form arrive from rules that never mention it.