Growth

What shape does a line make when its only rules are to grow, to stay smooth, and to never touch itself?

Differential line growth. Each edge is a spring holding a rest length, every node repels others inside a radius, and any edge stretched past a threshold gains a node in its middle. Because the rest length sits above the threshold, the curve keeps lengthening and repulsion has nowhere to put the surplus except folds. No target shape is specified anywhere.

Adjust the repulsion radius and the subdivision threshold, then let it run. Nothing here is a spline being drawn toward a designed outcome — the form is entirely a consequence of the three rules, and changing either number changes the character of the folding rather than the shape it aims for.

Reports the live node count and total chain length, which is the only description of the form that exists.

The figure shown under the canvas is computed by the run above, in this tab, from the settings currently selected. Change a control and it is recomputed. Nothing on this page is a stored or illustrative value.