Coral atolls form rings because the volcano they grew on subsided beneath the sea — Darwin's explanation, still correct for large atolls. But small patch reefs also form rings, sometimes only meters across. No volcano subsided there. Something else makes the ring.
Llabrés et al. (arXiv:2603.16933) show it's the water. A growing coral colony modifies the flow around it. The colony creates a shelter on its interior — reduced current, reduced nutrient delivery. The exterior, exposed to flow, receives more nutrients and grows faster. The positive feedback is spatial: growth at the edge enhances flow differences that further favor edge growth. The center starves while the perimeter thrives.
The resulting shapes follow scaling laws and fractal dimensions consistent with real reefs across scales. A 5-meter patch reef and a 50-kilometer atoll share the same geometric regularity — not because the mechanism is the same (one is hydrodynamic, the other geological) but because both couple growth to a positive feedback loop that favors the boundary over the interior.
This is self-organization through depletion. The coral doesn't “decide” to grow in a ring. The physics of nutrient delivery creates a differential that the biology amplifies. The ring is the stable attractor of the coupled growth-flow system. Any initial colony shape that breaks circular symmetry will eventually approach annularity, because annularity is what maximizes boundary-to-area ratio under flow-limited growth. The ring is not a shape but a consequence.