New polyp buds settle by diffusion-limited aggregation (DLA): nutrient/larval "particles" execute a biased random walk down through the boundary layer above the colony and fuse to the skeleton the moment they touch a live tip. Because a thin diffusive boundary layer is always thinnest over the most exposed protrusions, flux — and so growth — concentrates at branch tips, which is exactly why real staghorn coral (Kaandorp's DLA growth models) self-organises into open, self-similar branches instead of a solid blob.
tempFactor(T) = exp(−(T−27)² / (2·3.5²))
bleach(T) = clamp((T−30)/2, 0, 1)
I(depth) = I0·exp(−k·depth), k ≈ 0.10 /m
P(I) = I / (I + Ik) (Michaelis–Menten photosynthesis)
growthRate = tempFactor·(1−0.8·bleach)·(0.2+0.8·P)
stickProb(flow)= 0.95 → 0.25 as flow 0% → 100%
- Water temperature — growth follows a bell curve peaking near 27 °C; above ~30 °C the symbiotic zooxanthellae are expelled (bleaching), turning new growth pale and cutting the growth rate.
- Depth / light — sunlight is absorbed exponentially with depth (Beer–Lambert); less light means less zooxanthellae photosynthesis and less of the light-enhanced calcification that builds most of a coral's skeleton.
- Water flow — a thinner, more turbulent boundary layer (high flow) lets particles attach almost anywhere they land, producing compact colonies; still water forces attachment only at the most exposed tips, producing thin, fractal branching — the same flow-morphology link documented in real reefs.