Phyllotaxis · the golden angle simulation

Why do sunflowers, pinecones, and daisies place their seeds at the golden angle (≈137.5°) — what is special about it?

▶ Run the simulationSee the measured result

Units: degrees (the golden angle 360°/φ² = 360°·(2−φ), φ = (1+√5)/2)

How the lab tests it

Lay seeds out by Vogel's spiral (seed n at angle n·α, radius √n — uniform areal density for any α), sweep the divergence angle α, and measure the packing uniformity (the minimum nearest-neighbour gap) at each angle.

What it checks

a sharp GLOBAL packing optimum at the golden angle α* = 360°/φ² ≈ 137.508° — the largest minimum gap (most uniform packing); the measured argmax lands at 137.5°, matching it to within the sweep step, and collapses into radial spokes with wasted wedges a degree away. The golden angle wins because φ is the 'most irrational' number, hardest to approximate by a rational p/q that would line every q-th seed into a spoke (other 'noble' angles are weaker local optima)