This is a sunflower seed head built with Vogel's model. Every seed n is placed at angle θ = n · δ and distance r = c · √n from the centre.

• Drag Divergence angle δ just a fraction of a degree away from 137.5° and watch the tidy spiral arms split into gaps and radial spokes.
• Hit Snap to golden angle to jump back to the perfect packing.
• Switch Color mode to By spiral family to tint each Fibonacci-numbered arm differently.
• Press Animate growth to add seeds over time, the way a real flower head grows from the centre outward.

The golden angle. The golden ratio is φ = (1 + √5) / 2 ≈ 1.618. Dividing a full turn so the two parts are in golden proportion gives the golden angle 360° / φ² ≈ 137.507°. Because φ is the “most irrational” number — the hardest to approximate with simple fractions — successive seeds never line up into spokes, so they fill space with no wasted gaps.

Fibonacci parastichies. The visible spiral arms (called parastichies) come in two interlocking families, one clockwise and one counter-clockwise. Their counts are almost always two consecutive Fibonacci numbers — 21 and 34, 34 and 55, 55 and 89 — for the very same reason: the golden-angle placement makes Fibonacci ratios the best rational approximations to φ.

Why plants do it. Packing seeds, leaves, or florets at the golden angle maximises how densely they can be arranged without overlap and, for leaves, minimises how much each one shades the ones below — better light capture and more seeds per head.

Vogel's model (1979). Helmut Vogel showed that the simple formulas θ = n · 137.5° and r = c · √n reproduce the sunflower pattern remarkably well. The √n keeps the area per seed constant, so the head stays evenly dense as it grows.