Sketch · 2026-04-27
Phyllotaxis spiral.
Sunflowers, pinecones, and pineapples arrange seeds by rotating each new one a fixed angle from the last. When that angle is the golden angle (about 137.508°), the seeds pack tightly and you cannot pick out spiral arms. Move a hundredth of a degree off, and arms appear.
Note
The formula is from Helmut Vogel's 1979 paper. Each seed sits at radius r = c · √n and angle θ = n · α, where α is the divergence angle and n is the seed index. The square root keeps area per seed constant; the angle decides everything else.
The golden angle is the only divergence at which the resulting parastichy counts (the number of arms in each direction) are consecutive Fibonacci numbers. It is also the only one at which the seeds never line up into visible spokes, no matter how many you draw. Any rational fraction of a full turn produces obvious arms; the golden angle is the most irrational number you can choose.
Source
Vogel, H. (1979). A better way to construct the sunflower head. Mathematical Biosciences 44 (3–4): 179–189.