A plant grows its seeds one at a time, each turned from the last by a single fixed angle. Only ONE angle — the golden angle, 137.5° — packs them with no gaps and no spokes: the many unfolding evenly from the One by a single ratio. Slide toward the golden angle (or tap) and watch the spokes close.
Phyllotaxis: N florets placed at polar angle θ·i and radius √i, where θ is the divergence angle. The golden angle θ=π(3−√5)≈137.507° is the 'most irrational' turn — its continued fraction is all 1s — so no floret ever lands on a radial line already used, and the disc fills with uniform density and no seams. Nudge θ off the golden value and rational near-resonances snap the seeds into visible spokes and gaps. Evenness is measured as the uniformity of florets binned by angle; a fail-loud self-check throws unless the golden angle bins more evenly than a detuned angle.
A 2D Vogel-model sunflower with N≈420 seeds; real phyllotaxis adds growth dynamics and elastic packing. The golden angle, the placement and the angular-uniformity measure are computed exactly.