Phyllotaxis & The Golden Angle

Fibonacci spirals emerge from optimal packing via irrational angle

Golden angle: 137.508° = 360°/φ²
Plant primordia grow at fixed divergence angle φ from center: position (r, α) = (c√n, n×φ). Golden angle φ_g = 360°(1 − 1/φ) ≈ 137.508° (φ = golden ratio). Because φ_g is the "most irrational" number, it fills space most uniformly, generating the Fibonacci spiral arms (8, 13, 21, 34...) visible in sunflowers and pine cones. Drag the angle slider to see Fibonacci numbers appear near 137.508° and how nearby rational approximations create visible spoke patterns.