Golden Angle Emerges from Pushed Pattern-Forming Front as Optimal Phyllotaxis Solution — E8 Intelligence Research

FINDING: Phyllotaxis is governed by the golden angle (≈137.507°), which emerges from a pushed pattern-forming front (PDE) as the optimal packing solution for radially growing primordia, yielding Fibonacci spiral families. | MATH: Golden angle = 360° × (1 − 1/φ) = 360° × (1 − 0.6180339…) = 137.507764…°; equivalently 2π/φ² radians. Fibonacci numbers Fₙ satisfy Fₙ₊₁ = Fₙ + Fₙ₋₁, with Fₙ₊₁/Fₙ → φ = (1+√5)/2 = 1.6180339…; the complementary angle = 360°/φ² = 137.507…°; the smaller angle = 360°/φ = 222.492…° (or 137.507° as the acute turn). The PDE (from auxin transport, Meyerowitz–Traas) yields spiral phyllotaxis; the pushed front selects integer winding numbers (m, n) that are consecutive Fibonacci numbers, satisfying m/n → φ as radius grows. | CONNECTION: The golden angle is the irrational rotation that maximizes packing efficiency — it is the most irrational number (continued fraction [1;1,1,1,…]), giving the slowest approach to rational approximation, hence optimal spacing. This links di Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com