Fibonacci Matrix Spectral Radius Yields Golden Ratio in Phyllotaxis Fronts — E8 Intelligence Research

FINDING: Phyllotaxis divergence angle converges to golden ratio via spectral radius of Fibonacci matrix, optimizing packing in pushed pattern-forming fronts. | MATH: Fibonacci matrix \( F = {pmatrix} 1 & 1 \\ 1 & 0 {pmatrix} \); spectral radius \( φ = (1+√5)/2 ≈ 1.618 \); divergence angle \( 2π / φ^2 ≈ 137.5^∘ \); ratio \( 1/φ ≈ 0.618 \). | CONNECTION: Divergence angle yields golden angle \( 2π(1-1/φ) ≈ 137.5^∘ \), linked to optimal packing via continued fraction convergents \( Fₙ₋₁/F_n → 1/φ \); crystallographic-like lattice order emerges from auxin-driven PDE front selection. | DEPTH: 8 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com