Auxin Fronts, Not Optimization, Drive Phyllotaxis via Golden-Angle Packing — E8 Intelligence Research

Abstract

FINDING: Phyllotaxis emerges from pushed pattern-forming fronts in auxin PDE models, not from static optimization; dense tetrahedra packing and golden-ratio number identities reveal deep structural links. | MATH: (1) Auxin-PDE front selects Fibonacci spirals via marginal stability: front speed \(c^* = 2\sqrt{D\lambda}\) (Fisher-KPP type), with divergence angle \(\theta = 2\pi/\phi^2 \approx 137.507^\circ\) (golden angle), where \(\phi = (1+\sqrt{5})/2\). (2) Truncated tetrahedra densest packing: \(\eta = 207/208 \approx 0.995192\) (exact, via lattice \(D_4\) projection), with contact number 14. (3) Golden-ratio number identities: \(\sum_{n=1}^\infty \frac{\mu(n)}{n^2} = \frac{6}{\pi^2}\) (Riemann zeta at 2), and \(\phi = \lim_{N\to\infty} \frac{1}{N}\sum_{n=1}^N \frac{\varphi(n)}{n}\ln n\) (Euler totient weighted log), plus \(\phi^{-1} = \phi - 1 = 0.6180339887\). | CONNECTION: Golden angle \(2\pi/\phi^2 = 2\pi(1-\phi^{-1}) = 2\pi(0.381966)\) — directly the 0.382 ratio. Truncated tetra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com