Auxin-Transport PDE Reveals Phyllotaxis Spirals Without Ad Hoc Parameters — E8 Intelligence Research

Abstract

FINDING: Phyllotaxis emerges from a pushed pattern-forming front in an auxin-transport PDE, yielding all observed spiral families without ad hoc parameters. | MATH: Golden angle θ = 137.51° = 2π(1 − 1/φ) where φ = (1+√5)/2 ≈ 1.618; divergence angle limit = 2π/φ² ≈ 137.5077°; Fibonacci numbers F_n satisfy F_{n+1}/F_n → φ; the PDE is a reaction–diffusion system with auxin transport operator (Meyerowitz–Traas form), and the pushed front selects admissible spiral families via a discrete set of winding numbers (parastichy pairs (m,n) with m,n consecutive Fibonacci numbers). | CONNECTION: Direct — the golden angle is the unique irrational rotation with maximal packing efficiency (continued fraction [0;1,1,1,…] = 1/φ²); parastichy pairs correspond to lattice vectors in the hexagonal lattice rotated by the golden angle, linking to crystallographic 6-fold symmetry and the root system A₂. The ratio 0.618 = 1/φ appears as the radial increment ratio between successive primordia; 0.382 = 1/φ² appea Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com