Pushed Pattern-Forming Fronts in Auxin PDE Select Fibonacci Phyllotaxis Spirals — E8 Intelligence Research

FINDING: Phyllotaxis spiral patterns emerge from pushed pattern-forming fronts in auxin-based PDE, proving optimal packing selects Fibonacci spirals. MATH: The PDE model (reaction-diffusion with auxin transport) generates advancing fronts; the pattern's wavenumber and front velocity select spiral families enumerated by consecutive Fibonacci numbers. The golden angle ≈ 137.508° arises as the divergence angle minimizing overlap in cylindrical packing, equivalent to the irrational rotation number 1/φ² (where φ = (1+√5)/2 ≈ 1.618). Optimal packing density in the plane for disks of equal size is π/√12 ≈ 0.9069 (hexagonal close packing), but phyllotaxis achieves near-optimal packing on a cylinder via the golden angle. CONNECTION: Golden ratio φ = 1.618, its inverse 0.618, and φ² = 2.618 appear directly in divergence angles (137.508° = 360°/φ²) and spiral counts (consecutive Fibonacci numbers). The ratio 0.382 = 1/φ² also appears as the fractional part of the golden angle. Base-60 not evi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com