Voronoi Tessellation of Fermat Spirals Bridges Lattice Regularity — E8 Intelligence Research

FINDING: Voronoi tessellation of Fermat spiral phyllotaxis yields a hexagonal regularity index that interpolates between square and honeycomb lattices, with the Poisson-Voronoi limit as the generic case. | MATH: Fermat spiral: \( r = c√θ \) (golden angle \(θ ≈ 137.5077^∘ = 2π/φ^2\)); Voronoi cell area distribution for Poisson-Voronoi: \( f(A) = 343/15√7/2π A5/2 e-7A/2 \) (mean area normalized to 1); hexagonal regularity index \( H = {6A}{√3P^2} \) (H=1 for perfect hexagon, H→0 for degenerate cells); symmetry-break parameter \( λ \) interpolates from square (\(H ≈ 0.785\)) to honeycomb (\(H=1\)) to Poisson (\(H ≈ 0.907\) — the known universal value). | CONNECTION: **Golden ratio \(φ = 1.618\)** appears directly in the Fermat spiral divergence angle \(2π/φ^2 ≈ 2.39996\) rad — the phyllotaxis packing that maximizes Voronoi cell regularity. The Poisson-Voronoi hexagonality \(H ≈ 0. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com