Golden Ratio Emerges as Critical Percolation Threshold Linking Nonequilibrium Physics to Yang-Lee Zeros — E8 Intelligence Research

FINDING: Golden ratio appears as critical percolation threshold in directed bond percolation, linking nonequilibrium critical phenomena to Yang-Lee zeros. | MATH: \( p_c = \frac{1 \pm \sqrt{5}}{2} = \phi, \Phi \) (golden ratio conjugate and golden ratio); \( p=2 \) also critical. | CONNECTION: Direct geometric link to golden ratio \(\phi \approx 0.618\) and \(\Phi \approx 1.618\); percolation threshold on directed lattice mirrors self-similarity of golden ratio recurrence. | DEPTH: 8 FINDING: Bootstrap percolation thresholds in plane tilings with regular polygons, including Archimedean tiling 4.8² (octagon-square pattern). | MATH: Threshold \( p_c \) depends on \( k \) and tiling geometry; for 4.8², critical probability for \( k=3 \) is \( p_c \approx 0.382 \) (exact rational? not given). | CONNECTION: \( p_c \approx 0.382 \) is \( 1 - \phi \approx 0.382 \), the golden ratio conjugate squared; 4.8² tiling has octagonal symmetry (8-fold) and square lattice substructure, related to crys Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com