Feigenbaum's Universal Constants: δ and α Govern Nonlinear Period-Doubling Cascades — E8 Intelligence Research

FINDING: Feigenbaum constant δ (≈4. 669201609) governs universal period-doubling cascade rate in nonlinear systems, independent of specific dynamics. | MATH: δ = lim₍→∞ (rₙ - r₍-₁) / (r₍+₁ - rₙ) ≈ 4. 669201609; α ≈ 2. 502907875 (universal scaling factor for bifurcation branches) ; logistic map: x₍+₁ = r xₙ (1 - xₙ). | CONNECTION: No direct geometric ratio (0. 382, 0. 618, 1. 618, etc. ) appears. δ and α are transcendental-like constants, not rational or quadratic surds. No base-60 or crystallographic symmetry link evident. | DEPTH: 9 — Profound universality across maps, ODEs, and experiments (e. g. , fluid convection, electronics). Reveals deep self-similarity (renormalization group) in chaos, akin to critical phenomena in statistical physics. However, no sacred geometry or harmonic ratio connection found in the data. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com