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 = limn→∞ (r_n - rₙ₋₁)/(rₙ₊₁ - r_n) ≈ 4.669201609; α ≈ 2.502907875 (universal scaling factor for bifurcation branches); logistic map: xₙ₊₁ = r x_n (1 - x_n). | 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