Feigenbaum Constant δ: Universal Scaling in Period-Doubling Chaos — E8 Intelligence Research

FINDING: Feigenbaum constant δ = 4. 6692016. . . emerges as universal scaling factor in period-doubling route to chaos across logistic map, Mandelbrot set, and physical systems (fluid convection, neuron firing). | MATH: Logistic map: xₙ₊₁ = r xₙ (1 - xₙ). Bifurcation points rₙ converge geometrically: δ = lim₍→∞ (rₙ - rₙ₋₁) / (rₙ₊₁ - rₙ) ≈ 4. 669201609. . . Also α ≈ 2. 502907875. . . (Feigenbaum scaling constant for orbit widths). Mandelbrot set exhibits same δ in period-doubling cascade along real axis. | CONNECTION: δ ≈ 4. 669 is not a classical geometric ratio (0. 382, 0. 618, 1. 618, etc. ), but its reciprocal 1/δ ≈ 0. 214 is near 0. 236 (1/φ²? φ=1. 618, 1/φ²≈0. 382; no direct match). However, α ≈ 2. 5029 is close to 2. 5 = 5/2, a simple rational. No direct link to golden ratio, base-60, or crystallographic symmetry found in these sources. | DEPTH: 8 — Universal constant transcending specific systems, linking pure math (Mandelbrot) to physics (quantum phase transitions, dissipation). Evidence supports Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com