Feigenbaum Constant δ: Universal Scaling in Period-Doubling Chaos — E8 Intelligence Research
Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) · 2026
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_{n→∞} (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