Feigenbaum Constant Links Chaos to Mandelbrot Fractal Scaling — E8 Intelligence Research

FINDING: The Feigenbaum constant (δ ≈ 4.6692) governs period-doubling bifurcations in chaotic systems, and is directly linked to the Mandelbrot set's self-similar structure; the search results also reveal a spurious but notable numerical coincidence with the golden-ratio-derived scaling factor 2.618 in fractal zoom sequences. | MATH: Feigenbaum δ = lim_{n→∞} (δ_n / δ_{n+1}) ≈ 4.669201609...; Feigenbaum α ≈ 2.5029 (width scaling); logistic map x_{n+1} = r x_n (1 − x_n) bifurcates at r_∞ ≈ 3.5699; Mandelbrot set's period-doubling cascade converges with the same δ; note: 2.618 = φ² (φ = 1.618...), and 1/φ² ≈ 0.382, but δ ≠ φ² (4.669 ≠ 2.618) — the connection is *not* equality but structural analogy: both are universal scaling ratios in different dynamical regimes. | CONNECTION: The Mandelbrot set's main cardioid and period-2 bulb touch at the cusp; the ratio of successive bulb diameters along the real axis approaches 1/δ ≈ 0.214, not 0.382 or 0.618. However, the *external angle* of the Ma Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com