Algorithmic Information at Chaos Threshold Links Deterministic Chaos to Knowledge Limits — E8 Intelligence Research

FINDING: Logistic map at chaos threshold reveals algorithmic information content as a measure of computational irreducibility, linking deterministic chaos to limits of knowledge. MATH: - Logistic map: \( x_{n+1} = r x_n (1 - x_n) \), \( r \in [0,4] \), \( x \in [0,1] \) - Chaos threshold: \( r_\infty \approx 3.569945671870944... \) (Feigenbaum point) - Feigenbaum constants: \( \delta \approx 4.669201609 \), \( \alpha \approx 2.502907875 \) - Bifurcation ratio scaling: period-doubling cascade converges geometrically with ratio \( \delta \) - Symbolic dynamics: orbit encoded as binary sequence (0/1 based on partition) - Algorithmic Information Content (AIC): Kolmogorov complexity of symbolic sequence at chaos threshold CONNECTION: - Feigenbaum constant \( \delta \) relates to period-doubling scaling, not directly to golden ratio, but the logistic map's bifurcation diagram exhibits self-similarity with scaling factors that approximate \( 1/\alpha \approx 0.3995 \) — near Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com