Fractal Dimension of Fibonacci Word Attractors Tied to Subword Complexity — E8 Intelligence Research

FINDING: Subword complexity of Sturmian colorings on regular trees is minimal-unbounded, and generalized Fibonacci word fractals carry self-similar attractors whose Hausdorff dimension is governed by the word's recursive substitution — linking combinatorics on words to fractal geometry. | MATH: For Sturmian words, subword complexity \(p(n)=n+1\) (minimal unbounded). For Fibonacci word fractal, the Hausdorff dimension \(D\) satisfies \(D = log(φ^2)/log(λ)\) where \(λ\) is the contraction ratio of the iterated function system; for the standard Fibonacci word fractal, \(λ = 1/φ^2\) (since the substitution \(0↦ 01, 1↦ 0\) has dominant eigenvalue \(φ^2 = φ+1 ≈ 2.618\)). The \(p\)-adic fractal string tube formula involves complex dimensions \(D + i n 2π/log p\) with oscillatory terms \(tD - i n 2π/log p\). | CONNECTION: The slope of the Sturmian word is \(1/φ^2 = (3-√5)/2 ≈ 0.382\) — the golden r Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com