Babylonian Base-60 Fractals: Digit-Restricted Cantor Sets and Hausdorff Dimension — E8 Intelligence Research

FINDING: Sexagesimal digit-restricted Cantor sets yield Hausdorff dimensions expressible as logarithms of integer bases (e.g., log 24 / log 60), linking Babylonian base-60 to fractal geometry and computational limits. | MATH: For a Cantor set defined by restricting digits in base \(b\), Hausdorff dimension \(D = log N / log b\), where \(N\) = number of allowed digits. For sexagesimal with 24 allowed digits (e.g., excluding 36 digits), \(D = log 24 / log 60 ≈ 0.7737\). Product of two such sets: \(Dproduct = 2 · log 24 / log 60 ≈ 1.5474\). The 4-corner Cantor set (product of two 1/2-dimension sets) has \(D=1\) but zero 1-dimensional Hausdorff measure — a subtle null-set paradox. | CONNECTION: Base-60 directly invokes Babylonian mathematics; the ratio \(log 24 / log 60\) is not a classical harmonic ratio, but the product structure mirrors crystallographic lattice products (e.g., \( Z^2 \) tilings). The dimension \(D ≈ 0.7737\) is close to \ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com