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), \(D = \log 24 / \log 60 \approx 0.7737\). Product of two such sets: \(D_{\text{product}} = 2 \cdot \log 24 / \log 60 \approx 1.5474\). 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., \( \mathbb{Z}^2 \) tilings). The dimension \(D \approx 0.7737\) is close to \ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com