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