Base-2 Ultrametric Cantor Sets Mirror Base-60 Place-Value Structure — E8 Intelligence Research

FINDING: Ultrametric Cantor sets with scaling factor 1/2 exhibit a base-2 self-similarity whose measure-growth law mirrors base-60 place-value structure, linking p-adic-like geometry to classical fractal dimension. | MATH: For the standard ternary Cantor set, Hausdorff dimension \(d_H = \log 2 / \log 3 \approx 0.6309\). For the ultrametric Cantor set with scaling factor \(1/2\) (binary branching), the natural ultrametric \(d_u\) defined via relative infinitesimals and inversion yields a measure \(\mu\) satisfying \(\mu(B(x,r)) \propto r^{\alpha}\) with \(\alpha = \log 2 / \log 2 = 1\) for the binary case — but the *growth of measure* under the inversion rule introduces a multiplicative constant \(c\) such that \(\mu(B(x,r)) = c \cdot r^{d_H}\) where \(d_H\) is the Hausdorff dimension of the *embedded* Cantor set. For the ternary set, \(d_H = 0.6309\); for a binary Cantor set (scaling 1/2), \(d_H = 1\) (trivially, the interval). The sexagesimal analogy: base-60 place-value weights \(60^ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com