Fractal Self-Similarity in Ultrametric Cantor Sets and Computational Limits — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Ultrametric Cantor sets admit a natural scaling factor of 1/2 under base-2 digit truncation, structurally analogous to sexagesimal place-value but with Hausdorff dimension log(2)/log(3) for the classic ternary set — the search results converge on the fractal self-similarity of Cantor space as a model for discrete computational limits. | MATH: Classic Cantor set: Hausdorff dimension \(D = \log(2)/\log(3) \approx 0.6309\). Ultrametric Cantor set (Raut–Datta): metric \(d_u(x,y) = \theta^{-n}\) where \(n\) is the first differing digit in base-\(b\) expansion; scaling factor per level = \(1/b\). For base-2, \(b=2\), so \(d_u\) scales by \(1/2\) per refinement. Hausdorff dimension of product of two Cantor sets: \(D_1 + D_2\) (additive under product). Sexagesimal analogy: place value \(60^{-k}\) vs. binary \(2^{-k}\) — both are ultrametric bases; the ratio of scaling factors \(2/60 = 1/30\) is not a golden ratio but the *logarithmic* ratio \(\log(60)/\log(2) \approx 5.907\) is near 6 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212163516
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