This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A346639 #11 Jul 30 2021 08:48:55 %S A346639 1,3,4,9,6,8,3,8,2,0,1,9,5,5,7,7,5,7,3,1,1,5,5,3,9,0,8,1,3,1,4,3,1,9, %T A346639 9,0,0,4,9,7,9,3,6,1,4,2,9,1,8,8,7,6,7,7,4,9,4,8,4,4,1,5,3,7,5,4,2,2, %U A346639 2,6,1,3,5,1,8,3,0,4,9,9,0,3,9,9,8,9,9,6,1,6,3,1,2,0,2,4,2,3,6,5,2,2,4,3,5 %N A346639 Decimal expansion of the Hausdorff dimension of Hironaka's curve and equivalent carpets. %C A346639 McMullen calculates the Hausdorff dimension of various carpets, with the present constant being 3 parts in a 3 X 2 grid. %C A346639 +---+---+---+ %C A346639 | | S | | Fractal carpet with each S %C A346639 +---+---+---+ a shrunken copy of the whole. %C A346639 | S | | S | Any 3 parts not all in one row. %C A346639 +---+---+---+ %D A346639 Gerald Edgar, Measure, Topology and Fractal Geometry, second edition, section Hironaka's Curve, pages 232-234, where exercise 7.2.17 is to find McMullen's result. %H A346639 Robert Dickau, <a href="https://robertdickau.com/hironaka.html">Hironaka's Curve</a>, describing the curve construction. %H A346639 Curtis T. McMullen, <a href="https://doi.org/10.1017/S0027763000021085">Hausdorff Dimension of General Sierpiński Carpets</a>, Nagoya Mathematical Journal, volume 96, number 19, 1984, pages 1-9, see start of page 2. (Also <a href="http://www.math.harvard.edu/~ctm/gallery/">author's image gallery</a> showing Hironaka's M curve.) %F A346639 Equals log_2(1 + 2^log_3(2)). %e A346639 1.3496838201955775731155390813143199... %t A346639 RealDigits[Log2[1 + 2^Log[3, 2]], 10, 105][[1]] (* _Amiram Eldar_, Jul 27 2021 *) %o A346639 (PARI) log(1 + 2^(log(2)/log(3)))/log(2) \\ _Michel Marcus_, Jul 27 2021 %Y A346639 Cf. A346640 (metric dimension). %K A346639 cons,nonn %O A346639 1,2 %A A346639 _Kevin Ryde_, Jul 26 2021