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%I #11 Jul 30 2021 08:48:55
%S 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 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 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 Decimal expansion of the Hausdorff dimension of Hironaka's curve and equivalent carpets.
%C McMullen calculates the Hausdorff dimension of various carpets, with the present constant being 3 parts in a 3 X 2 grid.
%C +---+---+---+
%C | | S | | Fractal carpet with each S
%C +---+---+---+ a shrunken copy of the whole.
%C | S | | S | Any 3 parts not all in one row.
%C +---+---+---+
%D 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 Robert Dickau, <a href="https://robertdickau.com/hironaka.html">Hironaka's Curve</a>, describing the curve construction.
%H 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 Equals log_2(1 + 2^log_3(2)).
%e 1.3496838201955775731155390813143199...
%t RealDigits[Log2[1 + 2^Log[3, 2]], 10, 105][[1]] (* _Amiram Eldar_, Jul 27 2021 *)
%o (PARI) log(1 + 2^(log(2)/log(3)))/log(2) \\ _Michel Marcus_, Jul 27 2021
%Y Cf. A346640 (metric dimension).
%K cons,nonn
%O 1,2
%A _Kevin Ryde_, Jul 26 2021