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A343620 Decimal expansion of the Hausdorff dimension of 4 X 2 carpets with rows of 3 and 1 sub-parts.

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%I A343620 #10 Aug 07 2021 01:44:36
%S A343620 1,4,4,9,9,8,4,3,1,3,4,7,6,4,9,5,8,4,8,9,2,1,1,6,2,5,6,0,0,6,2,3,7,9,
%T A343620 1,5,6,6,3,5,7,3,4,7,8,4,1,2,3,3,8,1,8,9,2,5,3,1,5,4,1,2,5,8,6,3,1,1,
%U A343620 4,6,7,4,6,9,6,3,2,5,8,6,0,6,4,1,7,9,1,8,9,9,8,4,3,0,9,1,3,9,9,3,8,5,8,8,0
%N A343620 Decimal expansion of the Hausdorff dimension of 4 X 2 carpets with rows of 3 and 1 sub-parts.
%C A343620 Bedford (page 100 figure 34) gives this type of carpet as an example where the Hausdorff dimension differs from the capacity dimension (which is 3/2).
%C A343620   +---+---+---+---+    Fractal carpet with each S
%C A343620   |   | S | S | S |    a shrunken copy of the whole.
%C A343620   +---+---+---+---+    Any 3 parts in one row and
%C A343620   | S |   |   |   |    1 part in the other row.
%C A343620   +---+---+---+---+
%H A343620 Timothy Bedford, <a href="http://wrap.warwick.ac.uk/50539/">Crinkly Curves, Markov Partitions and Dimension</a>, Ph.D. thesis, University of Warwick, 1984, chapter 4.
%H A343620 Curtis T. McMullen, <a href="https://doi.org/10.1017/S0027763000021085">Hausdorff Dimension of General Sierpinski Carpets</a>, Nagoya Mathematical Journal, volume 96, number 19, 1984, pages 1-9, see page 1 dim(R) for the case n=4, m=2, t_0 = 1, t_1 = 3.
%F A343620 Equals log_2(1+sqrt(3)).
%e A343620 1.4499843134764958489211625600623791...
%t A343620 RealDigits[Log2[1 + Sqrt[3]], 10, 100][[1]] (* _Amiram Eldar_, Aug 04 2021 *)
%Y A343620 Cf. A346639 (3 X 2 carpets), A090388 (1+sqrt(3)).
%K A343620 cons,nonn
%O A343620 1,2
%A A343620 _Kevin Ryde_, Aug 04 2021