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%I #17 Apr 23 2021 05:17:17
%S 1,9,3,4,0,0,7,1,8,2,9,8,8,2,9,0,9,7,8,7,3,3,1,2,3,3,6,2,1,9,3,2,5,1,
%T 8,2,7,4,1,1,8,5,6,3,8,7,1,4,5,8,6,0,2,2,3,7,4,9,4,6,9,5,6,7,0,0,4,1,
%U 1,6,3,2,2,9,9,5,5,4,5,1,5,2,0,8,8,1,8
%N Decimal expansion of fractal dimension of boundary of Lévy dragon.
%C The Lévy dragon was named after the French mathematician Paul Lévy (1886-1971). - _Amiram Eldar_, Apr 23 2021
%H Scott Bailey, Theodore Kim and Robert S. Strichartz, <a href="http://www.jstor.org/stable/3072395">Inside the Lévy dragon</a>, Amer. Math. Monthly, Vol. 109, No. 8 (2002), pp. 689-703.
%H Paul Duvall and James Keesling, <a href="http://dx.doi.org/10.1155/S0161171297000872">The dimension of the boundary of the Lévy dragon</a>, Int. J. Math. and Math. Sci., Vol. 20, No. 4 (1997), pp. 627-632.
%H Paul Duvall and James Keesling, <a href="http://dx.doi.org/10.1090/conm/246">The Hausdorff dimension of the boundary of the Lévy dragon</a>, in: M. Barge and K. Kuperberg (eds.), Geometry and Topology in Dynamics, AMS Contemporary Mathematics, Vol. 246 (1999), pp. 87-97; <a href="https://arxiv.org/abs/math/9907145">arXiv preprint</a>, arXiv:math/9907145 [math.DS], 1999.
%H Larry Riddle, <a href="https://larryriddle.agnesscott.org/ifs/levy/levy.htm">Lévy Dragon</a>, Classic Iterated Function Systems.
%H Robert S. Strichartz and Yang Wang, <a href="https://www.jstor.org/stable/24900135">Geometry of Self-Affine Tiles I</a>, Indiana University Mathematics Journal, Vol. 48, No. 1 (1999), pp. 1-23; <a href="https://www.math.hkust.edu.hk/~yangwang/Reprints/boundaryI.pdf">alternative link</a>.
%F Equals 2*log_2(x), where x is the largest real root of x^9 - 3*x^8 + 3*x^7 - 3*x^6 + 2*x^5 + 4*x^4 - 8*x^3 + 8*x^2 - 16*x + 8 = 0. - _Amiram Eldar_, Apr 23 2021
%e 1.934007182988290978...
%t RealDigits[2*Log2[x /. FindRoot[x^9 - 3*x^8 + 3*x^7 - 3*x^6 + 2*x^5 + 4*x^4 - 8*x^3 + 8*x^2 - 16*x + 8, {x, 2}, WorkingPrecision -> 100]]][[1]] (* _Amiram Eldar_, Apr 23 2021 *)
%K nonn,cons
%O 1,2
%A _N. J. A. Sloane_, Jun 11 2011
%E More terms from _Amiram Eldar_, Apr 23 2021