A191689 Decimal expansion of fractal dimension of boundary of Lévy dragon.
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, 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, 1, 6, 3, 2, 2, 9, 9, 5, 5, 4, 5, 1, 5, 2, 0, 8, 8, 1, 8
Offset: 1
Examples
1.934007182988290978...
Links
- Scott Bailey, Theodore Kim and Robert S. Strichartz, Inside the Lévy dragon, Amer. Math. Monthly, Vol. 109, No. 8 (2002), pp. 689-703.
- Paul Duvall and James Keesling, The dimension of the boundary of the Lévy dragon, Int. J. Math. and Math. Sci., Vol. 20, No. 4 (1997), pp. 627-632.
- Paul Duvall and James Keesling, The Hausdorff dimension of the boundary of the Lévy dragon, in: M. Barge and K. Kuperberg (eds.), Geometry and Topology in Dynamics, AMS Contemporary Mathematics, Vol. 246 (1999), pp. 87-97; arXiv preprint, arXiv:math/9907145 [math.DS], 1999.
- Larry Riddle, Lévy Dragon, Classic Iterated Function Systems.
- Robert S. Strichartz and Yang Wang, Geometry of Self-Affine Tiles I, Indiana University Mathematics Journal, Vol. 48, No. 1 (1999), pp. 1-23; alternative link.
Programs
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Mathematica
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 *)
Formula
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
Extensions
More terms from Amiram Eldar, Apr 23 2021
Comments