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

1,2

Comments

The Lévy dragon was named after the French mathematician Paul Lévy (1886-1971). - Amiram Eldar, Apr 23 2021

Links

Table of n, a(n) for n=1..87.

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.

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

Example

1.934007182988290978...

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 *)

Crossrefs

Sequence in context: A097902 A139425 A356637 * A090485 A021521 A011011

Adjacent sequences: A191686 A191687 A191688 * A191690 A191691 A191692

Keyword

nonn,cons

Author

N. J. A. Sloane, Jun 11 2011

Extensions

More terms from Amiram Eldar, Apr 23 2021

Status

approved