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A191689 Decimal expansion of fractal dimension of boundary of Lévy dragon. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A198416 A097902 A139425 * 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

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Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)