

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
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OFFSET

1,2


COMMENTS

The Lévy dragon was named after the French mathematician Paul Lévy (18861971).  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. 689703.
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. 627632.
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. 8797; arXiv preprint, arXiv:math/9907145 [math.DS], 1999.
Larry Riddle, Lévy Dragon, Classic Iterated Function Systems.
Robert S. Strichartz and Yang Wang, Geometry of SelfAffine Tiles I, Indiana University Mathematics Journal, Vol. 48, No. 1 (1999), pp. 123; 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



