A272031 Decimal expansion of the Hausdorff dimension of the Heighway-Harter dragon curve boundary.

1, 5, 2, 3, 6, 2, 7, 0, 8, 6, 2, 0, 2, 4, 9, 2, 1, 0, 6, 2, 7, 7, 6, 8, 3, 9, 3, 5, 9, 5, 4, 2, 1, 6, 6, 2, 7, 2, 8, 4, 9, 3, 6, 3, 8, 3, 4, 0, 1, 1, 9, 3, 4, 7, 8, 1, 3, 8, 6, 9, 0, 9, 0, 9, 4, 5, 7, 9, 2, 1, 6, 6, 2, 8, 9, 5, 8, 8, 4, 1, 0, 6, 8, 9, 2, 6, 6, 4, 2, 2, 7, 4, 6, 4, 7, 1, 3, 9, 4, 2, 8, 1, 1, 2, 4

Offset

1,2

Comments

The value for 'twindragon' is the same.

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Angel Chang and Tianrong Zhang, On the Fractal Structure of the Boundary of Dragon Curve, Journal of Recreational Mathematics, volume 30, number 1, 1999-2000, pages 9-22. See also the pdf version.

Eric Weisstein's World of Mathematics, Dragon curve.

Wikipedia, Dragon curve.

Wikipedia, List of fractals by Hausdorff dimension.

Formula

Equals log_2((1+(73+6*sqrt(87))^(1/3)+(73-6*sqrt(87))^(1/3))/3).

From Kevin Ryde, Dec 06 2019: (Start)

Equals 2*log(A289265)/log(2) [Chang and Zhang, equation 9].

Equals log(A289265)/log(sqrt(2)). (End)

Example

1.5236270862024921062776839359542166272849363834011934781386909094...

Mathematica

RealDigits[Log2[(1 + (73+6*Sqrt[87])^(1/3) + (73-6*Sqrt[87])^(1/3))/3], 10, 100][[1]] (* Amiram Eldar, May 18 2021 *)

Prog

(PARI) log((1+(73+6*sqrt(87))^(1/3)+(73-6*sqrt(87))^(1/3))/3)/log(2)

Crossrefs

Cf. A014577, A191689 (Levy dragon), A327620 (tame twin-dragon).

Sequence in context: A021195 A019673 A229780 * A090183 A063572 A205294

Adjacent sequences: A272028 A272029 A272030 * A272032 A272033 A272034

Keyword

nonn,cons

Author

Stanislav Sykora, Apr 18 2016

Status

approved