A272031 - OEIS

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

(list; constant; graph; refs; listen; history; text; internal format)

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 *)