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
Examples
1.5236270862024921062776839359542166272849363834011934781386909094...
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.
Programs
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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 *)
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PARI
log((1+(73+6*sqrt(87))^(1/3)+(73-6*sqrt(87))^(1/3))/3)/log(2)
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)
Comments