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A341030
Decimal expansion of the perimeter of the convex hull around the dragon curve fractal.
3
4, 1, 2, 9, 2, 7, 3, 1, 0, 0, 1, 5, 3, 7, 0, 8, 2, 2, 7, 8, 5, 9, 3, 1, 4, 8, 3, 2, 9, 2, 3, 6, 2, 8, 0, 5, 4, 7, 7, 7, 2, 3, 7, 8, 1, 6, 1, 3, 8, 2, 6, 3, 8, 3, 1, 0, 2, 9, 8, 0, 3, 7, 5, 8, 4, 3, 4, 4, 6, 0, 4, 9, 5, 4, 4, 4, 2, 9, 4, 9, 7, 2, 5, 0, 7, 4, 8, 4, 2, 6, 7, 4, 5, 8, 4, 3, 8, 4, 3, 1, 6, 1, 8, 2, 9
OFFSET
1,1
COMMENTS
Benedek and Panzone determine the 10 vertices of the polygon which is the convex hull around the dragon fractal. The perimeter follows from these.
LINKS
Agnes I. Benedek and Rafael Panzone, On Some Notable Plane Sets, II: Dragons, Revista de la Unión Matemática Argentina, volume 39, numbers 1-2, 1994, pages 76-90.
Kevin Ryde, Iterations of the Dragon Curve, see index "HBf".
FORMULA
Equals 3/2 + (5/6)*sqrt(2) + (1/6)*sqrt(13) + (1/6)*sqrt(26).
Equals 2/3 + (1 + sqrt(2))*(5 + sqrt(13))/6.
Largest root of 81*x^4 - 486*x^3 + 693*x^2 - 282*x + 17 = 0 (all its roots are real).
EXAMPLE
4.1292731001...
MATHEMATICA
RealDigits[2/3 + (1 + Sqrt[2])*(5 + Sqrt[13])/6, 10, 120][[1]] (* Amiram Eldar, Jun 28 2023 *)
CROSSREFS
Cf. A341029 (finite hull areas).
Sequence in context: A128078 A331152 A264922 * A233528 A084604 A152253
KEYWORD
cons,nonn
AUTHOR
Kevin Ryde, Feb 02 2021
STATUS
approved