A341030 Decimal expansion of the perimeter of the convex hull around the dragon curve fractal.

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

Author

Kevin Ryde, Feb 02 2021

Keywords

• cons
• nonn

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.

Examples

			4.1292731001...
		

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000
• 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".

Crossrefs

Cf. A341029 (finite hull areas).

Programs

Mathematica

RealDigits[2/3 + (1 + Sqrt[2])*(5 + Sqrt[13])/6, 10, 120][[1]] (* Amiram Eldar, Jun 28 2023 *)

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).