A341030 - OEIS

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

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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

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".

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