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A349009
Decimal expansion of the area of the convex hull around the R5 dragon fractal.
5
9, 7, 6, 1, 6, 4, 0, 0, 2, 9, 1, 2, 7, 0, 3, 5, 1, 3, 4, 0, 6, 4, 0, 7, 1, 5, 8, 0, 8, 4, 2, 1, 1, 1, 2, 9, 7, 2, 6, 3, 1, 2, 1, 9, 9, 3, 1, 7, 3, 2, 6, 9, 0, 5, 2, 4, 3, 4, 9, 4, 8, 8, 0, 3, 0, 0, 8, 2, 8, 7, 3, 8, 6, 7, 9, 6, 5, 1, 1, 6, 0, 1, 1, 0, 7, 5, 0, 4, 2, 4, 7, 8, 8, 5, 1, 6, 1, 5, 8, 6, 3, 8, 6, 6, 9
OFFSET
0,1
COMMENTS
The fractal is taken scaled to unit length from curve start to end.
In the sum formula below, all HAtermf(j) > 0 and a simple upper bound is Sum_{j>=k} HAtermf(j) < 1/sqrt(5)^k.
LINKS
Kevin Ryde, Iterations of the R5 Dragon Curve, see index "HAf".
Kevin Ryde, PARI/GP Code
FORMULA
Equals 17/25 + Sum_{j>=1} HAtermf(j), where complex b=1+2*i and:
HAtermf(j) = (1/25)*(6*HAgrowf(1/b^j) + 2*HAgrowf((4+i)/b^j)),
HAgrowf(z) = MinReIm(ShearIm(RotQ(z))),
MinReIm(z) = min(abs(Re z), abs(Im z)),
ShearIm(z) = z + i*Im(z),
RotQ(z) = z if sign(Re z) = sign(Im z), or RotQ(z) = z*i otherwise.
Equals lim_{n->oo} A349008(n)/5^n.
EXAMPLE
0.97616400291270351340640715808421112...
PROG
(PARI) See links.
CROSSREFS
Cf. A349008 (finite areas), A349010 (fractal perimeter).
Sequence in context: A194554 A065467 A021839 * A094131 A021510 A199272
KEYWORD
cons,nonn
AUTHOR
Kevin Ryde, Nov 06 2021
STATUS
approved