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, Table of n, a(n) for n = 0..10000
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
KEYWORD
cons,nonn
AUTHOR
Kevin Ryde, Nov 06 2021
STATUS
approved