

A176416


Fixed point of morphism 0>0PPMM00, P>0PPMM0P, M=0PPMM0M (where P=+1, M=1)


2



0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1
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OFFSET

0,1


COMMENTS

Turns by 120 degrees of a dragon curve (see fxtbook link below).
Also fixed point of morphism F>F0FMFMFPFPF0F, 0>0, P>P, M>M (after deleting all F).
Let d(n) be the lowest nonzero digit in the radix7 expansion of (n+1), then if d(n)==[1,2,3,4,5,6] ==> a(n):=[0,+1,+1,1,1,0].


LINKS

Table of n, a(n) for n=0..78.
Joerg Arndt, Matters Computational (The Fxtbook), section 1.31.5 "Dragon curves based on radixR counting", pp.95101; image on p.98


PROG

(C++) /* CATalgorithm */
int bit_dragon_r7_2_turn(unsigned long &x)
/* Increment the radix7 word x and return (tr)
according to the lowest nonzero digit d of the incremented word:
d==[1, 2, 3, 4, 5, 6] ==> rt:=[0, +1, +1, 1, 1, 0] */
{
unsigned long s = 0;
while ( (x & 7) == 6 ) { x >>= 3; ++s; } /* scan over nines */
++x; /* increment next digit */
int tr = 2  ( (0x2f58 >> (2*(x&7)) ) & 3 ); x <<= (3*s); /* shift back */
return tr;
}


CROSSREFS

Cf. A080846 (with terdragon curve), A014577 (with Heighway dragon), A175337 (with R5dragon), and A176405 (with R7dragon).
Sequence in context: A138886 A269528 A099859 * A102460 A080908 A131720
Adjacent sequences: A176413 A176414 A176415 * A176417 A176418 A176419


KEYWORD

sign


AUTHOR

Joerg Arndt, Apr 17 2010


STATUS

approved



