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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 (list; graph; refs; listen; history; text; internal format)
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 radix-7 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 radix-R counting", pp.95-101; image on p.98

PROG

(C++) /* CAT-algorithm */

int bit_dragon_r7_2_turn(unsigned long &x)

/* Increment the radix-7 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 R5-dragon), and A176405 (with R7-dragon).

Sequence in context: A161382 A138886 A099859 * A102460 A080908 A131720

Adjacent sequences:  A176413 A176414 A176415 * A176417 A176418 A176419

KEYWORD

sign

AUTHOR

Joerg Arndt, Apr 17 2010

STATUS

approved

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Last modified April 27 06:52 EDT 2017. Contains 285508 sequences.