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A175337
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Fixed point of morphism 0 -> 00110, 1 -> 00111
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1
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0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0
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OFFSET
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0,1
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COMMENTS
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Turns (by 90 degrees) of a dragon curve (called R5-dragon in the fxtbook, see link below) which can be rendered as follows:
[Init] Set n=0 and direction=0.
[Draw] Draw a unit line (in the current direction). Turn left/right if a(n) is zero/nonzero respectively.
[Next] Set n=n+1 and goto (draw).
With counting in radix 5: whether the lowest nonzero digit is >2 (see C++ code).
With morphism F -> F0F0F1F1F, 0 -> 0, 1 -> 1: fixed point with all 'F' omitted.
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LINKS
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Table of n, a(n) for n=0..104.
Joerg Arndt, Fxtbook, section 1.31.5 "Dragon curves based on radix-R counting", pp.95-101; image on p.96
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PROG
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(C++) /* CAT algorithm */
bool bit_dragon_r5_turn(ulong &x)
/* Increment the radix-5 word x and return (tr) whether
the lowest nonzero digit of the incremented word is > 2. */
{
ulong s = 0;
while ( (x & 7) == 4 ) { x >>= 3; ++s; } /* scan over nines */
bool tr = ( (x & 7) >= 2 ); /* whether digit will be > 2 */
++x; /* increment next digit */
x <<= (3*s); /* shift back */
return tr;
}
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CROSSREFS
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Cf. A080846 (with terdragon curve) and A014577 (with Heighway dragon).
Sequence in context: A043545 A094754 A091225 * A132380 A021913 A156660
Adjacent sequences: A175334 A175335 A175336 * A175338 A175339 A175340
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KEYWORD
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nonn
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AUTHOR
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Joerg Arndt, Apr 15 2010
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STATUS
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approved
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