

A175337


Fixed point of morphism 0 > 00110, 1 > 00111


4



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

0,1


COMMENTS

Turns (by 90 degrees) of a dragon curve (called R5dragon 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.


LINKS



MATHEMATICA

Nest[Flatten[ReplaceAll[#, {0>{0, 0, 1, 1, 0}, 1>{0, 0, 1, 1, 1}}]]&, {0}, 3] (* Paolo Xausa, Nov 09 2023 *)


PROG

(C++) /* CAT algorithm */
bool bit_dragon_r5_turn(ulong &x)
/* Increment the radix5 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;
}


CROSSREFS

Cf. A080846 (with terdragon curve) and A014577 (with Heighway dragon).


KEYWORD

nonn


AUTHOR



STATUS

approved



