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%I #13 Aug 30 2014 18:57:21
%S 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,
%T 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,
%U 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
%N Fixed point of morphism 0 -> 00110, 1 -> 00111
%C Turns (by 90 degrees) of a dragon curve (called R5-dragon in the fxtbook, see link below) which can be rendered as follows:
%C [Init] Set n=0 and direction=0.
%C [Draw] Draw a unit line (in the current direction). Turn left/right if a(n) is zero/nonzero respectively.
%C [Next] Set n=n+1 and goto (draw).
%C With counting in radix 5: whether the lowest nonzero digit is >2 (see C++ code).
%C With morphism F -> F0F0F1F1F, 0 -> 0, 1 -> 1: fixed point with all 'F' omitted.
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.31.5 "Dragon curves based on radix-R counting", pp.95-101; image on p.96
%o (C++) /* CAT algorithm */
%o bool bit_dragon_r5_turn(ulong &x)
%o /* Increment the radix-5 word x and return (tr) whether
%o the lowest nonzero digit of the incremented word is > 2. */
%o {
%o ulong s = 0;
%o while ( (x & 7) == 4 ) { x >>= 3; ++s; } /* scan over nines */
%o bool tr = ( (x & 7) >= 2 ); /* whether digit will be > 2 */
%o ++x; /* increment next digit */
%o x <<= (3*s); /* shift back */
%o return tr;
%o }
%Y Cf. A080846 (with terdragon curve) and A014577 (with Heighway dragon).
%K nonn
%O 0,1
%A _Joerg Arndt_, Apr 15 2010
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