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 A176416 Fixed point of morphism 0->0PPMM00, P->0PPMM0P, M=0PPMM0M (where P=+1, M=-1) 2

%I

%S 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,

%T 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,

%U -1,-1,0,1,0,1,1,-1,-1,0,1,0,1,1,-1,-1,0,-1,0,1

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

%C Turns by 120 degrees of a dragon curve (see fxtbook link below).

%C Also fixed point of morphism F->F0FMFMFPFPF0F, 0->0, P->P, M->M (after deleting all F).

%C 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].

%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.98

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

%o int bit_dragon_r7_2_turn(unsigned long &x)

%o /* Increment the radix-7 word x and return (tr)

%o according to the lowest nonzero digit d of the incremented word:

%o d==[1,2,3,4,5,6] ==> rt:=[0,+1,+1,-1,-1,0] */

%o {

%o unsigned long s = 0;

%o while ( (x & 7) == 6 ) { x >>= 3; ++s; } /* scan over nines */

%o ++x; /* increment next digit */

%o int tr = 2 - ( (0x2f58 >> (2*(x&7)) ) & 3 ); x <<= (3*s); /* shift back */

%o return tr;

%o }

%Y Cf. A080846 (with terdragon curve), A014577 (with Heighway dragon), A175337 (with R5-dragon), and A176405 (with R7-dragon).

%K sign

%O 0,1

%A _Joerg Arndt_, Apr 17 2010

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Last modified April 13 16:36 EDT 2021. Contains 342936 sequences. (Running on oeis4.)