A156596 - OEIS

%I #9 Jul 16 2015 09:52:26

%S 1,0,1,2,0,2,0,2,1,0,1,2,0,2,0,2,1,0,1,0,1,2,0,2,1,0,1,0,1,2,0,2,1,0,

%T 1,0,1,2,0,2,0,2,1,0,1,2,0,2,0,2,1,0,1,0,1,2,0,2,1,0,1,0,1,2,0,2,1,0,

%U 1,0,1,2,0,2,0,2,1,0,1,2,0,2,0,2,1,0,1,2,0,2,0,2,1,0,1,0,1,2,0,2,1,0,1,0,1

%N Infinite Fibonacci word fractal sequence.

%C Apply to A143667 the map : 0 -> 12, 1 -> 10, 2 -> 02. or apply to A003849 (the Fibonacci word), after grouping the terms 2 by 2, the map : "00" -> "12", "01"->"10, "10"->"02". Draws the Fibonacci word fractal curve when applying the following drawing rule: if "0" then draw a segment forward, if "1" then draw a segment forward and turn 90A degs right, if "2" the draw segment and turn 90A degs left.

%D M. Lothaire, Combinatorics on words, Cambridge University Press.

%H Reinhard Zumkeller, <a href="/A156596/b156596.txt">Table of n, a(n) for n = 1..1000</a>

%H A. Monnerot-Dumaine, <a href="http://alexis.monnerot-dumaine.neuf.fr/articles/fibonacci%20fractal.pdf">Fibonacci word fractal</a>

%t Partition[Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}]&, {0}, 10], 2] /. {{0, 0} -> {1, 2}, {0, 1} -> {1, 0}, {1, 0} -> {0, 2}} // Flatten (* _Jean-François Alcover_, Jul 16 2015 *)

%o (Haskell)

%o a143667 n = a143667_list !! (n-1)

%o a143667_list = f a003849_list where

%o    f (0:0:ws) = 0 : f ws; f (0:1:ws) = 1 : f ws; f (1:0:ws) = 2 : f ws

%o -- _Reinhard Zumkeller_, Jul 29 2014

%Y A003849, A143667.

%K nice,nonn

%O 1,4

%A Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Feb 10 2009