%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
|