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 A156596 Infinite Fibonacci word fractal sequence. 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. REFERENCES M. Lothaire, Combinatorics on words, Cambridge University Press. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 A. Monnerot-Dumaine, Fibonacci word fractal MATHEMATICA 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 *) PROG (Haskell) a143667 n = a143667_list !! (n-1) a143667_list = f a003849_list where    f (0:0:ws) = 0 : f ws; f (0:1:ws) = 1 : f ws; f (1:0:ws) = 2 : f ws -- Reinhard Zumkeller, Jul 29 2014 CROSSREFS Sequence in context: A137899 A243822 A277150 * A282570 A026613 A117199 Adjacent sequences:  A156593 A156594 A156595 * A156597 A156598 A156599 KEYWORD nice,nonn AUTHOR Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Feb 10 2009 STATUS approved

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