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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
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
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
KEYWORD
nice,nonn
AUTHOR
Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Feb 10 2009
STATUS
approved