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A143668 Result of the morphing 01->01021212, 02->0102121201, 12->01021201, iterated from '01'. Sequence of the Fibonacci word fractal. 0
0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Letter '2' is always in an even position and '0' an odd position.
When replacing '2' by '0', equals the infinite Fibonacci word (see A003849).
This sequence produces the Fibonacci word fractal when applying the following turtle graphics rules: 0->draw segment+turn right, 1-> draw segment, 2-> draw segment+turn left (A. Monnerot-Dumaine 2008 see links).
This sequence is the [1->12, 2->01, 3->02]-transform of A123564. - Michel Dekking, Mar 03 2018
REFERENCES
M. Lothaire, Combinatorics on words, Cambridge University press.
LINKS
Alexis Monnerot-Dumaine, The Fibonacci Word Fractal, HAL Id : hal-00367972, 2009.
FORMULA
Let (b(n)) be the infinite Fibonacci word. if (b(n)=0 and n is even), then a(n)=2, else a(n)=b(n).
CROSSREFS
Sequence in context: A268041 A348248 A060024 * A029445 A274920 A316828
KEYWORD
nonn
AUTHOR
Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Aug 28 2008
STATUS
approved

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Last modified February 22 02:45 EST 2024. Contains 370239 sequences. (Running on oeis4.)