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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

%I #20 Mar 04 2018 10:31:54

%S 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,

%T 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,

%U 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

%N Result of the morphing 01->01021212, 02->0102121201, 12->01021201, iterated from '01'. Sequence of the Fibonacci word fractal.

%C Letter '2' is always in an even position and '0' an odd position.

%C When replacing '2' by '0', equals the infinite Fibonacci word (see A003849).

%C 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).

%C This sequence is the [1->12, 2->01, 3->02]-transform of A123564. - _Michel Dekking_, Mar 03 2018

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

%H Alexis Monnerot-Dumaine, <a href="https://hal.archives-ouvertes.fr/hal-00367972"> The Fibonacci Word Fractal</a>, HAL Id : hal-00367972, 2009.

%F 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).

%Y Cf. A003849, A123564.

%K nonn

%O 1,4

%A Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Aug 28 2008

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Last modified April 18 10:01 EDT 2024. Contains 371779 sequences. (Running on oeis4.)