A143668 Result of the morphing 01->01021212, 02->0102121201, 12->01021201, iterated from '01'. Sequence of the Fibonacci word fractal.

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

Offset: 1

Author

Alexis Monnerot-Dumaine, Aug 28 2008

Keywords

• nonn

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.
• Alexis Monnerot-Dumaine, The Fibonacci word fractal [Cached copy, with permission]

Crossrefs

Cf. A003849, A123564.

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).