Cutting sequence
The Fibonacci word is an example of a Sturmian word. The start of the cutting sequence shown here illustrates the start of the word 0100101001.
In digital geometry, a cutting sequence is a sequence of symbols whose elements correspond to the individual grid lines crossed ("cut") as a curve crosses a square grid.[1]
Sturmian words are a special case of cutting sequences where the curves are straight lines of irrational slope.[2]
References
- ↑ Monteil, T. (2011). "The complexity of tangent words". Electronic Proceedings in Theoretical Computer Science. 63: 152. doi:10.4204/EPTCS.63.21.
- ↑ Pytheas Fogg (2002) p.152
- Pytheas Fogg, N. (2002). Substitutions in dynamics, arithmetics and combinatorics. Lecture Notes in Mathematics. 1794. Editors Berthé, Valérie; Ferenczi, Sébastien; Mauduit, Christian; Siegel, A. Berlin: Springer-Verlag. ISBN 3-540-44141-7. Zbl 1014.11015.
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