Cutting sequence

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]

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.

Sturmian words are a special case of cutting sequences where the curves are straight lines of irrational slope.[2]

References
Notes
  1. Monteil, T. (2011). "The complexity of tangent words". Electronic Proceedings in Theoretical Computer Science. 63: 152–157. arXiv:1108.3632. doi:10.4204/EPTCS.63.21. S2CID 6350859.
  2. Pytheas Fogg (2002) p.152
Bibliography
  • Pytheas Fogg, N. (2002). Berthé, Valérie; Ferenczi, Sébastien; Mauduit, Christian; Siegel, A. (eds.). Substitutions in dynamics, arithmetics and combinatorics. Lecture Notes in Mathematics. Vol. 1794. Berlin: Springer-Verlag. ISBN 3-540-44141-7. Zbl 1014.11015.
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