cutting sequence

{{short description|Records individual grid lines crossed ("cut") as a curve crosses a square grid}}

File:Fibonacci word cutting sequence.png 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.{{Cite journal | last1 = Monteil | first1 = T. | doi = 10.4204/EPTCS.63.21 | title = The complexity of tangent words | journal = Electronic Proceedings in Theoretical Computer Science | volume = 63 | pages = 152–157 | year = 2011 | arxiv = 1108.3632 | s2cid = 6350859 }}

Sturmian words are a special case of cutting sequences where the curves are straight lines of irrational slope.Pytheas Fogg (2002) p.152