Editing Sierpiński carpet (section)

==Construction==
The construction of the Sierpiński carpet begins with a [[square (geometry)|square]]. The square is cut into 9 [[congruence (geometry)|congruent]] subsquares in a 3-by-3 grid, and the central subsquare is removed. The same procedure is then applied [[recursion|recursively]] to the remaining 8 subsquares, ''ad infinitum''. It can be realised as the set of points in the unit square whose coordinates written in base three do not both have a digit '1' in the same position, using the infinitesimal number representation of <math>0.1111\dots=0.2</math>.<ref>{{cite book | last1 = Allouche | first1 = Jean-Paul | last2 = Shallit | first2 = Jeffrey | author2-link = Jeffrey Shallit | isbn = 978-0-521-82332-6 | publisher = [[Cambridge University Press]] | title = Automatic Sequences: Theory, Applications, Generalizations | url = https://archive.org/details/automaticsequenc00jpal | url-access = limited | year = 2003 | zbl=1086.11015 | pages=[https://archive.org/details/automaticsequenc00jpal/page/n422 405]–406 }}</ref>

The process of recursively removing squares is an example of a [[finite subdivision rule]].