Editing Cantor set (section)

=== Cantor dust ===
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'''Cantor dust''' is a multi-dimensional version of the Cantor set. It can be formed by taking a finite [[Cartesian product]] of the Cantor set with itself, making it a [[Cantor space]]. Like the Cantor set, Cantor dust has [[Measure zero|zero measure]].<ref>{{cite book|author=Helmberg, Gilbert|title=Getting Acquainted With Fractals|publisher=Walter de Gruyter|year=2007|isbn=978-3-11-019092-2|page=46|url=https://books.google.com/books?id=PbrlYO83Oq8C&pg=PA46}}</ref>
[[File:Cantorcubes.gif|thumb|right|250px|[[Cantor cube]]s recursion progression towards Cantor dust]]
{|
|[[Image:Cantor dust.svg|thumb|'''Cantor dust''' (2D)]]
|[[Image:Cantors cube.jpg|thumb|'''Cantor dust''' (3D)]]
|}

A different 2D analogue of the Cantor set is the [[Sierpinski carpet]], where a square is divided up into nine smaller squares, and the middle one removed. The remaining squares are then further divided into nine each and the middle removed, and so on ad infinitum.<ref>{{cite book|author=Helmberg, Gilbert|title=Getting Acquainted With Fractals|publisher=Walter de Gruyter|year=2007|isbn=978-3-11-019092-2|page=48|url=https://books.google.com/books?id=PbrlYO83Oq8C&pg=PA48}}</ref> One 3D analogue of this is the [[Menger sponge]].