Cantor dust
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Cantor dust is a multi-dimensional version of the Cantor set.
Description
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 zero measure.
Sierpinski carpet and Menger sponge
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.
The 3D analogue of this is the Menger sponge.
