Cantor set
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In mathematics, the Cantor set is a self-similar set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and men
Cantor dust (3D)
Column capital with pattern evocative of the Cantor set, but expressed in binary rather than ternary. Engraving of Île de Philae from Description d'Égypte by Jean-Baptiste Prosper Jollois and Édouard Devilliers, Imprimerie Impériale, Paris, 1809-1828
Menger sponge
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In mathematics, the Menger sponge is a fractal curve. It is a three-dimensional generalization of the two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies o
Cantor set
…removed. The remaining squares are then further divided into nine each and the middle removed, and so on ad infinitum. One 3D analogue of this is the Menger sponge. Cantor introduced what we call today the Cantor ternary set C as an example "of a perfect point-set, which is not everywhere-dense in any interval…
An illustration of the iterative construction of a Menger sponge up to M3, the third iteration
One of the MegaMengers, at the University of Bath
A model of a Tetrix viewed through the center of the Cambridge Level-3 MegaMenger at the 2015 Cambridge Science Festival
3D-printed model Jerusalem cube