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Menger sponge
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In mathematics, the Menger sponge is a fractal curve. It is a three-dimensional generalization of the one-dimensional Cantor set and two-dimensional Sierpinski carpet. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension.
An illustration of the iterative construction of a Menger sponge up to M3, the third iteration
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
One of the MegaMengers, at the University of Bath
A model of a tetrix viewed through the centre of the Cambridge Level-3 MegaMenger at the 2015 Cambridge Science Festival
A model of a tetrix viewed through the centre of the Cambridge Level-3 MegaMenger at the 2015 Cambridge Science Festival
3D-printed model Jerusalem cube
3D-printed model Jerusalem cube
Cantor set
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In mathematics, the Cantor set is a 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 mentioned by German mathematician Georg Cantor in 1883.
Cantor dust (3D)
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'Ég
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