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Menger sponge





Menger sponge
A famous fractal solid that is the three-dimensional equivalent of the Sierpinski carpet (which, in turn, is the one-dimensional equivalent of Cantor dust). To make a Menger sponge, take a cube, divide it into 27 (= 3 × 3 × 3) smaller cubes of the same size and remove the cube in the center and the six cubes that share faces with it. What's left are the eight small corner cubes and twelve small edge cubes holding them together. Now, imagine repeating this process on each of the remaining 20 cubes. Repeat it again. And again ... ad infinitum. The Menger sponge was invented in 1926 by the Austrian mathematician Karl Menger (1902–1985).


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   • FRACTALS AND PATHOLOGICAL CURVES