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Sierpiński's Triangle

The Sierpinski Triangle (also with the original orthography Sierpi?ski), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set named after the Polish mathematician Waclaw Sierpiński who described it in 1915.
However, similar patterns appear already in the 13th-century Cosmati mosaics in the cathedral of Anagni, Italy, and other places, such as in the nave of the Roman Basilica of Santa Maria in Cosmedin.

Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction.

Comparing the Sierpinski triangle or the Sierpinski carpet to equivalent repetitive tiling arrangements, it is evident that similar structures can be built into any rep-tile arrangements.

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