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Sierpiński carpet

The Sierpiński carpet is a fractal because of the endless repetition of self-similar patterns.

 

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Explanation

Exactly from the middle of a square another square is removed that is one-ninth part of the plane. This procedure is then repeated in each of the remaining eight squares. It can be repeated infinitely.

step 0

step 1

step 2

step 3

step 4

 

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History Polish mathematician Wacław Sierpiński (1882 - 1962) worked on precursors to fractals.

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