The Sierpinski carpet is a plane fractal first described by Wacław Sierpinski in 1916. It generalizes the Cantor set to two dimensions, as does the related construction called Cantor dust. It is built by the technique of subdividing a shape into smaller copies of itself, removing one or more of those copies, and recursing; the same technique applied to an equilateral triangle, subdivided into four smaller triangles with the middle one removed at each step, produces the Sierpinski triangle instead, and a three-dimensional version built from cubes is called the Menger sponge.
Facts
Sierpinski Carpet
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Source Wikipedia: Wacław Sierpiński
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1. Wikipedia: Sierpinski carpet
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The Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916.
Properties
That is: the Sierpiński carpet is a compact subset of the plane with Lebesgue covering dimension 1, and every subset of the plane with these properties is homeomorphic to some subset of the Sierpiński carpet.
Attributed To: Wacław Sierpiński, Lead sentence, attribution
first described by Wacław Sierpiński in 1916
View the SourceWikipedia: Wacław Sierpiński
Principal Result Of: Wacław Sierpiński, Article textQuote, Principal Result Of: Wacław Sierpiński, Article text
Three well-known fractals are named after him (the Sierpiński triangle, the Sierpiński carpet, and the Sierpiński curve), as are Sierpiński numbers and the associated Sierpiński problem.
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