Sierpinski carpet for dummies

Plane fractal built from squares

"Sierpinski snowflake" redirects here. For other uses, see Sierpiński curve.

The Sierpiński carpet is a plane fractal first described by Wacław Sierpiński in 1916. The carpet is a generalization of the Cantor set to two dimensions; another such generalization is the Cantor dust.

The technique of subdividing a shape into smaller copies of itself, removing one or more copies, and continuing recursively can be extended to other shapes.

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For instance, subdividing an equilateral triangle into four equilateral triangles, removing the middle triangle, and recursing leads to the Sierpiński triangle. In three dimensions, a similar construction based on cubes is known as the Menger sponge.

Construction

The construction of the Sierpiński carpet begins with a square.

The square is cut into 9 congruent subsquares in a 3-by-3 grid, and the central subsquare is removed. The same procedure is then applied recursively to the remaining How to draw a sierpinski carpet in python using turtle GOLUN