Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit n → ∞ {\displaystyle n\to \infty } completely fill the unit square: thus their limit curve, also called the Sierpiński curve, is an example of a space-filling curve. Because the Sierpiński curve is space-filling, its Hausdorff dimension (in the limit n → ∞ {\displaystyle n\to \infty } ) is 2 {\displaystyle 2} .
Sierpiński curves are a recursively defined sequence of continuous closed plane fractal curves discovered by Wacław Sierpiński, which in the limit n → ∞ {\displaystyle n\to \infty } completely fill the unit square: thus their limit curve, also called the Sierpiński curve, is an example of a space-filling curve. Because the Sierpiński curve is space-filling, its Hausdorff dimension (in the limit n → ∞ {\displaystyle n\to \infty } ) is 2 {\displaystyle 2} .
Source: Wikipedia "Sierpiński curve" · CC BY-SA 4.0
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