Sierpinski curve
The Sierpiński curves are a recursively defined sequence of continuous closed fractal curves . The Sierpiński curve is an example of a space-filling curve that completely fills the unit square in the transition . They were defined in 1912 by the Polish mathematician Wacław Sierpiński .
properties
- The limit of the area enclosed by the Sierpiński curve is (in Euclidean metric).
- The Euclidean length of the curve is growing exponentially with : .
- Since the curve is space-filling, it has the Hausdorff dimension in the limit value .
Web links
Commons : Sierpinski curve - album with pictures, videos and audio files