Sierpiński curve

The Sierpiński curves are a recursively defined sequence of continuous closed fractal curves, which fill in the transition the unit square (so-called space-filling curve or FASS ). They were defined in 1912 by the Polish mathematician Waclaw Sierpiński.

The limit of the area enclosed by the curve Sierpiński area ( in Euclidean metric ). The Euclidean length of the curve, i.e., grows exponentially with.