Sierpinski Curve

There are several Fractal curves associated with Sierpinski. The above curve is one example, and the Sierpinski Arrowhead Curve is another. The limit of the curve illustrated above has Area

$$A={\textstyle{5\over 12}}.$$

The Area for a related curve illustrated by Cundy and Rollett (1989) is

$$A={\textstyle{1\over 3}}(7-4\sqrt{2}\,).$$

See also Exterior Snowflake, Gosper Island, Hilbert Curve, Koch Antisnowflake, Koch Snowflake, Peano Curve, Peano-Gosper Curve, Sierpinski Arrowhead Curve

References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 67-68, 1989.

Dickau, R. M. ``Two-Dimensional L-Systems.'' http://forum.swarthmore.edu/advanced/robertd/lsys2d.html.

Gardner, M. Penrose Tiles and Trapdoor Ciphers... and the Return of Dr. Matrix, reissue ed. New York: W. H. Freeman, p. 34, 1989.

Wagon, S. Mathematica in Action. New York: W. H. Freeman, p. 207, 1991.