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Sierpinski Curve

\begin{figure}\begin{center}\BoxedEPSF{SierpinskiCurve.epsf scaled 700}\end{center}\end{figure}

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


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

Dickau, R. M. ``Two-Dimensional L-Systems.''

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.

© 1996-9 Eric W. Weisstein