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Koch Antisnowflake

\begin{figure}\begin{center}\BoxedEPSF{KochAntisnowflake.epsf scaled 580}\end{center}\end{figure}

A Fractal derived from the Koch Snowflake. The base curve and motif for the fractal are illustrated below.

\begin{figure}\begin{center}\BoxedEPSF{KochAntisnowflakeMotif.epsf scaled 800}\end{center}\end{figure}

The Area after the $n$th iteration is

A_n = A_{n-1}-{1\over 3}{\ell_{n-1}\over a}{\Delta\over 3^n},

where $\Delta$ is the area of the original Equilateral Triangle, so from the derivation for the Koch Snowflake,

A \equiv \lim_{n\to\infty} A_n = (1-{\textstyle{3\over 5}})\Delta = {\textstyle{2\over 5}}\Delta.

See also Exterior Snowflake, Flowsnake Fractal, Koch Snowflake, Pentaflake, Sierpinski Curve


Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 66-67, 1989.

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 36-37, 1991.

mathematica.gif Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.

© 1996-9 Eric W. Weisstein