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Koch Antisnowflake


KochAntisnowflake

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

KochAntisnowflakeMotif

The area enclosed by pieces of the curve after the nth iteration is

 A_n=A_(n-1)+1/3(l_(n-1))/aDelta/(3^n),

where Delta is the area of the original equilateral triangle, so from the derivation for the Koch snowflake, the total area enclosed is

 A=lim_(n->infty)A_n=(1+3/5)Delta=8/5Delta.

See also

Exterior Snowflake, Gosper Island, Koch Snowflake, Pentaflake, Sierpiński Curve

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References

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.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 136, 1991.

Referenced on Wolfram|Alpha

Koch Antisnowflake

Cite this as:

Weisstein, Eric W. "Koch Antisnowflake." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KochAntisnowflake.html

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