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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=2/5Delta.
 

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