The fractal derived from the Koch snowflake when the triangular point of the motif faces inward when placed on the base curve as illustrated above may be termed the Koch antisnowflake.
The first few iterations of the Koch antisnowflake are illustrated above.
Let 
be the number of segments, 
be the length of a single segment, 
be the length of the perimeter,
and 
the enclosed area after the 
th iteration. Denote the area of the
initial 
triangle 
, and let the length of an initial 
side be 1. Then
Solving the recurrence equation with 
gives
![A_n=1/5[2+3(4/9)^n]Delta,](https://txtdot.deep-swarm.xyz/proxy/img?url=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FKochAntisnowflake%2FNumberedEquation1.svg){kind=small} |
(7) |
so as 
,
 |
(8) |
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.
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Cite this as:
Weisstein, Eric W. "Koch Antisnowflake." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KochAntisnowflake.html