# The Anti-Snowflake

Let's make another fractal. It's an interesting variation on the Koch Snowflake.

Directions:

Step One. Start with a large equilateral triangle. If you use the triangle grid paper, make the sides of your triangle 9 grid triangles long (or some other multiple of 3).

Step Two. Make a pinwheel:

1. Divide one side of the triangle into three parts and remove the middle section.

2. Replace it with two lines the same length as the section you removed, just like in the Koch Snowflake. But this time, instead of turning the section out to form a snowflake, turn them inside the triangle

3. Do this to all three sides of the triangle.

Step Three. Repeat the process with the "triangles" inside the pinwheel.

Original Triangle

First Iteration

Second Iteration

Once more...     Third Iteration

And one more time...

Fourth Iteration

Thought Questions:

1. Compare the perimeter of Anti-Snowflake with that of the Koch Snowflake.
2. Now compare their areas.

My thanks to William Mcworter, my mathematician caddy, who assists me immeasurably with the mathematics on my pages.

lanius@math.rice.edu