The Koch Snowflake / Curve
In: Mathematics
In math, there’s a type of object called a fractal, which essentially means a shape with a super wonky edge (infinitely wonky in fact). The Koch snowflake is an example of this. It’s called a snowflake because it looks like a snowflake.
To get the Koch snowflake, you start with a triangle. On each side, erase the middle third, and add another triangle. Then, on each side of the new shape, do the same thing. Over and over. Forever. (This is where the infinite wonky ness comes in).
I’m not aware of any uses of the Koch snowflake, but some other fractals have some interesting properties. For example, the Weierstrass function (look it up, it’s pretty cool looking) has corners at every point, and is an important counterexample in calculus. (In fact, the Koch snowflake shares the same property-its differentiable nowhere, but continuous everywhere).
Another interesting thing is that the Koch snowflake has infinite perimeter (after you’ve done the infinitely many steps, which strictly speaking means “in the limit as steps go to infinity”, but we don’t have to worry about that here), but only finite area.
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