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Koch Flake

Tools to calculate the area and perimeter of the Koch flake (or Koch curve), curve representing a fractal snowflake.

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Koch Flake -

Tag(s) : Geometry, Mathematics

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# Koch Flake

## Perimeter Calculator

Tools to calculate the area and perimeter of the Koch flake (or Koch curve), curve representing a fractal snowflake.

### How to calculate the Koch Flake Perimeter?

The length of the border of the flake is infinite. At each iteration, a border of length 1 become 4/3.

Starting from a straight line segment divided by 3, we obtain a broken line of 4 segments: the length is therefore increased by 4/3 (increase of 33%).

Example: After 2 iterations, a line of initial length $$l$$ has a new length of $$l \times \frac43 \times \frac43 = l \times \frac{16}{9}$$.

If the number of iterations is infinite, the length is infinitely increased by 4/3. The total length of this fractal curve is infinite. $$\lim\limits_{n \to +\infty} \left( \frac43 \right)^n = +\infty$$

### How to calculate the area of the Koch flake?

The area of the flake is finite and equals 8/5 of the area of the initial triangle.