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

Answers to Questions

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, a broken line of 4 segments os obtained: 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 times increased by 4/3. The total length of this fractal curve is infinite.

4 - Repeat from step 1 for each segment of the new figure

Mathematically speaking, the final drawing is called the Koch curve, and its base is a set of Cantor.

Source code

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