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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

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## Perimeter Calculator

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

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

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.

### 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.

## Source code

dCode retains ownership of the source code of the script Koch Flake. Except explicit open source licence (free / freeware), any algorithm, applet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any snippet or function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in PHP (or Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Koch Flake script for offline use, for you, your company or association, see you on contact page !

## Questions / Comments

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Koch Flake tool. Thank you.

Source : http://www.dcode.fr/koch-flake
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