dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day! A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

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

dCode retains ownership of the source code of the script Koch Flake online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Koch Flake script for offline use on PC, iPhone or Android, ask for price quote on contact page !