Search for a tool
Koch Flake

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

Results

Koch Flake -

Tag(s) : Geometry

Share
Share
dCode and more

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!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Thanks to your feedback and relevant comments, dCode has developed the best 'Koch Flake' tool, so feel free to write! Thank you!

Koch Flake

Sponsored ads

Area Calculator



Perimeter Calculator



Answers to Questions (FAQ)

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.

$$ \lim\limits_{n \to +\infty} \left( \frac43 \right)^n = +\infty $$

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.

For a side of the triangle $ a $, the final area of the flake is $ \frac{2a^2\sqrt{3}}{5} $

How to draw a Koch flake?

The algorithm is as follows:

0 - Draw an isosceles triangle and for each side (segment)

1 - Calculate the points at 1/3 and 2/3 of the segment

2 - Draw the isosceles triangle based on the segment formed with the 2 points found

3 - Remove the base of this new triangle

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 online 'Koch Flake' tool source code. Except explicit open source licence (indicated CC / Creative Commons / free), any 'Koch Flake' algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any 'Koch Flake' function (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and no data download, script, copy-paste, or API access for 'Koch Flake' will be for free, same for offline use on PC, tablet, iPhone or Android ! dCode is free and online.

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Thanks to your feedback and relevant comments, dCode has developed the best 'Koch Flake' tool, so feel free to write! Thank you!


Source : https://www.dcode.fr/koch-flake
© 2021 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
Feedback