Koch Snowflake (also known as the Koch Curve, Koch Star or Koch Island) — it is a mathematical curve and one of the earliest fractal curves described. It is based on the Koch curve, published by the Swedish mathematician Helge von Koch in a 1904 article entitled “On a continuous curve without tangents, constructed from elementary geometry.”

The progression for the snowflake region converges 8/5 times the area the original triangle, while the progression along the perimeter of the snowflake diverges to infinity. Therefore, the snowflake has a finite area bounded by an infinitely long line.

** Step 1: **

Draw an equilateral triangle. You can draw it with a compass or a protractor, or just look at it if you don`t want to spend too much time drawing a snowflake.

** Step 2: **

Divide each side into three equal parts. This is why it is convenient to divide the sides into three.

** Step 3: **

Draw an equilateral triangle on each middle part. Measure the length of the middle third to find out the length of the sides of these new triangles.

** Step 4: **

Separate each outside by a third. You can see the 2nd generation of triangles cover a bit of the 1st. These three segments should not be divided into three.

** Step 5: **

Draw an equilateral triangle on each middle section.

** **

The Koch Curve can be expressed by the following rewriting system ( Lindenmayer system ):

** Alphabet **: F

** Constants **: + ,?

** Axiom **: F

** Production rules **: F? F + FF + F

Here F means "pull forward", — means turn right 60 °, and + means turn left 60 °.

To create a Koch snowflake, you can use F ++ F ++ F (equilateral triangle) as an axiom.

` `
` ` |

** Output: ** < / p>

To create a complete snowflake with a Koch curve, we need to repeat the same drawing three times. So let`s try this.

` ` |

Output:

This article courtesy of ** Subhajit Saha **. If you are as Python.Engineering and would like to contribute, you can also write an article using contribute.python.engineering or by posting an article contribute @ python.engineering. See my article appearing on the Python.Engineering homepage and help other geeks.

Please post comments if you find anything wrong or if you`d like to share more information on the topic discussed above.

X
# Submit new EBook