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.
construction
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.
Lindenmayer system view
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.
To create a Koch curve:

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.
lengthSide / = 3.0

Output:
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