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.
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.
Divide each side into three equal parts. This is why it is convenient to divide the sides into three.
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.
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.
Draw an equilateral triangle on each middle section.
Lindenmayer system view
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.
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