The Koch snowflake is one of the earliest fractal curves described by mathematicians, and you can draw this fractal with a series of equilateral triangles. The full fractal has an infinitely long perimeter, so drawing the entire Koch snowflake would take an infinite amount of time. However, you can still draw the main foundation of the Koch fractal. Depending on the thickness of your drawing utensils and how big your first iteration is, you can draw a Koch snowflake of the 5 th or even 7 th order. We'll show you how to get started below!
Steps
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Draw an equilateral triangle. You can draw it with a compass or protractor, or just eyeball it if you don't want to spend too much time drawing the snowflake.
- It's best if the length of the sides are divisible by 3, because of the nature of this fractal. This will become clear in the next few steps.
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Divide each side in three equal parts. This is why it is handy to have the sides divisible by three.Advertisement
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Draw an equilateral triangle on each middle part. Measure the length of the middle third to know the length of the sides of these new triangles.
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Divide each outer side into thirds. You can see the 2 nd generation of triangles covers a bit of the first. These three line segments shouldn't be parted in three.
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Draw an equilateral triangle on each middle part.
- Note how you draw each next generation of parts that are one 3 rd of the mast one.
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Repeat until you're satisfied with the amount of iterations. It will become harder and harder to accurately draw the new triangles, but with a fine pencil and lots of patience you can reach the 8 th iteration. The one shown in the picture is a Koch snowflake of the 4 th iteration.
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Decorate your snowflake how you like it. You can colour it, cut it out, draw more triangles on the inside, or just leave it the way it is.Advertisement
Community Q&A
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QuestionCan I keep going? Do I have to continue with the triangles?Community AnswerBe creative! You can put in as many designs as you want! It doesn't all have to be triangles.
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QuestionBut how are they formed so symmetrical?T. ChinsenTop AnswererStep 1 of the article recommends making each length of the triangle side be divisible by three. This creates the symmetry of the next level of triangles.
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Tips
- Instead of drawing each iteration on the outside of the last one, try drawing it on the inside, and see what you get!Thanks
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Things You'll Need
- (Coloured) pencils / markers
- Protractor / ruler / compass (optional, but recommended)
- (Graph) paper
About this article
Thanks to all authors for creating a page that has been read 37,037 times.
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