Fractal Education: The Dragon Curve

I recently wrote about using the Sierpinski triangle to teach students about fractals. Another relatively easy fractal for young students to make is the dragon curve fractal. The dragon curve is created by folding a strip of paper in half over and over (in the same direction) and then placing all folds at 90o. The pictures below show what the curve looks like after 1, 2, 3, and 4 folds. (This is a great time to introduce the term ‘iteration’ to students. Iteration means the process of repeating. The curve with 4 folds is the 4th iteration.)

DragonCurve1-4Folds

If you start with a really long piece of paper, you may be able to fold it 5 or 6 times, but that is about the limit. If you could fold it 14 times, it would look like the picture below. If you kept folding, the curve would have the same shape, it would just be folded in on itself even more. Notice how each “section” of the curve looks like a smaller version of the whole curve.

dragon_curve

It can be difficult to make all the folds to lie at 90o angles, even with a small number folds, so I like to have students tape their curve down onto a piece of paper. If you size things correctly, you can put your folded paper dragon curve onto a picture of a high-iteration dragon curve, as shown below – a great example of how a fractal looks similar at different scales.  You can print my directions and handout here.

IMG_0519

You can also use colored paper or cardstock to make some dragon fractal art. Take a look at these lovely dragon curves at CutOutFoldUp.com. If you are interested in the math behind the dragon curve, this page at The Fractal Umbrella explains how to mathematically describing the fold sequences.

Numberphile has a great video about the dragon curve (below) that covers many fascinating facts about the curve, including why it is also known as the Jurassic Park fractal.

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