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Dragon curves

By David, 1 October 2020 Activity

Strip of paper folded at regular intervals making a pattern

The true dragon curve is the shape you get from an infinite number of folds.

In this sample from More Hands-on Science, we’re looking at infinitely detailed shapes known as fractals. If you do this activity, you can discover a fractal called the dragon curve!

You will need

  • Several long strips of paper
  • Sticky tape (optional)

What to do

  1. Take a strip of paper, fold it in half end to end, and make a crease. Open the strip out and then re-fold it to turn the crease into a right angle.
  2. A strip of paper folded to make a right angleTake a new strip of paper. Fold it in half and then fold it in half again, putting the left end over the right end each time. Open it up, and then adjust each crease to be a right angle like before.
  3. A strip of paper folded mulitple times.Take a third strip of paper. Fold it in half three times, being careful to put the left end over the right end each time. Lay it on its side and adjust the creases to be right angles, as before. Continue to follow this pattern to make a 4-fold shape and a 5-fold shape.
  4. Strip of paper folded at regular intervals making a patternMake two 4-fold shapes and see if you can make the 5-fold shape out of them. Can you see a pattern in these shapes? (Hint: You may wish to use sticky tape to hold more complex shapes together.)
  5. See if you can make a 6-fold shape by arranging 5-fold shapes.

What’s happening?

The shapes you’ve been making are called dragon curves. You can make a bigger dragon curve by starting with a larger piece of paper and folding it in half more times. However, after about five folds, it becomes difficult to fold the paper in half.

You can also combine two smaller dragon curves to make a larger one. To do this, you’ll need to put the correct ends together so they meet at a right angle. There are a few different ways you could do this, but only one of them is correct – to check, compare it with a single-folded curve.

Although we’re calling all these shapes ‘dragon curves’, there’s actually only one shape that’s truly a dragon curve. The true dragon curve is the shape you get from an infinite number of folds.

Smaller sections of the dragon curve – like the ones in this activity – are also known as the Jurassic Park dragon. This is because they were found on the section title pages of Michael Crichton’s famous novel, Jurassic Park.

Real-life maths

If you made a mistake in this activity, don’t worry! That’s real-life maths.

Lots of patterns can be made from doing the same thing over and over. But the patterns can react differently when a mistake is made. Sometimes a mistake doesn’t change the result that much – for example, if you get one of the last folds backwards in this activity. But other mistakes can have huge consequences!

The area of mathematics that looks at how patterns react to mistakes or changes is called chaos theory. Chaos theory is important in a whole range of things, from weather prediction to asteroid tracking.

 

Cover of More hands on science book

Get your copy today!

 

This activity comes from More Hands-on Science, a book packed with 50 science projects for you to do at home.
Order your copy online on the CSIRO Publishing website

 

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