Sunday, 7 February 2016

How to make a fractal: suitable for 6 years and up

Dear Reader,

Have you ever heard the word 'fractal'?

Did you know that fractals are mathematical shapes that are made of tiny pieces that are all copies of the whole, like clouds, ferns and broccoli?

One of my favourite lessons in maths is to teach pupils how to make one of these:

This is a paper fractal, made from an ordinary sheet of A4 and some scissors.  It will take around 15-30 minutes to make and is a beautiful example of 3D from 2D.  Once you have the technique, you can try different cuts, different sizes and different complexities to make something truly amazing.

The technique we are using is called 'iteration', which means doing something over and over again, in this case at a smaller and smaller scale.  The steps get repeated over and over again, so its a great lesson to teach because once it 'clicks' for people you can see them enjoying racing ahead and doing it independently.  See when this happens for you!

1.  Take your piece of paper and fold in half lengthways.  From the folded edge, find halfway along (you can use a ruler or judge by eye) and cut, but only to halfway up.  The resulting object looks a little like a pair of shorts!

2. Fold one half of the paper upwards.

3.  This is the only slightly tricky part.  Unfold it again and tuck it in backwards as shown. This is simply taking the quarter of the paper that you have just folded upwards and instead tucking it in the rest of the paper, reversing the fold.

4.  Your piece of paper should now look like this:

5.  Look at the three rectangles created in this L-shape. Treat the top left and bottom right as if they were the original piece of paper - do the same thing again for each of them in turn.

6. You have completed the second iteration, which involved two cuts (the first involved one).  How many do you think the third will need?  

That's right, 4! :-)

7. Now look at the shape you have.  It has four rectangles along the diagonal, each of which you will treat as the original - cut, fold, tuck, then repeat for each of the other three parts.

8.  By now, you should have worked out how to carry on by yourself.  You can continue to the fourth iteration - which involves eight cuts - but its gets tricky to fold and tuck.  I can't do five unless I start with bigger paper, but you might be able to!

The resulting shape is very fun to play with.  You can also experiment by doing curved cuts which can result in heart shapes (or a pile of cut-up pieces of paper...)


Please tweet or post your pictures if you manage to make one, however simple.

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