Now that the Chinese New Year has arrived, 2012 is officially the Year of the Dragon. This is extremely exciting and for an interesting maths challenge, one has to try making a fractal dragon.
First all all your need a flat open space. My back garden was fine. And you need lots of sticks. Fractal dragons are expansive creatures so I would use 30cm sticks. (I started out with 60cm sticks and had to redo as the dragon was too big for my garden).
Take a stick and place it on the ground.
Take another stick and put it perpendicular to the first one.
Are you beginning to see how the dragon is formed. Look at the shape. Count the number of sticks. Try and look for the pattern’s rule.
You’ve probably worked out that each move involves doubling the numbers of sticks. The sticks are called “line segments”. Below it is easier to see that another rule is that the pattern is rotated through ninety degrees at each stage.
I did not make this fractal dragon from the brilliance of my mind. It’s taken me until now to really see the pattern. I had to have repeated attempts before it began to click and I understood what was going on.
I think children and young people will find the same thing. Begin by just making it. I took photos using my iPhone at each stage in this YouTube video which gives a step-by-step guide.
I also found this video helpful too. What both clips show is how, as the dragon grows, the right angles seem to become lost as the dragon becomes increasingly curvy.
My final fractal dragon was made using 64 sticks. It is a baby in fractal terms. However, it was an interesting challenge. I’m now curious to know if it is possible to walk the length of the dragon without covering any line segment (stick) more than once. Hmm…