## The Jurassic Park Fractal

Have you ever read Jurassic Park? I know you saw the movie, but did you read the book? Did you notice the bizarre drawings on the chapter heading pages? They look kind of like partial squares. They're labeled First Iteration, Second Iteration, etc., and they get more and more complex with each iteration.

I'm going to show you how to make this fractal by paper-folding. So Cool! For the Jurassic Park Fractal we are going to start with a narrow strip of paper, let's say approximately 1" by 11". Construction paper works really well because it has a little more stiffness.

Take the strip in both hands, fold the paper over left onto right, and crease. Now fold it again in the same way, left to right, and crease, and again, left onto right and crease, and again left onto right and crease. You have folded it four times in all, right? Before you open the paper out, can you imagine what it will look like unfolded? Let's unfold and see. Now you may be saying, this is just a mess of folded paper. How can this be a fractal? Well, we have to put some order to it.

Lay the paper on its edge. Crease all the folds as right angles. Then rotate it until it matches up with the figure below. Be sure to find the closed-up square. See? You did it! It's the same shape!

### Jurassic Park, Chapter One,

"At the earliest drawing of the fractal curve, few clues to the underlying mathematical structure will be seen" - IAN MALCOLM

Now this is pretty cool too. Let the computer take over the paper-folding process. THE COMPUTER CAN'T FOLD PAPER. No, it does it with numbers rather than paper. Many steps (or iterations) later the fractal would look like this:

I'd like to acknowledgeHeinz-Otto Peitgen for his presentation of this material, and Sarah Seastone at The Math Forum for her assistance with the images.

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Copyright 1996-2007 Cynthia Lanius URL http://math.rice.edu/~lanius/frac/jupr.html - Print Version