FRACTALS UNLEASHED
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    Imagine flying in a space shuttle looking at the coast of Britain. From such a great distance the coast looks perfectly straight, going from north to south. But, as you approach the earth something tells you the coast is not perfectly straight... Of course! As you go into the upper atmosphere you realize that it has thousands of bays, harbors, capes, and peninsulas that you could not see from a distance. Thinking that now you have a detailed picture of the coast, you turn towards one of the harbor beaches, which seems to be straight... However, as you get closer to it, you see that it too has thousands of smaller bays, harbors, capes, and peninsulas! Wondering if this will ever end you decide to get even closer... Eventually you wind up on the beach looking at the coast through a microscope. You can now see every grain of sand clearly, but, it too has thousands of indentations and extrusions!
    The fact that any small part of the coast will look similar to the whole thing was first noted by Benoit Mandelbrot. He called shapes like this fractals. Fractals are figures with an infinite amount of detail. When magnified, they don’t become more simple, but remain as complex as they were without magnification. In nature, you can find them everywhere. Any tree branch, when magnified, looks like the entire tree. Any rock from a mountain looks like the entire mountain. The theory of fractals was first developed to study nature. Now it is used in a variety of other applications. And, of course, beauty is what makes them popular!

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