What Is a Fractal?
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Fractals are a different kind of image. They are born in mathematical equations and then begin a life of their own in an infinite universe very different from ours. In a way they are quite alien; in another way they echo our own world and speak to us of new worlds that may be reached by following their path.
We can find fractals in nature. A bank of drifting clouds, the rippling eddies in a mountain stream, a shoreline, a distant mountain range, a seashell, a single tree---all these are fractals.
If you look at a tree from a distance, you can see its overall shape. As you come nearer, you can start to see the branches and, if you walk a little closer you can see the leaves. Now you can see the great detail in the bark: the complex layering and the intricate textures.
This is the nature of fractals; no matter how close you get to the fractal, you can still see complex detail. If you were to walk towards a square, you wouldn't see such detail. You would very quickly find yourself walking toward a pretty boring line.
Each fractal that you see is a photograph of infinity. Although there is a beginning place, there is no end to a fractal. Let's take that tree again as an example. Take an 8x10 photograph of this tree and include all of it---exposed roots, trunk, branches, crown. This is our beginning place. Now zoom in with your camera, and take a picture of a single branch. Zoom again, but this time focus on a leaf, and then come closer and focus on the serrated edge of that leaf. If the leaf edge is enlarged into an 8x10 photo, a picture of the entire tree at that scale would now be as large as a football field.
Now imagine that your camera has magical properties and can reveal minute detail that your unaided eyes cannot see. Zoom closer until a single serration fills your viewport. Zoom again into that that leaf, and again, and again. Now you can see the inner structure, the tiny fibers that make up the whole. By now, your tree has grown larger that the distance from earth to the moon. Zoom again, and then three times more. Now your photograph shows cellular structures. Zoom again into the heart of a single cell, closer, closer until you can see the tiny organelles of that cell. Again, move closer. Now the coils of DNA can be seen. And now your tree has grown as big as the universe.