What is a Fractal?
The easiest way to explain it is to just show you. Look at the fractal tree in the bottom right corner. It begins as a
A Fractal is any geometric shape or curve in which any part is "statistically identical" to the whole. So what does all that mean? line, but after a certain distance (say 2 inches) the line branches. The two new lines each run 1 and 1/2 inches respectively, and then they both split again. These four new lines run 1 inch and split again, and so on and so forth forever. When this happens infinitely, it creates some amazing effects, like the infinite triangles to the right. No matter how close you get, the pattern always repeats, and there is always a deeper level - ad infinitum (and if you stare too long, ad nausium too!.)
Ok, so why Fractals?
So why Fractals? Because they existed before we did, they are a product of the natural world, because nature does strange math, and that in itself creates awe and wonder.
Yes Virginia, snowflakes are fractals, as are various types of crystal growths, leaves of plants, ferns, mushrooms, all kinds of things come in fractals. There are even fractals within your body, your circulatory system, the bronchial paths of your lungs, there are fractals literally everywhere.
Fractals don't just appear on the micro level, but on large scales. River basins, Lakes, Canyons and Mountain Ranges can all be fractals as well.
So seeing as they were here first, and they somehow have been able to infiltrate every part of nature, maybe the the answer is, why not Fractals?