Simply put, fractals are shapes which show similar features at different sizes. Much as a very close inspection of a rock can show similar features to an aerial view of a mountain, fractal shapes are characterized by this property of self-similarity.
         Much of what goes into fractals is based on mathematics. Sometimes the math is complicated; sometimes it isn't. But you do not need to know or understand the mathematics behind the art to appreciate it. That is, in fact, one reason the Loop was created in the first place. For those that would like to deal with the math, there are many places that talk about the math behind fractals. I will not do so here.
         There are some who will feel that if this is all just based on mathematics, that it cannot be art. (Insert rude raspberry here.) Fractal art does not pop out of nowhere, mathematics notwithstanding. To produce an aesthetically pleasing fractal image (which goes a long way towards making it art) requires enormous input on the part of the artist. It also requires patience, and an eye for form and color—skills that are required for virtually any artistic discipline.
         Most fractal exploring is done by starting with a simple fractal image, perhaps 12" large on the screen. The artist then selects a small section of the image and magnifies it, so it takes up the entire screen space. A small section of this magnified image is then selected, and in turn magnified. The process is repeated indefinitely, the artist exploring ever smaller regions. Within just a few magnifications, the original 12" image has been magnified so it's as large as the state of Maine. (For those of you unfamiliar with US geography, that's about 150 miles or 240 km across.) Further magnifications can expand the original image so large that it's greater than the width of the known universe. The mathematics have no end; only the precision of our computers limits the depth of exploration.

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