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A fractal is a shape which is generated mathematically.
While the form of a fractal can be very detailed and intricate the mathematical expression responsible for the fractal is usually quite simple. 'Zooming' in repeatedly on a true fractal shape reveals ever more structure - the details repetitive yet never quite the same.
Fractal forms abound in nature; a tree, a fern leaf, a cloud, a coastline, are all fractal in character.
Fractal art is where art and mathematics meet.
I use Ultra Fractal to generate, combine and colour the fractal forms. Any further processing of the image, including mounting for web display, is done using Adobe Photoshop, although I've been trying a program called the Gimp more recently.