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Fractal art is a form of digital artwork created through the use of computer software. The central component in this type of artwork is the use of a particular mathematical equation to generate an initial fractal image. This image is then utilized by an artist in a number of different ways, including zooming in or out, moving the image around within a frame, and trying different color iterations, to create a final piece. Fractal art is created through the use of a computer but is not computer-generated, as it still requires the work of an artist.
The basic idea behind fractal art is the visual expression of a complex mathematical equation in a way that generates an image that is self-similar. This means that one small section of the image resembles the overall image itself. An example of this in the natural world can be seen in coastlines that appear rough and jagged when seen from a great distance overhead, and each small section closer up continues to have a similar rough appearance. The fractals used to create fractal art have a self-similar nature, so that one tiny aspect of the image is similar in appearance to the whole.
This self-similarity is coupled with the fact that fractals are theoretically infinitely small in size, so that an artist can zoom in on an image forever. Basically a mathematical equation is used to generate an initial fractal image, which itself may not appear like much. An artist then uses this base image to find and generate a much more impressive work that is then presented as a piece of fractal art. This means that using a computer software program to generate the image itself is only one small part of the creative process.
Once the image is created, then the artist uses various pieces of software, including the fractal generating program, to create a work of fractal art. The artist can zoom in on different sections of the image; in theory, he or she can magnify the image infinitely, and look for variations to find new and different aspects of a fractal. Different parts of the initial image can be explored by the artist to find a part of the fractal that is interesting and worth further development. Various mathematical iterations can be used to alter the colors of the image, and it can be further manipulated in subtle and complex ways to create a final piece of fractal art that serves to visualize mathematics.