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A 'fractal' is an image generated by the plot of a reiterative mathematical process. The formula is chosen so that the terms corresponding to the coordinates of a point, when entered into the formula, produce another set of terms, which are processed, and so on, until the result fails to satisfy some arbitrary test. The number of iterations at that point is then used to select a color from a corresponding color map. This is done for each point on the plot.
This sounds terribly tedious, and would be if one had to do the calculations by hand, but many programs are available that reduce the process to selecting a formula from a list, picking a start point and maximum number of iterations, and letting it run.
The program I use is called Winfract. It is a Windows version of an even more powerful DOS program called Fractint. Both programs are available as freeware. A good place to find out all about Fractint is at The Fractint Homepage. You can get all the info you need there about all the various aspects of Fractint, as well as sources for download.
After I have produced an image I like, I further process it with Paint and PhotoEnhancer, to rework the size and tune up the color spectrum.
If you find this interesting, I highly recommend visiting Gumbycat's Cyberhome, where you will find many, many, beautiful artworks far more detailed than mine.
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