If you want to create your own fractals to perhaps display them on a web site or to sell prints, it is important to respect copyright issues and make sure you own your fractals completely. Fortunately, this is quite straightforward.
The best way to be sure that you are creating an original new fractal is by starting from scratch. You can either start from the default fractal that is opened when starting Ultra Fractal, or by clicking New on the File menu, and then Fractal. You can freely use all formulas, transformations, and coloring algorithms that come with Ultra Fractal or that are in the public formula database.
If you start a fractal by modifying someone else's fractal, creating something original is less easy. The general consensus is that if you make enough modifications so that your fractal does not look like the original fractal anymore, the copyright from the original fractal no longer applies. This could include selecting different fractal formulas or coloring algorithm, zooming in or out, modifying parameters, and so on. The distinction between making enough modifications and barely changing the original fractal is subjective, of course. Therefore, you should always contact the creator of the original fractal to ask for permission before considering your derived fractal to be yours only.
As mentioned above, formulas are free to use. However, modifying formulas is another issue. Generally, you can modify formulas for your own use, but you may not distribute them. If you want to distribute a modified formula, you must ask the original formula author for permission first.
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