Reading a book about fractals I saw an image of a fractal that looked pretty much the same as the ones I was getting with Frax4D. These were called quaternions. Now that I knew what I was actually dealing with I did a quick google search and found the freeware Quat. It was much more powerful than Frax4D and also more open to animation. Although it was only a single image generator it was open enough for me to write a small plugin that was feeding Quat with parameters for animation sequences. Furthermore you could choose between four different formulas. Below are some examples.
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