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Many years ago I wrote this fractal generator: http://uberto.fractovia.org/

It was shareware but then I put it as open source. It's written in Delphi, a language that I don't use anymore. So I'm playing lately with the idea of rewriting on some other lang (scala maybe?).

On the mathematical part I'm not expert at all, so I don't know if there is something a mathematician would find interesting. Maybe none because of software like Mathematica. I really don't know.

For the graphic oriented people I implemented some algos for continuous coloring, including the ones listed here:

Continuous coloring of a Mandelbrot fractal

but I'd like to add some new ones.

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    If I were that mathematician in a fractal program, I'd be looking for a way out.2011-05-11

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You might look to Mandelbrot's own work, a lot of which has to do with boundaries, also the relations of similar shapes on different scales and fractal dimension.

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    @Uberto, probably [The Fractal Geometry of Nature](http://en.wikipedia.org/wiki/The_Fractal_Geometry_of_Nature)2011-04-11
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For inspiration, try Xaos and the books The Beauty of Fractals and The Science of Fractal Images.