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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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    Subjectively, implementing different ways of coloring a fractal (check the refs for these, I don't remember them all now) would be nice. Certainly, being able to zoom in any region should be implemented.2010-12-12
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    my program can do much more than that. It also has several fractal, showing the julia set of any mandelset point, showing escape orbits etc.2010-12-12
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    Oh, I remember using Fractal Forge when I was in college. Any plans to re-write it in a more portable language so it also compiles/runs on *nix?2010-12-12
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    An interesting feature would be to do batch generation on different zoom levels, so the output can be more easily stitched into an MJPEG or something.2010-12-12
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    That is runs on *nix, and can export to a vector format, of course.2010-12-12
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    If you end up supporting [DjVu](http://en.wikipedia.org/wiki/DjVu) as an export format, I'd be very amused...2010-12-12
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    The avi generation is already there. Be able to run on *nix and using a more general format are of course on top of the list (I'm not using windows since ages). Not sure about DjVu -> why? About vector format -> considering that a fractal is a map of values I see no way to natively generate a vector image.2010-12-13
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    special functions support would be nice.2011-04-11
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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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    Can you post me a link or the name of a book?2011-01-20
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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.