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Many years ago I wrote this fractal generator:

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. – J. M. Dec 12 '10 at 13:05
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? – Willie Wong Dec 12 '10 at 14:42
That is runs on *nix, and can export to a vector format, of course. – Jonas Teuwen Dec 12 '10 at 15:42
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. – Uberto Dec 13 '10 at 10:19
If I were that mathematician in a fractal program, I'd be looking for a way out. – Gerry Myerson May 11 '11 at 1:10

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? – Uberto Jan 20 '11 at 9:48
@Uberto, probably The Fractal Geometry of Nature – lhf Apr 11 '11 at 10:42

For inspiration, try Xaos and the books The Beauty of Fractals and The Science of Fractal Images.

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