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Cast IXBrother And SisterI Heart Fractals 2
Brother And Sister
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Description: MDZ generalized celtic | mandelbrot variant
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Keywords: mdz variant mandelbrot celtic 
Posted by: jwm-art November 14, 2010, 09:49:47 PM

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Filesize: 464.16kB
Date: February 13, 2011, 04:53:17 PM
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By: popol4444
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hermann
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December 04, 2010, 09:00:05 AM


I have implemented an interactive gallery using this algorithm.
With a Java-Plugin in the prowser it is possible to explore more details.
Very interesting structures.
http://www.wackerart.de/celtic-mandelbrot.html
jwm-art
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November 18, 2010, 11:51:51 AM
I've been applying some Mandelbrot exploration techniques to this fractal:






hermann
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November 18, 2010, 11:20:19 AM
Some of the result from my research last night:





jwm-art
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November 17, 2010, 05:54:25 PM
I decided to ask the question in the programming sub forum:
http://www.fractalforums.com/programming/mandelbrot-variation-ii-(does-it-have-a-name)
hermann
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November 17, 2010, 05:22:25 PM
Do we have a name for it?
In my applet I named it celtic mandelbrot.
jwm-art
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November 17, 2010, 04:07:55 PM
I suppose it could be considered a 2D "hybrid"? Or perhaps it's a cannibalistic fractal shocked
hermann
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November 16, 2010, 09:52:54 PM
I have implemented the formula in my fractal generator applet.
http://www.wackerart.de/fractal.html
Algorithm->Celtic->Celtic Mandelbrot.
Proposal: Use the Gold Mine Layout for the first exploring steps. For greater details use adaptive layouts.

The following structure I have discovered this evening, on my first expedition through this fractal.
Very interesting fractals can be created by this algorithm.
One can find mixtures of structures normely created by algorithms like mandelbrot, mandelbar, burning ship and glynn algorithms.

hermann
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November 16, 2010, 10:58:43 AM
Thanks for the formula.
I'll try to implement it.
jwm-art
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November 15, 2010, 12:35:14 PM
I used a combination of Mandelbrot and its "Generalized Celtic" variant:

Code:
   for (wz = 1; wz <= depth; ++wz)
    {
        wim = 2.0 * wre * wim + c_im;
        if (wz % 2) /* if iteration count is odd */
            wre = fabsl(wre2 - wim2) + c_re; /* generalized celtic */
        else
            wre = wre2 - wim2 + c_re;         /* mandelbrot */
        wim2 = wim * wim;
        wre2 = wre * wre;
        if (wim2 + wre2 > 4.0F)
            return wz;
    }
hermann
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November 15, 2010, 09:56:00 AM
A combination of a mandelbar and a mandelbrot!
Which kind of algorithm did you use?

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