Print Page - Mandelbrot Variation II (Does it have a name?)

Title: Mandelbrot Variation II (Does it have a name?)
Post by: jwm-art on November 17, 2010, 05:49:34 PM

After reading about a variant of the Mandelbrot set which is apparently classified in UltraFractal as "Generalized Celtic Mandelbrot"[1] I came up with another variation which is a hybrid between that and the Mandelbrot Set. For odd iterations it calculates the "Generalized Celtic" and for even iterations just the Mandelbrot Set:

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;
    }

I am wondering if anyone knows if this has a name or not, or, has an idea for a suitable name. My Linux program MDZ (http://jwm-art.net/mdz/) can generate this fractal and calls it (temporarily) "Variant". Here are some other images of it:

(http://nocache-nocookies.digitalgott.com/gallery/4/1095_14_11_10_9_49_46.jpeg)
(http://nocache-nocookies.digitalgott.com/gallery/4/1095_14_11_10_9_32_32.jpeg)
(http://nocache-nocookies.digitalgott.com/gallery/4/1095_17_11_10_4_50_59.jpeg)

[1] http://www.fractalforums.com/programming/mandelbrot-variation

Title: Re: Mandelbrot Variation II (Does it have a name?)
Post by: jwm-art on November 20, 2010, 01:18:05 PM

I've named it "Mandel-Celtic-Hybrid" in the new release of MDZ (coming shortly).

Title: Re: Mandelbrot Variation II (Does it have a name?)
Post by: hermann on December 13, 2010, 04:02:10 PM

I use the name Celtic Mandelbrot for the above version.
http://www.wackerart.de/celtic-mandelbrot.html (http://www.wackerart.de/celtic-mandelbrot.html)
And the name Mandelbrot Celtic for the algorithm where generalized celtic part and mandelbrot part are exchanged.

Is there also special celtic algorithm, when a generalized celtic algorithm exists?

Hermann

(http://www.wackerart.de/FractalGraphicsIII/celtic-mandelbrot-45-re.jpg)

(http://www.wackerart.de/FractalGraphicsIII/celtic-mandelbrot-21.jpg)

Title: Re: Mandelbrot Variation II (Does it have a name?)
Post by: yv3 on December 20, 2010, 08:58:14 PM

nice kitties, have you noticed them? :)

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Fractal Software => Programming => Topic started by: jwm-art on November 17, 2010, 05:49:34 PM