16
May
07

Nebulabrot

Mathematica 4.2, 8/3/04; C++ version: 5/16/07

This beautiful variation of the Mandelbrot set kind of resembles a nebula or a hologram. The Nebulabrot is a variation of Melinda Green’s Buddhabrot technique. The coloring method shown here was adapted from Paul Bourke’s web site:

(* runtime: 10 minutes *)
Mandelbrot[zc_] := Length[NestWhileList[#^2 + zc &, 0, Abs[#] < 2 &, 1, 1000]];
n = 275; image = Table[0, {n}, {n}];
Do[If[Mandelbrot[xc + I yc] < 1000, Module[{z = 0, iter = 0}, While[Abs[z] < 2, z = z^2 + xc + I yc; {i, j} = Floor[n{Im[z] + 1.5, Re[z] + 2}/3]; If[0 < i <= n && 0 < j <= n, image[[i, j]] += xc + I yc]; iter++]]], {xc, -2.0, 1.0, 0.01}, {yc, -1.5, 1.5, 0.01}];
Show[Graphics[RasterArray[Map[Hue[Arg[#]/Pi, 1, Min[Abs[#]/18, 1]] &, image, {2}]], AspectRatio -> 1]];

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5 Responses to “Nebulabrot”


  1. May 7, 2008 at 7:51 am

    This is pretty cool stuff. I don’t think i’ve seen a colorful representation of the mandelbrot set quite like this.

    What kind of college degrees do you have if you don’t mine me asking?

  2. 2 Bret Comnes
    August 12, 2008 at 6:37 am

    What would be the best way to get a high resolution image of this kind of fractal? I want to make this my desktop background. 😀

  3. 3 nylander
    August 12, 2008 at 4:51 pm

    Here is a larger version that you can use for your computer’s background:

  4. 4 Bret Comnes
    August 16, 2008 at 4:51 am

    Thanks! I hope someday I can render one myself.

  5. 5 Bret Comnes
    August 21, 2008 at 4:20 am

    Mathematica 6.0.1 spits out something quite ugly.

    I got some error:
    RasterArray::obs: RasterArray is obsolete. Translating to Raster. >>

    So I simply just changed RasterArray to Raster and that yielded no output even though there was no obvious syntax changes. Ill work on it.


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