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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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?

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. 😀

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

Thanks! I hope someday I can render one myself.

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RasterArray::obs: RasterArray is obsolete.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.