Re: Re: Mandelbrot Set & Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg48054] Re: [mg48029] Re: Mandelbrot Set & Mathematica
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 9 May 2004 03:02:28 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <c7fhp4\$oar\$1@smc.vnet.net> <200405080523.BAA11576@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I don't understand the expression "=BE" in the 4th line of your code.

AGUIRRE ESTIBALEZ Julian wrote:

> On Fri, 7 May 2004, fake wrote:
>
>
>>I'm looking for a program using Mathematica commands to obtain the
>>Mandelbrot set representation without using the .m file "Fractal"
>>done some tests.
>>TIA
>
>
> This is what I did for a Dynamical Systems course. It is based on code
> from the help files. It includes knowledge about points that are in the
> Mandelbrot set.
>
> Clear[c, test, niter, BlackWhite, mandelbrot];
> BlackWhite = If[# == 1, GrayLevel[0], GrayLevel[1]]&;
> niter = 100;
> test = (Abs[#] =BE 2) &;
> mandelbrot[c_] := 0 /; Abs[c] > 2;
> mandelbrot[c_] := 1 /; Abs[c + 1] < 1/4;
> mandelbrot[c_] := 1 /; 16 Abs[c]^2 < 5 - 4 Cos[Arg[c]];
> mandelbrot[c_] := (Length@NestWhileList[(#^2+c)&,c,test,1,niter]-1)/niter;
> DensityPlot[mandelbrot[x + y I], {x, -2, .5}, {y, 0, 1},
>     PlotPoints -> {600, 300},
>     Mesh -> False,
>     ImageSize -> 600,
>     AspectRatio -> Automatic,
>     ColorFunction -> BlackWhite];
>
> Color can be added defining new color functions. I like
>
> rainbow = Hue[.8(1 - #)]&
>
> Julian Aguirre
> UPV/EHU
>
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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