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MathGroup Archive 2004

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Re: Re: Mandelbrot Set & Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48067] Re: [mg48029] Re: Mandelbrot Set & Mathematica
  • From: AGUIRRE ESTIBALEZ Julian <mtpagesj at lg.ehu.es>
  • Date: Mon, 10 May 2004 06:51:23 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

On Sat, 8 May 2004, Murray Eisenberg wrote:

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

It should be >= .

Julian

> 
> 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"
> >>downloadable from Mathworld. Please report the Timing parameter if you have
> >>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
> 
> 

Julian Aguirre			| Voice:  +34 946012659
Departamento de Matematicas	| Fax:    +34 944648500
Universidad del Pais Vasco	| Postal: Aptdo. 644, 48080 Bilbao, Spain
				| email:  mtpagesj at lg.ehu.es


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