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MathGroup Archive 2004

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RE: RE: Re: Mandelbrot Set & Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48118] RE: [mg48090] RE: Re: Mandelbrot Set & Mathematica
  • From: "DrBob" <drbob at bigfoot.com>
  • Date: Fri, 14 May 2004 00:12:18 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Sorry again, but your previous message said >=, not <=. It's still posted on
Google Groups, and I checked to make sure.

DrBob

www.eclecticdreams.net


-----Original Message-----
From: AGUIRRE ESTIBALEZ Julian [mailto:mtpagesj at lg.ehu.es] 
To: mathgroup at smc.vnet.net
Subject: [mg48118] [mg48090] RE: Re: Mandelbrot Set & Mathematica

On Tue, 11 May 2004, DrBob wrote:

> Sorry, but that just doesn't work, even after changing =BE to >=. There
are
> only two colors (even using your rainbow function), and no fractal
> "antennae".

As noted in a previous message, it should be "<=" instead of ">=": iterate
while test gives True. Sorry for the misprint. As for the colors, I have
no problem with them. The "antennae" are hard to see. You will have to
choose a different region for the DensityPlot, use more points and make
niter larger.

Julian

> -----Original Message-----
> From: AGUIRRE ESTIBALEZ Julian [mailto:mtpagesj at lg.ehu.es] 
To: mathgroup at smc.vnet.net
> Subject: [mg48118] [mg48090]  Re: Mandelbrot Set & Mathematica
> 
> 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
> 
> 
> 
> 

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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