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