RE: RE: Re: Mandelbrot Set & Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg48141] RE: RE: Re: Mandelbrot Set & Mathematica
- From: AGUIRRE ESTIBALEZ Julian <mtpagesj at lg.ehu.es>
- Date: Fri, 14 May 2004 20:58:55 -0400 (EDT)
- References: <c81hcq$4s4$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On Fri, 14 May 2004, DrBob wrote: > Sorry again, but your previous message said >=, not <=. It's still posted on > Google Groups, and I checked to make sure. > > DrBob The previous message I refered to was not my original poster. In any case, it should be "<=". But I found a more serious error in the code. The line mandelbrot[c_] := 1 /; 16 Abs[c]^2 < 5 - 4 Cos[Arg[c]]; is supposed to represent the points in the cardiod, but defines a different set. It should be changed to mandelbrot[c_] := 1 /; Abs[1-Sqrt[1-4c]]<=1; > -----Original Message----- > From: AGUIRRE ESTIBALEZ Julian [mailto:mtpagesj at lg.ehu.es] To: mathgroup at smc.vnet.net > Subject: [mg48141] 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: [mg48141] 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 > > > > 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