RE: Re: Mandelbrot Set & Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg48084] RE: [mg48029] Re: Mandelbrot Set & Mathematica
- From: "DrBob" <drbob at bigfoot.com>
- Date: Tue, 11 May 2004 05:20:07 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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". DrBob www.eclecticdreams.net -----Original Message----- From: AGUIRRE ESTIBALEZ Julian [mailto:mtpagesj at lg.ehu.es] To: mathgroup at smc.vnet.net Subject: [mg48084] [mg48029] 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