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MathGroup Archive 2004

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Re: Mandelbrot Set & Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48077] Re: Mandelbrot Set & Mathematica
  • From: drbob at bigfoot.com (Bobby R. Treat)
  • Date: Tue, 11 May 2004 05:19:59 -0400 (EDT)
  • References: <c7fhp4$oar$1@smc.vnet.net> <200405080523.BAA11576@smc.vnet.net> <c7kl93$2ju$1@smc.vnet.net> <c7nn8d$dlh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You left x2 and y2 undefined.

Bobby

"Roger L. Bagula" <rlbtftn at netscape.net> wrote in message news:<c7nn8d$dlh$1 at smc.vnet.net>...
> Nothing real special: he just uses a test to get the escape
> radius.
> In fact I can't get any antenna on his program: it's just a very bad 
> implicit approximation, I think. If might work better as an IFS than as 
> he gave it?
> here's one of a kind I invented in about 1994 and called a "fake fractal";
> Fake fractal in Mathematica:(based on fractal Weierstrass function and 
> cardiod implicit function)
> 
> v=N[Log[2]/Log[3]];
> c[x_,y_]=Sum[(2^(-v*n))*Cos[2^n*ArcTan[x,y]],{n,1,8}];
> ContourPlot[(x2+y2+c[x,y]*x)2-c[x,y]^2*(x2+y2),{x,-4,4},{y,-4,4},
>    PlotPoints -> {300, 300},
>      ImageSize -> 600,
>       ColorFunction->(Hue[2#]&)]
> 
> Murray Eisenberg wrote:
> > I don't understand the expression "=BE" in the 4th line of your code.
> > 
> > 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
> >>
> >>
> > 
> >


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