Re: Re: Mandelbrot Set & Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg48110] Re: [mg48064] Re: Mandelbrot Set & Mathematica
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Thu, 13 May 2004 00:09:00 -0400 (EDT)
• References: <c7fhp4\$oar\$1@smc.vnet.net> <200405080523.BAA11576@smc.vnet.net> <c7kl93\$2ju\$1@smc.vnet.net> <200405101051.GAA13872@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I can't see your point, but I think you have at least two syntax errors in
your piece of code. x2 and y2 should read x^2 and y^2?

Tomas Garza
Mexico City

----- Original Message -----
From: "Roger L. Bagula" <rlbtftn at netscape.net>
To: mathgroup at smc.vnet.net
Subject: [mg48110] [mg48064] Re: Mandelbrot Set & Mathematica

> Nothing real special: he just uses a test to get the escape
> 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"
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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