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MathGroup Archive 2004

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Re: Mandelbrot Set & Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48100] Re: Mandelbrot Set & Mathematica
  • From: "Roger L. Bagula" <rlbtftn at netscape.net>
  • Date: Thu, 13 May 2004 00:08:28 -0400 (EDT)
  • References: <c7fhp4$oar$1@smc.vnet.net> <200405080523.BAA11576@smc.vnet.net> <c7kl93$2ju$1@smc.vnet.net> <c7nn8d$dlh$1@smc.vnet.net> <c7q6e4$rpq$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

x up 2 ... y up 2
newsgroup the posting strips the power / up character...
And I posted the Mandelbrot with Postscipot so people could just load it 
and see it.


Bobby R. Treat wrote:
> 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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