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MathGroup Archive 2004

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Re: Mandelbrot Set & Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48064] Re: Mandelbrot Set & Mathematica
  • From: "Roger L. Bagula" <rlbtftn at netscape.net>
  • Date: Mon, 10 May 2004 06:51:19 -0400 (EDT)
  • References: <c7fhp4$oar$1@smc.vnet.net> <200405080523.BAA11576@smc.vnet.net> <c7kl93$2ju$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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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