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 > >> > >> > > > >

**References**:**Re: Mandelbrot Set & Mathematica***From:*AGUIRRE ESTIBALEZ Julian <mtpagesj@lg.ehu.es>