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 >>>> >>>> >>> >>> >

**Follow-Ups**:**Re: Re: Mandelbrot Set & Mathematica***From:*Murray Eisenberg <murray@math.umass.edu>

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