Re: Mathematica 6.0 Desperation

*To*: mathgroup at smc.vnet.net*Subject*: [mg83670] Re: Mathematica 6.0 Desperation*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Wed, 28 Nov 2007 05:26:04 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <figtq9$fa7$1@smc.vnet.net>

Jesus M. Goiri wrote: > I have tried some items that seem to hang Mathematica 6.0. However > they work perfectly fine in the 5.2 version. I have tried to > discover the flaw and I have not been able to do so. The problem > pertains at some code I extracted from a book about Mathematica > applications by Boccara, particularly the examples that relate to > fractals, Julia and Mandelbrot Sets. > > I have below the lines of code. I you try them, I'd wish to see if > you are able to make them work. > > Yours sincerely, > > Jesus M, Goiri > > Clear[JuliaTest] > JuliaTest = Compile[{x, y, {n, _Integer}, {c, _Complex}}, > Module[{z, num = 0}, z = x + y I; > While[Abs[z] < 2.0 && num < n, z = z^2 + c; num++]; num]] > DensityPlot[JuliaTest[x, y, 50, -0.75 + 0.5 I], > {x, 1.24, 1.27}, {y, -0.13, -0.1}, PlotPoints -> 500, > Mesh -> False, ColorFunction -> Hue] The graphic engine in v6 has changed dramatically. The option *PlotPoints* set to 500 is much to high. Use a smaller value and increase it if needed (and keep in mind that there exists now several other options that control the speed and the quality of a plot). The following example use the default value for *PlotPoints* and plots the Julia set in matter of seconds. Clear[JuliaTest] JuliaTest = Compile[{x, y, {n, _Integer}, {c, _Complex}}, Module[{z, num = 0}, z = x + y I; While[Abs[z] < 2.0 && num < n, z = z^2 + c; num++]; num]] DensityPlot[ JuliaTest[x, y, 50, -0.75 + 0.5 I], {x, 1.24, 1.27}, {y, -0.13, -0.1}, PlotPoints -> Automatic, Mesh -> False, ColorFunction -> Hue] Regards, -- Jean-Marc