[Q] problem with ColorFunction in ListDensityPlot

*To*: mathgroup at smc.vnet.net*Subject*: [mg3114] [Q] problem with ColorFunction in ListDensityPlot*From*: glgesm at engr.psu.edu (Gary L. Gray)*Date*: Fri, 2 Feb 1996 03:36:35 -0500*Organization*: Penn State University - Engineering Science & Mechanics*Sender*: owner-wri-mathgroup at wri.com

I am putting together a demo for a class in which I am trying to use Newton-Raphson to iterate the equation z^3 - 1 = 0. I then want to plot which points in the complex plane go to which root by coloring the initial starts points three different colors (results in a fractal). Here is what I am doing: I first define the function I will be iterating: f[z_] := N[z - (z^3 - 1)/(3 z^2)]; Then I create the an array of points in which each element of the array corresponds to the root to which the iteration converges for a given starting value: p = Table[ FixedPoint[ f, x + I y, SameTest -> (Abs[#1 - #2] < 10.^-4 &)], {x, -2, 2, 0.01}, {y, -2, 2, 0.01}]; Then I label the points 1, 2, or 3 depending on which root the starting value converges to: points = Table[ Which[Im[p[[i,j]]] < -0.8, 1, Im[p[[i,j]]] > 0.8, 2, True, 3], {i, Length[p]}, {j, Length[p]} ]; Now, I get a grayscale density plot by using the following command: ListDensityPlot[points, Mesh -> False, MeshRange -> {{-2, 2}, {-2, 2}}] The question is, how do I color it say Red, Blue, and Green? Why doesn't the following command work? ListDensityPlot[points, Mesh -> False, ColorFunction -> ( Which[ # == 1, RGBColor[0,0,1], # == 2, RGBColor[1,0,0], True, RGBColor[0,1,0] ]& ) ] Thank you, /---------------------------------------------------------\ | Gary L. Gray Engineering Science & Mechanics | | Assistant Professor Penn State University | | mailto:glgesm at engr.psu.edu (814) 863-1778 | | http://www.esm.psu.edu/HTMLs/Faculty/GGray.html | \=========================================================/ ==== [MESSAGE SEPARATOR] ====