ColorFunction based on data

Question

I have a list of numbers, and I would like to plot them using ArrayPlot (which is easy, usually :)). I would like to be able to color the elements of the plot based on the average of the list: one color if the number is above average, another if it is below. I have tried a couple of things, but so far, no joy.

First thing I tried is have a module around the colorFun defined by me and the ArrayPlot, to calculate the mean, since I don't want it to be kernel-wide (many other plots will come with the same technique), and then define, inside the module, the colorFun:

  Module[
  {a, mean, colorFun},
    a = RandomInteger[{0, 100}, 100];
    mean = Mean[a];
    colorFun[z_] := If[z <= mean, Red, Blue];
    ArrayPlot[List@a, ImageSize -> Full, ColorFunction -> colorFun]
  ]

but this didn't work, since the plot would return all in the same color. It's actually not clear to me why.

I also tried to move colorFun in the form:

colorFun[z_]=RGBColor[{ , , }]    

with 2 functions of z and mean for two elements and 0 for the third. The idea of using this approach instead of the if is that I could blend the colors (the further from the average, the more intense/bright the color I am plotting with).

Any ideas?

Thanks!

Answer 1

For concreteness, here's how one might do Plato's suggestion:

Module[{a, mid, colorFun},
       BlockRandom[SeedRandom[42]; (* for reproducibility *)
                   a = RandomInteger[{0, 100}, 100]];
       mid = Mean[a];
       colorFun[z_] := If[z <= mid, Red, Blue];
       ArrayPlot[{a}, ColorFunction -> colorFun, ColorFunctionScaling -> False]]

To demonstrate the approach I proposed, I'll use it to implement your more fine-grained idea to have the color's intensity proportional to its distance from the mean, using Blend[]:

Module[{a, hi, lo, mid, colorFun},
       BlockRandom[SeedRandom[42];
                   a = RandomInteger[{0, 100}, 100]];
       {lo, mid, hi} = Through[{Min, Mean, Max}[a]];
       colorFun[z_] := Blend[{{0, Red}, {Rescale[mid, {lo, hi}], White}, {1, Blue}}, z];
       ArrayPlot[{a}, ColorFunction -> colorFun]]

Answer 2

I am now using this as a color function:

colorFun[z_] := Blend[{Red, Darker@Green}, (z - 1)/mean];

and it's working more or less fine. Please, never mind the noise, but maybe it will be useful for somebody else.

Also I am using, as suggested by PlatoManiac, ColorFunctionScaling -> False.