Fixed color scale in multiple density plots

Question

I think there should be a simple solution for my current problem, but neither StackOverflow (or the help of Mathematica) or Google have it.

I have to plot multiple density plots with a color function.

ListAnimate[Table[
    ListDensityPlot[ListOfResults[[i]], 
        ColorFunction -> "TemperatureMap", PlotRange -> All, 
        PlotLabel -> i], 
    {i, 1, Length[ListOfResults]}], AnimationRunning -> False]

The main problem is that for each plot, the extreme colors are assigned to the maximum and minimum values of the current plot. I want the extreme values of the color function to be the global maximum of minimum of my complete data set.

Answer 1

You need the option ColorFunctionScaling -> False along with a color function that can handle the actual range of your data.

Given:

dat = {{1, 1, 1, 1}, {1, 2, 1, 2}, {1, 1, 3, 1}, {1, 2, 1, 4}};

You could either divide this data by a value sufficient to get it into the range of your ColorFunction before plotting it:

ListDensityPlot[#, Mesh -> All, ColorFunction -> "TemperatureMap", 
   ColorFunctionScaling -> False] & /@ {0.1 dat, 0.2 dat, 0.3 dat}

Or you could do this manual scaling inside your ColorFunction:

ListDensityPlot[#, Mesh -> All, 
   ColorFunction -> (ColorData["TemperatureMap"][#/10] &), 
   ColorFunctionScaling -> False] & /@ {dat, 2 dat, 3 dat}

---

An effort to make this more convenient:

multiPlot[list_List, opts : OptionsPattern[]] := 
  GraphicsRow[
    ListDensityPlot[#, ColorFunctionScaling -> False, opts] & /@ 
      Rescale[list, {Min@list, Max@list}]
  ]

SeedRandom[30];

data = RandomInteger[9, {3, 4, 4}];

multiPlot[data, Mesh -> All, ColorFunction -> "TemperatureMap"]