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Is there a way to use a logarithmic scale in the colour legend of a ListContourPlot? The contours can be logged by taking the Log10 of the data, but this doesn't transfer to the legend. As an example, with the code:

test = Flatten[Table[{i, j, Log10[RandomReal[{0, 1*^10}]]}, {j, 1, 100}, {i, 1, 100}], 1];

ListContourPlot[test, InterpolationOrder -> 0, PlotLegends -> Automatic, 
    Contours -> 20, ColorFunction -> "Rainbow", ColorFunctionScaling -> True, 
    PlotRange -> All]

Mathematica graphics

I get equally spaced contours for values <7, 8, 9 and 10. Could I plot these data with equally spaced contours corresponding to values 0.1, 1 and 10?

Another example, where you'd expect to see logarithmic data:

test = Flatten[Table[{i, j, Log10@Exp[-(i + j)^2]}, {j, 1, 10}, {i, 1, 10}], 1];
ListContourPlot[test, InterpolationOrder -> 0, 
 PlotLegends -> Automatic, Contours -> 20, ColorFunction -> "Rainbow",
  ColorFunctionScaling -> True, PlotRange -> All]

Mathematica graphics

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  • $\begingroup$ One way is to segment the data into as many sections as you want color resolution, 1) order set 2) divide into k equaly large parts 3) make a function that returns which division a value would lie in divided by number of divisions 4) scale ColorFunctions argument with that manually, I tried implementing this but got stuck here's how far I got $\endgroup$
    – ssch
    Commented Dec 17, 2012 at 19:28
  • $\begingroup$ I wonder if the CustomTicks package can be used here. $\endgroup$
    – Eli Lansey
    Commented Dec 17, 2012 at 19:34
  • $\begingroup$ Misunderstood the question, but I guess you could still pass the divisions to Contours $\endgroup$
    – ssch
    Commented Dec 17, 2012 at 19:58
  • $\begingroup$ Do you get something close to what you need playing with the parameters in PlotLegends -> BarLegend[{"Rainbow", {0, 1}}, Function[{min, max}, Rescale[{.1, 1, 5, 10}, {0, 10}, {min, max}]]]? $\endgroup$
    – kglr
    Commented Dec 17, 2012 at 22:53
  • $\begingroup$ Thank you all for your valuable help! Unfortunately I was not yet able to solve my problem. Using kguler's suggestion, the tick values in the legend are displayed as I would want them, but the colour gradation stays the same - not logarithmic as I would like. To make myself clear, the jump in colour from 0.1 to 1 is smaller than the jump from 1 to 10, and so on. Any further suggestions are appreciated! Thanks $\endgroup$
    – user5071
    Commented Dec 18, 2012 at 11:51

1 Answer 1

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+50
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I think I found a way to solve the problem.

Using a different example:

test = Flatten[Table[{i, j, Exp[RandomReal[{0, 10}]]}, {j, 1, 100}, {i, 1, 100}], 1];

min = Log[10, Min[test[[;; , 3]]]];
max = Log[10, Max[test[[;; , 3]]]];

ListContourPlot[test,
InterpolationOrder -> 0, 
Contours -> Flatten[Table[{1., 2., 5.}*10^n, {n, 1, 4}]], 
ColorFunction -> Function[{f}, ColorData["Rainbow"][(Log[10, f] - min)/(max - min)]],
ColorFunctionScaling -> False,
PlotLegends -> BarLegend[Automatic, All], 
PlotRange -> All]

The result is

enter image description here

Thank you all for your input!

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