Same Colors to Match Two Contour Plots

Question

I have two contour plots:

c1 = ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
  FrameTicks -> None]
c2 = ContourPlot[10*Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
  FrameTicks -> None]

I want to be able to compare them not only in terms of numbers but also in terms of colors. So same value -> same color.

How can I make sure that the colors between the two contour plots match ? Also, they should have one unique legend.

Answer 1

Find the narrowest range that covers the range of both plots and use it as color function range in both plots:

range = MapThread[# @ #2 &, {{Min, Max}, Transpose @
 (Through[{MinValue, MaxValue}[{#, 0 <= x <= 4 Pi,  0 <= y <= 4 Pi}, {x, y}, Reals]] & /@ 
   {Cos[x] + Cos[y], 10 Cos[x] + Cos[y]})}]
{c1, c2} =  ContourPlot[#, {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
  FrameTicks -> None, PlotLegends -> Automatic,ImageSize -> 300,
  ColorFunction -> ColorData[{"Rainbow", range}], ColorFunctionScaling -> False] & /@ 
   {Cos[x] + Cos[y], 10 Cos[x] + Cos[y]};

Row[{c1, c2}]

To use the default color function with the new color range change "Rainbow" above to "M10DefaultDensityGradient" to get: