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I am trying to align color scale for continuous plots that have different ranges. Here the color scale exhibits a discontinuity even with the same PlotRange

Show[
 DensityPlot[x^2 + y^2, {x, 0, 1}, {y, -1, 1}, PlotRange -> {0, 2}],
 DensityPlot[(x^2 + y^2)*Exp[x], {x, -1, 0}, {y, -1, 1}, 
  PlotRange -> {0, 2}],
 PlotRange -> {{-1, 1}, {-1, 1}}
 ]

Does anyone know how to solve this issue?

Thanks

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You should have a look at ColorFunctionScaling option. When set to False in your case it gives

Show[
   DensityPlot[x^2 + y^2, {x, 0, 1}, {y, -1, 1}, 
      PlotRange -> {0, 2}, ColorFunctionScaling -> False], 
   DensityPlot[(x^2 + y^2)*Exp[x], {x, -1, 0}, {y, -1, 1}, 
      PlotRange -> {0, 2}, ColorFunctionScaling -> False], 
   PlotRange -> {{-1, 1}, {-1, 1}}
]

enter image description here

An alternative would be to use

f[x_?Positive, y_] := x^2 + y^2
f[x_?Negative, y_] := (x^2 + y^2)*Exp[x];
DensityPlot[f[x, y], {x, -1, 1}, {y, -1, 1}]
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