I have produced used the following code to create a contour plot:

ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}]

However, I would like to modify this plot so that when the function is positive the shading is blue, and when it is negative the shading is red.

Now I know there's already similar threads on this site to achieving this but I would like to impose another condition which makes things trickier.

I would also like the contours lines to have the OPPOSITE colour to the shading (i.e if the region is shaded blue then I want the contours to be red). The contours can be isolated by turning shading off:

ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
 ContourShading -> None]

So I would like the contours to be coloured as follows:

The Contours

Combined with the shading, I hope that the final image will look like this:

The Goal

Final Result

I would be really grateful if someone could shed some light on this.

I'm really hoping there's a way of implimenting an IF statement which will condition on the sign of the function.

Thanks in advance!


A non-hackish method using Mesh and MeshFunctions:

ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
 ContourShading -> {Red, Blue}, Contours -> {{0}},
 Mesh -> 4, MeshFunctions -> {Max[Cos[#] + Cos[#2], 0] &, Min[Cos[#] + Cos[#2], 0] &}, 
 BaseStyle -> Thick, MeshStyle -> {Red, Blue},
 PlotPoints -> 100

enter image description here

Here is a way using only contours but requiring manually generated styles. I was hoping that a function could be given directly to Contours for automatic generation but at least as I formulated it this did not work.

ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
  ContourShading -> {Red, Red, Red, Red, Red, Blue, Blue, Blue, Blue, Blue}, 
  Contours -> Array[If[# > 0, {#, Red}, {#, Blue}] &, 9, {-2, 2}]


sty = If[# > 0, {#, Blue}, {#, Red}] & /@ Range[-2, 2, 1/2]

ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi},
 ContourShading -> (sty[[All, 2]] /. {Red -> Blue, Blue -> Red}), Contours -> sty]

enter image description here

  • $\begingroup$ Nice! (IOU one upvote.) $\endgroup$ – J. M. will be back soon Feb 21 '16 at 19:54
  • $\begingroup$ @J.M. Thanks! I don't know if this is best however. I often wonder how Heike would do it were she here. $\endgroup$ – Mr.Wizard Feb 21 '16 at 19:57
  • $\begingroup$ This Alternative solution is really nice as it uses terminology of which I am familiar with. However, could I ask why you've included 'Red', and 'Blue' five times each in the list? $\endgroup$ – Mr S 100 Feb 21 '16 at 20:26
  • $\begingroup$ @MrS100 Because unlike the first method I could not separate the number contour lines from the number of contour fill styles. With only ContourShading -> {Red, Blue} here I would get a striped plot instead. $\endgroup$ – Mr.Wizard Feb 21 '16 at 20:29
  • $\begingroup$ Thanks for the prompt reply. I've just tested this now and I see exactly what you mean. I'm struggling to understand what the function & /@ Range[#, #2, 1/2] &[-2, 2]' is doing as changing the values dramatically changes the result. I ask this because I have not seen this function before used in this context and I am keen to understand your choice of parameters. $\endgroup$ – Mr S 100 Feb 21 '16 at 20:35

Yet another hackish solution that however regenerates the contour plot multiple times is the following combination:

 (* Generate the shaded areas *)
 ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi},
  ColorFunctionScaling -> False,
  ColorFunction -> Function[z, If[z >= 0, Blue, Red]],
  ContourStyle -> None

 (* Generate the contours *)
    Boole[#1[Cos[x] + Cos[y], 0]] (Cos[x] + Cos[y]),
    {x, 0, 4 Pi}, {y, 0, 4 Pi}, Contours -> 4,
    ContourStyle -> Directive[Thick, #2], ContourShading -> None
    ] &,
  {{Greater, Less}, {Red, Blue}}

Mathematica graphics

Mr. Wizard's solution presented in his answer above is clearly superior, but I put this together before I saw his answer, so I thought I might as well post it anyway.

  • $\begingroup$ I like this response as this is how I initially thought about approaching the problem - by essentially combining two results. Upvoted $\endgroup$ – Mr S 100 Feb 21 '16 at 20:37

I would also define my color style and use it like this:

contours[n_?OddQ, color1_, color2_] := Module[{m},
  m = IntegerPart[n/2];
  cont = n; 
  col = Join[ConstantArray[color1, m], {Gray}, 
    ConstantArray[color2, m]];];

contours[11, Blue, Red]

p1 = ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
   ContourShading -> None, ContourStyle -> col, Contours -> cont];
p2 = ContourPlot[Cos[x] + Cos[y], {x, 0, 4 Pi}, {y, 0, 4 Pi}, 
   ColorFunction -> (If[# <= 0, Red, Blue] &), 
   ColorFunctionScaling -> False, Contours -> 1];
Show[p2, p1]

enter image description here

not ot get something close to your Goal picuter you can sue Show

  • 1
    $\begingroup$ I somehow didn't see this answer before adding the second method to mine; sorry if I plagiarized accidentally, and +1. $\endgroup$ – Mr.Wizard Feb 21 '16 at 20:20
  • 1
    $\begingroup$ Upvoted. This is a clever solution to the problem. I've only just become familiar with the show function today, but it been of use already. $\endgroup$ – Mr S 100 Feb 21 '16 at 20:38
  • $\begingroup$ @Mr.Wizard not at all and thanks for Upvote :-) $\endgroup$ – Algohi Feb 21 '16 at 20:41

This rather hackish solution relies on the fact that the Tooltip[] objects within the output of ContourPlot[] store the height of the corresponding (set of) contours:

ContourPlot[Cos[x] + Cos[y], {x, 0, 4 π}, {y, 0, 4 π}, 
            ColorFunction -> (Blend[{Red, Blue}, LogisticSigmoid[2 #]] &), 
            ColorFunctionScaling -> False, Contours -> 20] /.
Tooltip[stuff_, c_] :> Tooltip[Prepend[Cases[stuff, _Line],
                                       Directive[{Blue, Red}[[UnitStep[c] + 1]],
                                       Opacity[0.5], CapForm["Butt"]]], c]

looks a bit trippy to me

  • $\begingroup$ Thanks for the response J. M! I've upvoted as the code works as required. $\endgroup$ – Mr S 100 Feb 21 '16 at 20:36

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