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Let's define some sample data

data = {{-3, -1}, {-2, -1}, {-1, -1}, {-0.2, -0.2}, {0, 0}, {0.5, 0.5},
        {2, 2}, {3, 2}, {4, 2}};

and create the corresponding list plot

L0 = ListPlot[data, Joined -> True, PlotStyle -> {Black, Thick}]

enter image description here

Now, I want the following: change the color at different segments of the thick line. For example:

  • for $-2.4 < x < -1.1$ ---> red thick
  • for $-0.2 < x < 0.94$ ---> blue thick
  • for $2.22 < x < 3.4$ ---> green thick
  • in all other cases ---> black thick

IMPORTANT NOTE: The real data contain thousands of pairs which cannot be separated into sections. Only the intervals on the x axis are known. So, I want a continuous line with different colors in each segment.

What would be an elegant and quick way to do this?

Many thanks in advance!

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  • $\begingroup$ The simplest? Separate the data into sections, run ListPlot[sectioned, PlotStyle -> {Directive[Thick, Blue], Directive[Thick, Blue], Directive[Thick, Green], Directive[Thick, Black]}] where the styles in PlotStyle are in the correct order. $\endgroup$ – rcollyer Oct 10 '16 at 17:59
  • $\begingroup$ Should be doable with the judicious use of ColorFunction and Piecewise[]. $\endgroup$ – J. M. is slightly pensive♦ Oct 10 '16 at 18:03
  • $\begingroup$ @rcollyer It's not that simple! The real data contain thousands of pairs which cannot be separated into sections. Only the intervals on the $x$ axis are known. So, I want a continuous line with different colors in each segment. $\endgroup$ – Vaggelis_Z Oct 10 '16 at 18:03
  • $\begingroup$ @J.M. i thought that too but when you try it, Mathematica blends the colors over and does not make a sharp border.. $\endgroup$ – Julien Kluge Oct 10 '16 at 18:09
  • $\begingroup$ You're correct, the boundary points represent a problem. I like the Mesh solutions propose below. Far simpler. $\endgroup$ – rcollyer Oct 10 '16 at 18:43
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data = {{-3, -1}, {-2, -1}, {-1, -1}, {-0.2, -0.2}, {0, 0}, {0.5, 0.5},
        {2, 2}, {3, 2}, {4, 2}};

ListPlot[data, Joined -> True, PlotStyle ->Thick, 
 (* MeshFunctions -> {# &},*) 
 Mesh -> {{-2.4, -1.1, -0.2, 0.94, 2.22, 3.4}}, 
 MeshStyle -> PointSize[0], 
 MeshShading -> Riffle[{Red, Blue, Green}, Black, {1, -1, 2}]]

Mathematica graphics

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  • $\begingroup$ Great answer! What if there is no gap between blue and green? Will it still work or there will be a black point? $\endgroup$ – BlacKow Oct 10 '16 at 18:47
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    $\begingroup$ I like that. I wondered why you used MeshFunctions->{#&}. Is there a reason for that? $\endgroup$ – Julien Kluge Oct 10 '16 at 18:51
  • $\begingroup$ @BlacKow, this works only for the case with no overlaps. If the list of breakpoints have duplicate elements as in {-2.4, -1.1, -0.2, 0.94, .94, 3.4} then you can use MeshShading->{Black, Red, Black, Blue, Green} $\endgroup$ – kglr Oct 10 '16 at 18:55
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    $\begingroup$ @JulienKluge, good point; the default value of MeshFunctions is #&, so it is redundant. $\endgroup$ – kglr Oct 10 '16 at 18:58
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    $\begingroup$ @Vaggelis_Z, it inserts Black in every other position in the list {Red,Blue, Green} starting from position one. Without it Riffle[{Red,Blue, Green}, Black] would give {Red, Black,Blue, Black, Green}. See Riffle $\endgroup$ – kglr Oct 10 '16 at 19:11
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We use an unscaled ColorFunction with a Piecewise which uses your definitions. Interestingly one have to alter the Mesh-settings to allow a sharp color-border otherwise it will blend over.

L0=ListPlot[data,Joined->True,PlotStyle->Thick,ColorFunction->Function[{x,y},Piecewise[{{Red,-2.4<x<-1.1},{Blue,-0.2<x<0.94},{Green,2.22<x<3.4}},Black]],ColorFunctionScaling->False,Mesh->200,MeshShading->{Automatic},MeshStyle->None]

enter image description here

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  • $\begingroup$ Is it just my impression or the middle part is not so smooth? I see it like a bunch of dots... $\endgroup$ – Vaggelis_Z Oct 10 '16 at 18:35
  • $\begingroup$ Uhm well, it looks good to me on my machine. Try to Increase the Mesh-option. Can you show a screenshot? $\endgroup$ – Julien Kluge Oct 10 '16 at 18:38
  • $\begingroup$ The Mesh-option does not have any affect. Try to enlarge the image you posted and you will see that the middle line is not a real straight line! It looks like a join of dots or something else! $\endgroup$ – Vaggelis_Z Oct 10 '16 at 18:43
  • $\begingroup$ I'm on OSX, MMA 11.0.0.0 and I see the same behavior, but only for this answer. Other options show a smooth curve. $\endgroup$ – N.J.Evans Oct 10 '16 at 19:07
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As alternative you can follow up idea of separation. Since we don't know if you have the endpoints of your regions in your data set , we can use Interpolation and then break it up into several pieces.

limitF[f_, {xmin_, xmax_}] := 
  Piecewise[{{f[#], xmax > # > xmin}}, Infinity] &;
data = {{-3, -1}, {-2, -1}, {-1, -1}, {-0.2, -0.2}, {0, 0}, {0.5, 
    0.5}, {2, 2}, {3, 2}, {4, 2}};
fun = Interpolation[data, InterpolationOrder -> 1];
separated = 
  limitF[fun, #] & /@ {{-2.4, -1.1}, {-0.2, 0.94}, {2.2, 3.4}};

So separated is list of functions that present fun in different regions.

Plot[Evaluate[{fun[x]}~Join~(#[x] & /@ separated)], {x, -3, 4}, 
 PlotStyle -> {Directive[Thick, Black], Directive[Thick, Red], 
   Directive[Thick, Blue], Directive[Thick, Green]}]

enter image description here

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