How to render level curves in several colors.

Questions
1

I have a function of two variables defined on a region D in the x-y plane and I am looking at the contour curves of the form f(x,y)=cnst for several different constants. I am using the command ContourPlot[…] to plot the function and it’s level curves and I would like to render the level curves in different colors. Alas, the function RGBColor[…] is not an option for ContourPlot[…]. Is there any other way to render the level curves in a chosen color? As an example, I have the following code.

a=0;b=1;c=0;d=2;
f[x_,y_]=Sin[Pi x]^2 Sin[Pi y]^2;

ContourPlot[f[x,y],{x,a,b},{y,c,d},
      ContourShading->False,
      AspectRatio->Automatic,
      Contours->{0,.2,.5,.7,.9},
      PlotPoints->100,
      AspectRatio->1,
      DisplayFunction->$DisplayFunction];
2

Consider using the Option ContourStyle:

Clear[f];
f[x_, y_] := Sin[Pi x]^2 Sin[Pi y]^2;

ContourPlot[
    f[x, y], 
    {x, 0,1}, {y, 0,2}, 
    ContourShading -> None, 
     AspectRatio -> Automatic, Contours -> {0, .2, .5, .7, .9}, 
     PlotPoints -> 100, AspectRatio -> 1, 
     ContourStyle -> {Red, Blue, Green, Yellow, Orange}
]
3

Adding the command "ContourStyle → {Red, Blue, Green, Yellow, Orange} " To my code results in a plot of the contour curves that are all orange colored. They are not {Red, Blue, Green, Yellow, Orange}
in that order.

4

Can I know the output? I mean I am interested in this, but I wanna see the output. :slight_smile:

5

(* Sorry about the mixup in the code the I posted. The cut and paste function somehow missed up the translation and left out a bunch of stuff. I think this post is correct. It shows my problem with the colors of the level curves. *)
a = 0; b = 1; c = 0; d = 2;
f[x_, y_] := Sin[Pi x]^2 Sin[Pi y]^2;

  p1 = ContourPlot[f[x, y], {x, a, 
          b}, {y, c, d}, ContourShading -> False, AspectRatio -> Automatic, 
  Contours -> {.7}, PlotPoints -> 100, ContourStyle -> RGBColor[1, 0, 1],
        AspectRatio -> 1];
  
  p2 = ContourPlot[f[x, y], {x, a, b}, {y, c, d}, ContourShading -> 
        False, AspectRatio -> Automatic, Contours -> {.9}, PlotPoints -> 
          100, ContourStyle -> RGBColor[1, 0, 1],
        AspectRatio -> 1];
  
  p3 = ContourPlot[f[x, 
        y], {x, 0, 1}, {y, 0, 2}, ContourShading -> None, AspectRatio -> 
  Automatic, Contours -> {0, .5, .7, .9}, PlotPoints -> 100,
      ColorFunction -> {RGBColor[0, 0, 0], RGBColor[1, 1, 0], RGBColor[
        0, 1, 0], GBColor[0, 0, 1]}, 
          ContourStyle -> {RGBColor[0, 0, 0], RGBColor[1,
           1, 0], RGBColor[0, 1, 0], GBColor[0, 0, 1]},
      AspectRatio -> 1]
6

(* Here is some code that shows my problem witn=h cotour colors. The cut and paste function did not work right in my revious post *)
a = 0; b = 1; c = 0; d = 2;
f[x_, y_] := Sin[Pi x]^2 Sin[Pi y]^2;
p1 = ContourPlot[f[x, y], {x, a, b}, {y, c, d}, ContourShading → False,
AspectRatio → Automatic, Contours → {.7},
PlotPoints → 100, ContourStyle → RGBColor[1, 0, 1],
AspectRatio → 1];
p2 = ContourPlot[f[x, y], {x, a, b}, {y, c, d}, ContourShading →
False, AspectRatio → Automatic, Contours → {.9}, PlotPoints →
100, ContourStyle → RGBColor[1, 0, 1],
AspectRatio → 1];
p3 = ContourPlot[f[x, y], {
x, 0, 1}, {y, 0, 2}, ContourShading → None, AspectRatio → Automatic,
Contours → {0, .5, .7, .9}, PlotPoints → 100, ContourStyle → {
RGBColor[0, 0, 0], RGBColor[1, 1, 0], RGBColor[0,
1, 0], GBColor[0, 0, 1]},
AspectRatio → 1]

7

Typo GBColor should be RGBColor. AspectRatio is specified twice, earlier one takes precedence.

ContourPlot[f[x, y], {x, 0, 1}, {y, 0, 2},
 ContourShading -> None,
 AspectRatio -> Automatic,
 Contours -> {0, .5, .7, .9},
 ContourStyle -> {RGBColor[0, 0, 0], RGBColor[1, 1, 0], RGBColor[0, 1, 0], RGBColor[0, 0, 1]}]

8424plot.png
8424plot.png285×540 14.2 KB

8

I see that you have succeded in doing what I want to do. But when I try to use your code on my machine it does not work correctly. I am attaaching my code as a file if you want to look at it I would be most greatful. Dave Barnes.

contours.nb (108 KB)

9

Hi David,

the code still exhibits the missing ‘R’ typo in one of the RGBColor heads.
Furthermore, you appear to be using Mathematica version 5.2.

We may be looking at a bug that’s 10 years or older.

It that’s so, the following code may be a work-around.

Show@MapThread[
ContourPlot[f[x, y], {x, a, b}, {y, c, d}, ContourShading → False,
AspectRatio → Automatic, Contours → {#1}, PlotPoints → 100,
ContourStyle → #2,
AspectRatio → 1] &,
{{0, .5, .7, .9}, {RGBColor[0, 0, 0], RGBColor[1, 1, 0],
RGBColor[0, 1, 0], RGBColor[0, 0, 1]}}
]