ContourPlot - unequal contour spacing

Question

how can i specify the contour spacing or how the color range is distributed amongst the function values?

Let's say i plot some function depending on x and y. Function values differ between [0, 1]. I want that mathematica makes ...let's say 10 contours for the function value range [0,0.9] and another 10 contours for the rest of the range [0.9,1]. Further more the last Contour of the [0,0.9] range is supposed to be thicker, in order to show that from here on the contour spacing is finer.

thx for your help

thats alot so far for your help, my actual question has been answered already. but a follow-up question has arisen for me since the implementation of your codes does not work with my actual function and i don't know why. I have purged that function and the functions it calls from most variables and replaced them by constants for simplicity reasons. I hope it's ok so.

eislexpl[epsilon_, n2_, x_] :=  28 (epsilon)^2 - 1 + 
((-2 Log[E^(1/2) x])/x^2 + (2.7(0.3 - epsilon))/x + 
(10 epsilon^2 n2^(3/2))/x^(3/2));

eislminx2[epsilon_?NumericQ, n2_?NumericQ] := 
(minx = FindArgMin[{eislexpl[epsilon, n2, x], 0 < x}, x];
eislexpl[epsilon, n2, minx]);

ueislexpl[epsilon_, h_, n1_, n2_] := 
n1 (40  epsilon^2 - 1) + (1 -1.27 ) (1 + (n1 - 1) HeavisideTheta[1 - n1] - 
(-1 + Exp[-(n1 - 1)]) HeavisideTheta[n1 - 1]) + n2  eislminx2[epsilon, n2] + 
(h - n1 - n2) (28  epsilon^2 - 1);

ueislexpl[epsilon_, h_, n1_, n2_] is the function i want to plot with ContourPlot. If i use :

ContourPlot[
 ueislexpl[0.1, 5, n1, n2], {n1, 0, 5}, {n2, 0, 5 - n1}, 
 Contours -> (Function[{min, max}, 
 Module[{r1, r2}, 
 Join[r1 = Range[min, .1 max, (.1 max - min)/10], 
      r2 = Range[.1 max + .01, max, (max - .1 max - .01)/10]]]]), 
 ContourStyle -> (Join @@ {Table[Thick, {Length@r1}], 
     Table[Thin, {Length@r2}]})]

It should plot a contourplot with 10 divisions for the value range [min,0.1 max] and 10 more divisions for [0.1 max, max]. But my result is 3 divisions.

What do i have to change?

Answer 1

Something like this?

ContourPlot[
 1 - Exp[-x - y]
 , {x, 0, 2}
 , {y, 0, 2}
 , PlotRange -> {0, 1}
 , Contours -> Join[Range[0, 0.9, 0.1], Range[0.9, 1, 1/100]]
 , ContourStyle -> Join[Table[Thick, {10}], Table[Thin, {9}]]
 ]

EDIT:

About the follow-up question, the function should look like this:

ContourPlot[
 ueislexpl[0.1, 5, n1, n2]
 , {n1, 0, 5}
 , {n2, 0, 5 - n1}
 , PlotPoints -> 100
 , Contours -> (
   Function[{min, max},
    Module[{r1, r2, ret},
     ret = Join[
       r1 = Range[min, min + ( max - min)/10, (max - min)/100], 
       r2 = Range[1/100 (19 max + 81 min), max, (9 (max - min))/100]
       ];
     Print[{min, max, r1, r2}];
     ret
     ]])
 , ContourStyle -> (
   Join @@ {Table[Thick, {Length@r1}], Table[Thin, {Length@r2}]}
   )
 ]

{-4.39976,-3.40577,{-4.39976,-4.38982,-4.37988,-4.36994,-4.36,-4.35006,-4.34012,-4.33018,-4.32024,-4.3103,-4.30036},{-4.2109,-4.12144,-4.03198,-3.94252,-3.85306,-3.7636,-3.67415,-3.58469,-3.49523,-3.40577}}

I included a Print statements to get feedback on where the Contours are been placed. No idea why the plot is missing a half.

Answer 2

An alternative syntax for Contours that combine contours and styles:

cntrplt[expr_, arg1_, arg2_, contours : {{_, _} ..}, opts : OptionsPattern[]] := 
    ContourPlot[expr, arg1, arg2, Contours -> Join @@ Thread /@ contours, opts];

Using @rhermans' example:

cntrplt[1 - Exp[-x - y], {x, 0, 2}, {y, 0, 2}, 
        {{Range[0, .9, 1/10], Thick}, {Range[.91, 1, 1/100], Thin}}, 
        PlotRange -> {0, 1}]

Update:

a way so that i don' have to give the specific values of the range of the function values like [0,1] but rather say: make 10 contours for [min, 0.9 max] and 10 contours for [0.9 max, max]

ContourPlot[1 - Exp[-x - y], {x, 0, 2}, {y, 0, 2}, 
  Contours -> (Function[{min, max}, 
                 Module[{r1, r2}, 
                    Join[r1 = Range[min, .9 max, (.9 max - min)/10], 
                         r2 = Range[.9 max + .01, max, (max - .9 max - .01)/10]]]]),
  ContourStyle -> (Join @@ {Table[Thick, {Length@r1}], Table[Thin, {Length@r2}]})]

Answer 3

Borrowing from @rhermans:

Framed[ContourPlot[Sin[x y], {x, 0, 2}, {y, 0, 2},
  Contours -> Join[Range[0, 0.9, 0.1], Range[0.91, 1, 0.01]],
  Frame -> {{True, False}, {True, False}},
  ColorFunction -> "Pastel",
  ContourStyle -> 
   Join[Table[Directive[Brown, Thick], {10}], Table[Directive[Dashed, Thin], {9}]],
  ContourLabels -> Function[{x, y, z}, Text[Framed[z], {x, y}, Background -> White]],
  ImageSize -> 600],
 FrameMargins -> 20]