How to assign special colors to the output of DensityPlot?

Question

I have created the following function for plotting

plotDynamical[iterMethod_, points_] := 
 DensityPlot[
  iterAlgorithm[iterMethod], {t, xxMin, xxMax}, {s, yyMin,yyMax}, 
  PlotRange -> {1,4}, ColorFunction -> {Orange, Blue, Black, Green}, 
  PlotPoints -> points]

The possible results of " iterAlgorithm[iterMethod] " are 1 , 2, 3 or 4. I would like to assigning colours to numbers like so: Orange to 1,Blue to 2,Black to 3 and Green to 4. How can I do this?

complete my Algorithm is:

F = Compile[{{t, _Real}, {s, _Real}}, {t^2 + s^2 - 4, -Exp[t] + s - 
     1}];
dF = Compile[{{t, _Real}, {s, _Real}}, {{2 t, 2 s}, {-E^t, 1}}];
invdF = Compile[{{t, _Real}, {s, _Real}}, {{1/(
     2 E^t s + 2 t), -((2 s)/(2 E^t s + 2 t))}, {E^t/(
     2 E^t s + 2 t), (2 t)/(2 E^t s + 2 t)}}];

rootF[1] = {-1.59832066552612835, 1.202235854627582} ;
rootF[2] = {0, 2} ;


rootPosition = 
 Compile[{{t, _Real}, {s, _Real}}, 
  Which[Norm[{t, s} - rootF[1]] < 10.0^(-10), 3,
   Norm[{t, s} - rootF[2]] < 10.0^(-10), 2, True, 
   1], {{rootF[_, _], _Real, _Real}}];

iterPsM10 = Compile[{{t, _Real}, {s, _Real}},
  Block[{v = F[t, s], w = dF[t, s], u = invdF[t, s], x, y, z, dFz, Q, 
    uu, vv, Fu, vu, invdFvu},
   x = {t, s};
   y = x - (1/2 ) u.v;
   z = 1/3 (4 y - x);
   dFz = dF @@ ({z[[1]], z[[2]]});
   Q = Inverse[w - 3 dFz];
   uu = y + Q.v;
   Fu = F @@ ({uu[[1]], uu[[2]]});
   vv = uu + 2 Q.Fu;
   vu = 1/2 (vv + uu);
   invdFvu = invdF @@ ({vu[[1]], vu[[2]]});
   uu - invdFvu.Fu]];

iterAlgorithm[iterMethod_, lim_] := 
 Block[{ct, r}, ct = 0; r = rootPosition[t, s];
  While[(r == 1) && (ct < lim), ++ct; {t, s} = iterMethod[t, s]; 
   r = rootPosition[t, s]];
  If[Head[r] == Which, r = 0];(*"Which" unevaluated*)Return[r]];

limIterations = 1000;
xxMin = -5; xxMax = 5; yyMin = -5; yyMax = 5;

plotDynamical[iterMethod_, points_] := 
 DensityPlot[iterAlgorithm[iterMethod, limIterations],
  {t, xxMin, xxMax}, {s, yyMin, yyMax}, PlotRange -> {0, 3}, 
  ColorFunction -> {Green, Black, Orange, Blue},
  PlotPoints -> points, 
  Epilog -> {White, PointSize[.02], Point[rootF[1]], Point[rootF[2]]}];


plotDynamical[iterPsM10, 56]

Answer 1

As you don't provide a working example I have used a simple function to plot a DensityPlot. You can use for example a Piecewise function as the ColorFunction to determine the colour of your data points:

DensityPlot[Sin[x y], {x, 0, 3}, {y, 0, 3}, 
 ColorFunction -> 
  Function[{x, y}, 
   Piecewise[{{Orange, 0 <= x < 0.25}, {Blue, 0.25 >= x < 0.5}, {Red, 
      0.5 <= x < 0.75}, {Green, 0.75 <= x <= 1}}, Yellow]], 
 PlotPoints -> 50]

In your case you would have to set the ranges to Piecewise[{{Orange, x==1},{Blue, x==2},{ and so on

Answer 2

(Minor brain failure, but after applying the jumper cables...)

Here is a function that returns a value in the set (1, 2, 3, 4):

fn = Floor @ Mod[# + Sin[#2], 4, 1] &

In a DensityPlot:

DensityPlot[fn[t, s], {t, 0, 10}, {s, 5, 15}, PlotPoints -> 50, 
 ColorFunction -> {Orange, Blue, Black, Green}]

Or as a ContourPlot:

ContourPlot[fn[t, s], {t, 0, 10}, {s, 5, 15},
 Contours -> {1, 2, 3, 4},
 ContourShading -> {Green, Orange, Blue, Black},  (* thanks kguler *)
 PlotPoints -> 50
]