plotting - How to assign special colors to the output of DensityPlot?

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]

Comments

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