SetLorenz[σ_, r_, 
          b_] := 
Module[{s = σ, bb = b, 
            rr = r}, 
f1[t_, x_, y_, 
              z_] = -s*(x - y); 
f2[t_, x_, y_, 
              z_] = -x*z + r*x - y; 
f3[t_, x_, y_, 
              z_] = x*y - bb*z; 
F[
              t_, {x_, y_, z_}] = {f1[t, x, y, z], f2[t, x, y, z], 
              f3[t, x, y, z]};];

Runge3[initt_,  finalt_,  initx_,  inity_,  initz_,  
          steps_] := 
Module[{it = initt, ft = finalt, j, 
            m = steps}, 
h = (ft - it)/
              m; 
T = 
            Table[it  + (j - 1) h, {j, 1, 
                m + 1}]; 
R = {initx, inity, 
              initz}; 
P = 
            Table[{}, {m}]; 
PP = 
            Table[{}, {m}]; 
PPPP = 
            Table[{}, {m}]; 
For[j = 1, 
            j < m + 1, j++, 
k1 = 
              h F[T[[j]], R]; 
k2 = 
              h F[T[[j]] + h/2, R + k1/2]; 
k3 = 
              h F[T[[j]] + h/2, R + k2/2]; 
k4 = 
              h F[T[[j]] + h, R + k3]; 
Rnew = 
              R + 1/6 (k1 + 2 k2 + 2 k3 + k4); 
R = 
              Rnew; 
P[[j]]  =  
              R[[1]]; 
PP[[j]]  =  
              R[[2]]; 
PPPP[[j]] = 
              R[[3]];
];
];

SetLorenz[10, 27, (8/3)];
Runge3[0.0, 100.0, 30, 10, 40, 50000];
rec1 = Interpolation[P];
rec2 = Interpolation[PP];
rec3 = Interpolation[PPPP];
blah = 
        ParametricPlot3D[{rec1[t], rec2[t], rec3[t]}, {t, 1000, 50000}, 
          PlotPoints -> 15000, Axes -> False, 
          PlotRange -> All, 
          DisplayFunction -> Identity];
Show[
        blah /. Line[
              l : {_, __}] :> ({Hue[((0.04 First[Plus @@ #(1/2)])/π)], Line[#1]} &) /@ Partition[l, 2, 1], 
        DisplayFunction -> $DisplayFunction];

newist  =  Table[{0, 0, 0}, {1}];
a = Random[Real, {-30, 30}];
aa = Random[Real, {-10, 10}];
aaa = Random[Real, {-40, 40}];
SetLorenz[10, 27, (8/3)];
Runge3[0.0, 100.0, a, aa, aaa, 50000];
rec1 = Interpolation[P];
rec2 = Interpolation[PP];
rec3 = Interpolation[PPPP];
newist  =  Table[{0, 0, 0}, {1}];
a = Random[Real, {-30, 30}];
aa = Random[Real, {-10, 10}];
aaa = Random[Real, {-40, 40}];
SetLorenz[10, 27, (8/3)];
Runge3[0.0, 100.0, a, aa, aaa, 50000];
rec11 = Interpolation[P];
rec12 = Interpolation[PP];
rec13 = Interpolation[PPPP];
blah2 = 
        ParametricPlot3D[{{rec1[t], rec2[t], rec3[t]}, {rec11[t], rec12[t], 
              rec13[t]}}, {t, 1000, 50000}, PlotPoints -> 15000, 
          Axes -> False, PlotRange -> All, 
          PlotStyle -> {{RGBColor[1, 0, 0]}, {RGBColor[0, 1, 
                  0]}}];