Complex Functions Viz

grad[x_] := {1, 0.2, 0.1} + x {-1, 0.8, 0.4};
\[Delta] = 0.005; range =
 Table[{x, y}, {y, -1, 1, \[Delta]}, {x, -1, 1, \[Delta]}];
z[{x_, y_}] :=
 1/((z - 0.5) (z - I/2 - 0.3) (z + 0.4)) /. {z -> x + I y};
color[z_] := (1 -
    Tanh[Abs[z]] Sin[10 Log[Abs[z]]]) grad[(Arg[z] + Pi)/(2 Pi)];
data = Map[color[z[#]] &, range, {2}];
Image[data]