CartesianMap[func_,{x0_,x1_,dx_},{y0_,y1_,dy_}]:=
Module[{x,y,coords,lines},
coords=Table[N[func[x+I y]],{x,x0,x1,dx},{y,y0,y1,dy}];
coords=Map[{Re[#],Im[#]}&,coords,{2}];
lines=Map[Line,Join[coords,Transpose[coords]]];
Show[Graphics[lines],AspectRatio->Automatic,Axes->Automatic]]

CartesianMap[ Cos,{0.4,π-0.4,(π-0.8)/19},{-2,2,4/16}]