mandelbrotEquation= Compile[{{C,_Complex},{Nmax,_Integer},{rmax,_Real}},Length[FixedPointList[#^2 +C&,C,Nmax,SameTest->(Abs[#2]> rmax&)]]];

showMandelbrotSet[{zmin_,zmax_},Nmax_,rmax_]:=Module[{x,y},DensityPlot[
mandelbrotEquation[x + I y,Nmax,rmax],Evaluate[{x,Re[zmin],Re[zmax]}],Evaluate[{y,Im[zmin],Im[zmax]}],Mesh-> False,AspectRatio ->Automatic,Frame-> False,ColorFunction-> Hue,PlotPoints ->300
]
] /;Im[zmin]≠ 0 || Im[zmax]≠ 0;

showMandelbrotSet[{-2 - 1.1I,0.5 + 1.1I},50,2.0]