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Problem with a diagram


I am constructing a bifurcation diagram for interval 0.15 <= alpha <= 0.75 but it always go into loop and can't find an error. I used word alpha for greek symbol.

recursive equation is: 
In[1]:= f[x_]:=(1-alpha)x+((alpha*0.8)/0.25)-((alpha*ArcTan[4x])/0.25) 
In[2]:= f[x]


I used:

ListPlot[
    Flatten[Table[
         Transpose[{
             Table [alpha, {129}],
             NestList[f, Nest[f,0.5,500],128]
         }],
       {alpha,0,0.75,0.001}
   ],1],
   PlotStyle->PointSize[0.001],Axes->False,Frame->True];

Can anyone help me please?


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