lmin=2.;lmax=4.;k=2000;nmin=10000;nmax=20000;

l=Range[lmin,lmax,(lmax-lmin)/(k-1)];

Rek[x_?VectorQ]:=l*x*(1-x);

XIter=RecurrenceTable[{x[n+1]==Rek[x[n]],x[0]==ConstantArray[0.01,k]},x,{n,nmin,nmax}];

TXIter=Transpose[Ceiling[XIter*k]];

dane=Map[Tally,TXIter,1];

tablica=Table[{dane[[i]][[j]][[1]],i}->Log[dane[[i]][[j]][[2]]],{i,Length[l]},{j,Length[dane[[i]]]}];

tablica=SparseArray[Flatten[tablica]];

ArrayPlot[tablica,DataReversed->True,Frame->True,FrameLabel->{"Atraktor","Parametr l"},ImageSize->Scaled[0.9],ColorFunction->"PlumColors"]