Bifurcations[n_,m_]:=Module[{p=0.934235}, s={}; c=3.0;
  Do[S[x_]:=c x(1-x);
     Do[p=S[p],{n/10}]; c=c+1/m;
     Do[p=S[p]; s=Append[s,{c,p}],{n}];Print["Parameter=",c],{m}];
  Show[Graphics[{PointSize[0.001],Map[Point,s]}]]];

Example1:=Bifurcations[30,30];
Example2:=Bifurcations[200,50];

