Module[{}, M=500; c=3.0; s=Table[{},{M}]; 
  S[x_]:=c x(1-x); 
  Do[p=Random[]; c=c+1/M; Do[p=S[p],{M}]; Print["c=",c];
     Do[p=S[p]; s[[j]]=Append[s[[j]],Point[{c,p}]],{M}],
  {j,M}];Show[Graphics[{PointSize[0.001],s}]] ];
