(* Number of iterations *)

nmax=20;

x[0]=0.3;

f[x_]:=1-2*x^2;

Do[x[n+1]=f[x[n]],{n,0,nmax}];

y[0]=0.3001;

Do[y[n+1]=f[y[n]],{n,0,nmax}];

Show[ListPlot[Table[{n,x[n]},{n,1,nmax}],PlotJoined->True],
ListPlot[Table[{n,y[n]},{n,1,nmax}],PlotJoined->True]]

Do[Print[{n,x[n],y[n]}],{n,0,nmax}]