Q[1]=Q[2]=1;
Q[n_] := Q[n] = Q[n-Q[n-1]] + Q[n-Q[n-2]];

ListPlot[Q/@Range[1000]]

?Nest

Animate[
DensityPlot[
Abs[Nest[(#^2+0.3)&, x+I y, n]],
{x,-2,2},{y,-2,2}, PlotRange -> {0,1}, PlotPoints -> 50
],
{n,1,8,1}
]

?Animate