  We study the stationary states for the nonlinear Schr\"odinger equation on
the Fibonacci lattice which is expected to be realized by Bose-Einstein
condensates loaded into an optical lattice. When the model does not have a
nonlinear term, the wavefunctions and the spectrum are known to show fractal
structures. Such wavefunctions are called critical. We present a phase diagram
of the energy spectrum for varying the nonlinearity. It consists of three
portions, a forbidden region, the spectrum of critical states, and the spectrum
of stationary solitons. We show that the energy spectrum of critical states
remains intact irrespective of the nonlinearity in the sea of a large number of
stationary solitons.
