  A recently developed model of interacting composite fermions, is used to
investigate different composite-fermion phases. Their interaction potential
allows for the formation of both solid and new quantum-liquid phases, which are
interpreted in terms of second-generation composite fermions and which may be
responsible for the fractional quantum Hall states observed at unusual filling
factors, such as nu=4/11. Projection of the composite-fermion dynamics to a
single level, involved in the derivation of the Hamiltonian of interacting
composite fermions, reveals the underlying self-similarity of the model.
