  The electronic properties of graphene under any arbitrary uniaxial strain
field are obtained by an exact mapping of the corresponding tight-binding
Hamiltonian into an effective one-dimensional modulated chain. For a periodic
modulation, the system displays a rich behavior, including quasicrystals and
modulated crystals with a complex spectrum, gaps at the Fermi energy and
interesting localization properties. These features are explained by the
incommensurate or commensurate nature of the potential, which leads to a dense
filling of the reciprocal space in the former case. Thus, the usual
perturbation theory approach breaks down in some cases, as is proved by
analyzing a special momentum that uncouples the model into dimers.
