  An exact mapping of the tight-binding Hamiltonian for a graphene's nanoribbon
under any armchair uniaxial strain into an effective one-dimensional system is
presented. As an application, for a periodic modulation we have found a gap
opening at the Fermi level and a complex fractal spectrum, akin to the
Hofstadter butterfly resulting from the Harper model. The latter can be
explained by the commensurability or incommensurability nature of the resulting
effective potential. When compared with the zig-zag uniaxial periodic strain,
the spectrum shows much bigger gaps, although in general the states have a more
extended nature. For a special critical value of the strain amplitude and
wavelength, a gap is open. At this critical point, the electrons behave as
relativistic Dirac femions in one direction, while in the other, a
non-relativistic Schr\"odinger behavior is observed. Also, some topological
states were observed which have the particularity of not being completly edge
states since they present some amplitude in the bulk. However, these are edge
states of the effective system due to a reduced dimensionality through
decoupling. These states also present the fractal Chern beating observed
recently in quasiperiodic systems.
