  Suspended graphene samples are observed to be gently rippled rather than
being flat. In [M. Friedrich, U. Stefanelli. Graphene ground states,
arXiv:1802.05049], we have checked that this nonplanarity can be rigorously
described within the classical molecular-mechanical frame of
configurational-energy minimization. There, we have identified all ground-state
configurations with graphene topology with respect to classes of
next-to-nearest neighbor interaction energies and classified their fine nonflat
geometries.
  In this second paper on graphene nonflatness, we refine the analysis further
and prove the emergence of wave patterning. Moving within the frame of [M.
Friedrich, U. Stefanelli. Graphene ground states, arXiv:1802.05049], rippling
formation in graphene is reduced to a two-dimensional problem for
one-dimensional chains. Specifically, we show that almost minimizers of the
configurational energy develop waves with specific wavelength, independently of
the size of the sample. This corresponds remarkably to experiments and
simulations.
