  The dynamics of patterns in large two-dimensional domains remains a challenge
in non-equilibrium phenomena. Often it is addressed through mild extensions of
one-dimensional equations. We show that full 2D generalizations of the latter
can lead to unexpected dynamical behavior. As an example we consider the
anisotropic Kuramoto-Sivashinsky equation, that is a generic model of
anisotropic pattern forming systems and has been derived in different instances
of thin film dynamics. A rotation of a ripple pattern by $90^{\circ}$ occurs in
the system evolution when nonlinearities are strongly suppressed along one
direction. This effect originates in non-linear parameter renormalization at
different rates in the two system dimensions, showing a dynamical interplay
between scale invariance and wavelength selection. Potential experimental
realizations of this phenomenon are identified.
