  We establish sharp nonlinear stability results for fronts that describe the
creation of a periodic pattern through the invasion of an unstable state. The
fronts we consider are critical, in the sense that they are expected to mediate
pattern selection from compactly supported or steep initial data. We focus on
pulled fronts, that is, on fronts whose propagation speed is determined by the
linearization about the unstable state in the leading edge, only. We present
our analysis in the specific setting of the FitzHugh-Nagumo system, where
pattern-forming uniformly translating fronts have recently been constructed
rigorously, but our methods can be used to establish nonlinear stability of
pulled pattern-forming fronts in general reaction-diffusion systems. This is
the first stability result of critical pattern-selecting fronts and provides a
rigorous foundation for heuristic, universal wave number selection laws in
growth processes based on a marginal stability conjecture. The main technical
challenge is to describe the interaction between two separate modes of marginal
stability, one associated with the spreading process in the leading edge, and
one associated with the pattern in the wake. We develop tools based on
far-field/core decompositions to characterize, and eventually control, the
interaction between these two different types of diffusive modes. Linear decay
rates are insufficient to close a nonlinear stability argument and we therefore
need a sharper description of the relaxation in the wake of the front using a
phase modulation ansatz. We control regularity in the resulting quasilinear
equation for the modulated perturbation using nonlinear damping estimates.
