  Spontaneous pattern formation from a uniform state is a widely studied
nonlinear optical phenomenon that shares similarities with non-equilibrium
pattern formation in other scientific domains. Here we show how a single layer
of atoms in an array can undergo nonlinear amplification of fluctuations,
leading to the formation of intricate optical patterns. The origin of the
patterns is intrinsically cooperative, eliminating the necessity of mirrors or
cavities, although introduction of a mirror in the vicinity of the atoms
significantly modifies the scattering profiles. The emergence of these optical
patterns is tied to a bistable collective response, which can be qualitatively
described by a long-wavelength approximation, similar to a nonlinear
Schr\"odinger equation of optical Kerr media or ring cavities. These collective
excitations have the ability to form singular defects and unveil atomic
position fluctuations through wave-like distortions.
