  In pattern forming systems such as Rayleigh-Benard convection or directional
solidification, a large number of linearly stable, patterned steady states
exist when the basic, simple steady state is unstable. Which of these steady
states will be realized in a given experiment appears to depend on unobservable
details of the system's initial conditions. We show, however, that weak,
Gaussian white noise drives such a system toward a preferred wave number which
depends only on the system parameters and is independent of initial conditions.
We give a prescription for calculating this wave number, analytically near the
onset of instability and numerically otherwise.
