Before revision:  We find that a spatial pattern that is damped in time in a deterministic system may be sustained and amplified by stochasticity , most strikingly at an optimal spatio-temporal noise level. In addition, we find that spatially-smoothed noise alone causes pattern formation even without spatial coupling .
After revision:  We find that a spatial pattern that is damped in time in a deterministic system may be sustained and amplified by stochasticity . We find that spatially-smoothed noise alone causes pattern formation even without spatial coupling .