We summarize recent results concerning the stability of spatially‐coherent, time‐periodic states in noisy, classical, discrete‐time, many‐body systems with short‐range interactions. Generic stability of periodic k‐cycles with k≳2 can be achieved only by rules carefully constructed to exploit lattice anisotropy and so suppress droplet growth. For ordinary rules which do not utilize spatial anisotropy in this way, periodic k‐cycles with periods k≳2 are metastable rather than stable under generic conditions, losing spatial coherence through nucleation and growth of droplets.