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We study the long-time dynamics of a forest-fire model with deterministictree growth and instantaneous burning of entire forests by stochastic lightningstrikes. Asymptotically the system organizes into a coarsening self-similarmosaic of synchronized patches within which trees regrow and burnsimultaneously. We show that the average patch length <L> grows linearly withtime as t-->oo. The number density of patches of length L, N(L,t), scales as<L>^{-2}M(L/<L>), and within a mean-field rate equation description we findthat this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} forx-->oo. In one dimension, we develop an event-driven cluster algorithm to studythe asymptotic behavior of large systems. Our numerical results are consistentwith mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR

Synchronization and coarsening (without self-organized criticality) in a forest-fire model