Sedimentation on carbonate platforms is commonly found to lag relative sea-level change, particularly when platforms reestablish themselves after emersion. Models of platform sedimentation usually reproduce this lag with the help of special lag parameters. A cellular automaton is used here to model the way that platforms are colonized by carbonate-producing organisms. This model shows that lag is a natural result of colonization and is considerably more complex than allowed for by other sedimentation models. The model predicts that there are two types of platform (one in shallow water, the other in deeper water) which are cross-coupled dynamical attractors.