It is clear that carbonate strata are complex and incomplete, but the nature and origins of the complexity, and the origin and distribution of hiatuses remain poorly understood. A three-dimensional numerical forward model of carbonate platform systems has been used to investigate how variations in complexity and completeness arise in carbonate strata. The model includes depth-dependent carbonate production occurring as a stochastic mosaic of producing elements across a topographic surface. It also includes depth-dependent sediment erosion, transport, and deposition governed by a regional transport direction that can vary stochastically through time, and by wave refraction that causes local variations in transport direction. Combined mosaic production and variable sediment transport create a complex distribution of prograding islands, generating self-organizing, shallowing-upward parasequences of variable thickness and variable lateral extent. Hiatuses occur throughout the parasequences, not just at the base and top, generated by nondeposition due to mosaic production, and by erosional scour. This erosion is triggered by variations in water depth and fetch distance, created by complex island morphologies. Preserved strata represent between 15 and 60% of total elapsed time measured at a 2 ky resolution, and much of the preserved thickness represents punctuated deposition, with depositional events spanning only a few thousand years. Stratigraphic completeness depends on subsidence rate and sediment transport rate, so that completeness generally increases with increasing subsidence rate and decreasing transport rate, but shows a nonlinear relationship with subsidence rate. This suggests that reliable estimates of completeness of ancient carbonate strata require more than knowledge of subsidence rate and sea-level change, particularly because the real situation is likely to be considerably more complex than represented in this model. The stochastic production mosaic and stochastic variations in regional transport direction create complex strata, whereas the self-organizing island progradation process creates simpler, ordered strata. A combination of the two processes creates an intermediate level of complexity, producing strata consisting of laterally impersistent parasequences with numerous erosion surfaces and complex stacking patterns and complex thickness distributions. This has important implications for parasequence correlation in outcrop and the subsurface.