Assortative mating--marriage of a man and a woman with similar social characteristics--is a commonly observed phenomenon. In the existing literature in both sociology and economics, this phenomenon has mainly been attributed to individuals' conscious preferences for assortative mating. In this paper, we show that patterns of assortative mating may arise from another structural source even if individuals do not have assortative preferences or possess complementary attributes: dynamic processes of marriages in a closed system. For a given cohort of youth in a finite population, as the percentage of married persons increases, unmarried persons who newly enter marriage are systematically different from those who married earlier, giving rise to the phenomenon of assortative mating. We use microsimulation methods to illustrate this dynamic process, using first the conventional deterministic Gale-Shapley model, then a probabilistic Gale-Shapley model, and then two versions of the encounter mating model.