Systematic testing of autonomous vehicles operating in complex real-world scenarios is a difficult and expensive problem. We present Paracosm, a framework for writing systematic test scenarios for autonomous driving simulations. Paracosm allows users to programmatically describe complex driving situations with specific features, e.g., road layouts and environmental conditions, as well as reactive temporal behaviors of other cars and pedestrians. A systematic exploration of the state space, both for visual features and for reactive interactions with the environment is made possible. We define a notion of test coverage for parameter configurations based on combinatorial testing and low dispersion sequences. Using fuzzing on parameter configurations, our automatic test generator can maximize coverage of various behaviors and find problematic cases. Through empirical evaluations, we demonstrate the capabilities of Paracosm in programmatically modeling parameterized test environments, and in finding problematic scenarios.