Analytic Procgen with Composable Design Space Expressions

When designing procedural content generation systems for games, we imagine that there is a space of potential designs, and each of those designs affords a space of potential play.However, in most generative systems, there is a complex relationship between input parameters and the design or play properties of system outputs.As generators grow in complexity, it becomes harder to predict what experiences players will have in the generated design.In both constructive and solver-based approaches, this leads to uncertainty about how changes to the generator itself will affect the distribution of outputs.In this paper, we contribute a new method for constructing generators by manipulating closed-form expressions for spaces of designs and their associated play properties.The resulting generators have highly predictable running times, precisely controllable output distributions, and allow enforcing arbitrary constraints about their outputs.We offer a sequence of increasingly complex examples showing how to compute design-interaction expressions and use them for generation.Finally, we document scaling strategies for handling design-interaction spaces where millions of gameplay states are reachable in each of trillions of designs.