High Dimensional Procedural Content Generation

Video games are a dynamic medium experienced over time. While there are many Procedural Content Generation (PCG) approaches for generating video game levels, they often use representations that abstract away this dynamic nature. In this paper, we introduce a novel, domain-independent ``cake'' representation for game levels over time which implicitly encodes dynamic information. We present a novel level generation approach Playtrace Reconstructive Partitioning (PRP) specifically developed for this cake representation. We compare against six state-of-the-art PCG approaches in the game domain of Sokoban, and find that our approach can generate valid levels without sacrificing solution diversity. We believe our cake representation more neatly encodes the implicit dynamic nature of games compared to existing representations, which allows for our domain-agnostic level generation algorithm PRP.

Procedural Content Generation (PCG) enables game content to be created algorithmically without direct manual level-design effort, but it introduces a serious evaluation problem: generated content may become unbalanced, blocked, repetitive, or technically unsolvable. This paper presents Momentum, an endless-runner game that integrates runtime terrain generation, environment object spawning, and autonomous agent-based evaluation into a single gameplay loop. Ground tiles and environmental objects are generated dynamically as the player advances, object placement follows a constraint-driven mechanism inspired by Wave Function Collapse (WFC), and the runtime navigation surface is rebuilt asynchronously to remain consistent with the streamed environment. Two autonomous evaluation agents move ahead of the player and inspect the generated path: an aerial scanner that examines the corridor geometrically, and a ground-traversal agent that validates the same region from a navigational perspective. The evaluation pipeline combines ray casting, volumetric physics sweeps, obstacle-layer filtering, and structured crash reporting to identify problematic generated scenarios before they reach the player. The work demonstrates how generation and validation can be unified within the same runtime loop, rather than treating evaluation as a separate offline pass. Around this implementation, the paper formulates a measurable evaluation framework along the canonical PCG axes of playability, diversity, controllability, and runtime performance, derives a structural saturation bound on the spawner from its own placement constraints, and quantifies the per-segment scanning cost of the agents from first principles.

Constraint-based game content generators that learn local constraints from existing content, such as Wave Function Collapse (WFC), can generate visually satisfying game levels but face challenges in optimizing global properties, such as playability. On the other hand, reinforcement-learning-trained generators can optimize global properties---because such properties can easily be included in reward functions---but the results can be visually dissatisfying. In this paper, we explore ways to combine these methods. Specifically, we constrain the action space of a PCGRL generator with constraints learned by WFC, effectively allowing the PCGRL generator to achieve global properties while being forced to adhere to local constraints. To better analyze how this hybrid content generation method operates, we vary the number and type of inputs, and we test whether to randomly collapse the starting state and exclude rare patterns. While the method is sensitive to hyperparameter tuning, the best of our trained generators produce visually satisfying and playable puzzle-platform game levels---such as Lode Runner levels---with desired global properties.