High Dimensional Procedural Content Generation

Procedural content generation (PCG) has made substantial progress in shaping static 2D/3D geometry, while most methods treat gameplay mechanics as auxiliary and optimize only over space. We argue that this limits controllability and expressivity, and formally introduce High-Dimensional PCG (HDPCG): a framework that elevates non-geometric gameplay dimensions to first-class coordinates of a joint state space. We instantiate HDPCG along two concrete directions. Direction-Space augments geometry with a discrete layer dimension and validates reachability in 4D (x,y,z,l), enabling unified treatment of 2.5D/3.5D mechanics such as gravity inversion and parallel-world switching. Direction-Time augments geometry with temporal dynamics via time-expanded graphs, capturing action semantics and conflict rules. For each direction, we present three general, practicable algorithms with a shared pipeline of abstract skeleton generation, controlled grounding, high-dimensional validation, and multi-metric evaluation. Large-scale experiments across diverse settings validate the integrity of our problem formulation and the effectiveness of our methods on playability, structure, style, robustness, and efficiency. Beyond quantitative results, Unity-based case studies recreate playable scenarios that accord with our metrics. We hope HDPCG encourages a shift in PCG toward general representations and the generation of gameplay-relevant dimensions beyond geometry, paving the way for controllable, verifiable, and extensible level generation.