High Dimensional Procedural Content Generation

TL;DR

This paper introduces High-Dimensional Procedural Content Generation (HDPCG), a framework that incorporates non-geometric gameplay dimensions into level generation, enhancing controllability and expressivity in game design.

Contribution

The paper formalizes HDPCG, presenting algorithms for augmenting geometry with gameplay dimensions like space and time, validated through large-scale experiments and Unity case studies.

Findings

Validated effectiveness on playability and style metrics

Demonstrated reachability in 4D space with Direction-Space

Captured action semantics with Direction-Time

Abstract

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.