Extend Wave Function Collapse to Large-Scale Content Generation

TL;DR

This paper introduces Nested WFC, a new algorithm framework that enables large-scale and infinite content generation in procedural design by reducing time complexity and conflict issues.

Contribution

It proposes a Nested WFC framework with a tileset preparation strategy and weight-brush system, facilitating scalable, deterministic, and infinite content generation.

Findings

Reduces time complexity of WFC for large-scale content

Enables generation of aperiodic, infinite content with minimal tiles

Proves the system's suitability for game design applications

Abstract

Wave Function Collapse (WFC) is a widely used tile-based algorithm in procedural content generation, including textures, objects, and scenes. However, the current WFC algorithm and related research lack the ability to generate commercialized large-scale or infinite content due to constraint conflict and time complexity costs. This paper proposes a Nested WFC (N-WFC) algorithm framework to reduce time complexity. To avoid conflict and backtracking problems, we offer a complete and sub-complete tileset preparation strategy, which requires only a small number of tiles to generate aperiodic and deterministic infinite content. We also introduce the weight-brush system that combines N-WFC and sub-complete tileset, proving its suitability for game design. Our contribution addresses WFC's challenge in massive content generation and provides a theoretical basis for implementing concrete games.