# Extend Wave Function Collapse to Large-Scale Content Generation

arXiv: https://arxiv.org/abs/2308.07307 · HTML: https://mlsanity.com/paper/2308.07307/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 24 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 2 of 2)

- [Open-Ended Learning Leads to Generally Capable Agents](https://mlsanity.com/paper/2107.12808/) (2021)
- [PCGRL: Procedural Content Generation via Reinforcement Learning](https://mlsanity.com/paper/2001.09212/) (2020)

## Built on by (most cited first, 2 of 2)

- [Punch Out Model Synthesis: A Stochastic Algorithm for Constraint Based Tiling Generation](https://mlsanity.com/paper/2501.14786/) (2025)
- [A Markovian Framing of WaveFunctionCollapse for Procedurally Generating Aesthetically Complex Environments](https://mlsanity.com/paper/2509.09919/) (2025)

## Abstract (arXiv)

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.