A Markovian Framing of WaveFunctionCollapse for Procedurally Generating Aesthetically Complex Environments
Abstract
Procedural content generation often requires satisfying both designer-specified objectives and adjacency constraints implicitly imposed by the underlying tile set. To address the challenges of jointly optimizing both constraints and objectives, we reformulate WaveFunctionCollapse (WFC) as a Markov Decision Process (MDP), enabling external optimization algorithms to focus exclusively on objective maximization while leveraging WFC's propagation mechanism to enforce constraint satisfaction. We empirically compare optimizing this MDP to traditional evolutionary approaches that jointly optimize global metrics and local tile placement. Across multiple domains with various difficulties, we find that joint optimization not only struggles as task complexity increases, but consistently underperforms relative to optimization over the WFC-MDP, underscoring the advantages of decoupling local constraint satisfaction from global objective optimization.
Cite
@article{arxiv.2509.09919,
title = {A Markovian Framing of WaveFunctionCollapse for Procedurally Generating Aesthetically Complex Environments},
author = {Franklin Yiu and Mohan Lu and Nina Li and Kevin Joseph and Tianxu Zhang and Julian Togelius and Timothy Merino and Sam Earle},
journal= {arXiv preprint arXiv:2509.09919},
year = {2026}
}