Expressive Wave Function Collapse

Abstract

Procedural Content Generation methods enable the creation of varied content algorithmically. Wave Function Collapse (WFC) is one such method. It is a tile-based local constraint solver commonly applied to world and map generation for grid-based content; it is able to create varied output from the same set of rules. While WFC is versatile, content generated with it is i) limited to one grid, ii) based on uniform tiles and iii) must use the same tile set and constraints throughout the grid. Due to these limitations, large classes of content are excluded, such as structured objects. Structured objects consist of an assembly of multiple components, each possibly based on a different tile set. We therefore propose Expressive Wave Function Collapse (XWFC), a major extension of WFC that enables solving and combining multiple grids with different Non-Uniform Tile (NUT) sets. Additionally, we can guarantee NUT shape and size preservation even under WFC’s Overlapping Model. With these generalizations, new domains are within reach for structured objects based on NUT sets, such as Tetris or LEGO.