Non-Uniform Tile Wave Function Collapse

Abstract

Procedural Content Generation methods enable the creation of varied content algorithmically. One such method is Wave Function Collapse (WFC), a tile-based local constraint solver commonly applied to texture, map and level generation for grid-based content; it is able to create varied output from the same set of rules, usually derived from an input sample. However, a glaring limitation of WFC is that it only operates on tiles of the same shape and size. We propose Non-Uniform Tile Wave Function Collapse (nutWFC), an extension of WFC that supports multi-cellular tiles with varying shapes and sizes, so-called Non-Uniform Tiles (NUTs). Familiar examples of such tiles can be found in LEGO ® and Tetris. The algorithm guarantees NUT shape and size preservation even under WFC's Overlapping Model in three dimensions. We show that nutWFC is a super-set of WFC that harmonizes strict NUT shape and size constraints with WFC's output diversity without significant performance penalties. We illustrate the expressive power of nutWFC with a few results that explore the advantages of NUTs and would therefore not be feasible with WFC.