Better Resemblance without Bigger Patterns: Making Context-sensitive Decisions in WFC

Gumin's WaveFunctionCollapse (WFC) algorithm attempts to generate output designs that resemble provided input designs. While the algorithm's constraint-solving core is able to ensure that no local patterns are adjacent in the outputs that were not adjacent in the input, it does not accurately reproduce statistical properties of the input designs. Examining the algorithm's behavior at the level of pattern adjacencies, we show that there are large gaps between the statistics of the input and output designs, even when applying Gumin's search heuristic intended to influence output statistics. By offering a very small revision to this search heuristic, we show that the resemblance of outputs to inputs can be dramatically improved. Another way of improving resemblance is to increase the size of local patterns considered by WFC, but this can easily lead to a kind of overfitting that results in the outputs plagiarizing large portions of the input design. By contrast, our alternate revision increases resemblance without increasing pattern size. The simplicity of our method, requiring a very localized change to existing WFC implementations, allows it to be immediately applied to a wide range of applications.