Maxim Gumin's WaveFunctionCollapse (WFC) algorithm is an example-driven image generation algorithm emerging from the craft practice of procedural content generation. In WFC, new images are generated in the style of given examples by ensuring every local window of the output occurs somewhere in the input. Operationally, WFC implements a non-backtracking, greedy search method. This paper examines WFC as an instance of constraint solving methods. We trace WFC's explosive influence on the technical artist community, explain its operation in terms of ideas from the constraint solving literature, and probe its strengths by means of a surrogate implementation using answer set programming. CCS CONCEPTS• Theory of computation → Constraint and logic programming; Random walks and Markov chains; • Applied computing → Media arts; Fine arts; • Mathematics of computing → Solvers;

Procedural content generation via machine learning (PCGML) is typically framed as the task of fitting a generative model to full-scale examples of a desired content distribution. This approach presents a fundamental tension: the more design effort expended to produce detailed training examples for shaping a generator, the lower the return on investment from applying PCGML in the first place. In response, we propose the use of discriminative models (which capture the validity of a design rather the distribution of the content) trained on positive and negative examples. Through a modest modification of WaveFunctionCollapse, a commercially-adopted PCG approach that we characterize as using elementary machine learning, we demonstrate a new mode of control for learning-based generators. We demonstrate how an artist might craft a focused set of additional positive and negative examples by critique of the generator's previous outputs. This interaction mode bridges PCGML with mixed-initiative design assistance tools by working with a machine to define a space of valid designs rather than just one new design.

We describe WaveFunctionCollapse (WFC), a new family of algorithms for content generation. WFC was recently invented by independent game developer Maxim Gumin and has since been adopted and adapted by other game developers. Trends in academic research on content generation have only recently suggested the use of ideas from constraint solving and machine learning, so it is surprising to see these manifested in inthe-wild algorithms developed outside of an academic context. We illuminate the common components in this family of algorithms by way of a rational reconstruction. Through experiments with the reconstruction we probe the impact of design choices made in various adaptations of WFC (e.g. the role of backtracking, search heuristics, or pattern classification and rendering strategies). This work highlights a mode of incremental content generation that has been overlooked by past surveys of content generation methods.

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Procedural Content Generation (PCG) is deeply embedded in many games. While there are many taxonomies of the applications of PCG, less attention has been given to the poetics of PCG. In this paper we present a poetics for generative systems, including a descriptive framework that introduces terms for complex systems (Apollonian order and Dionysian chaos), the form that describes the shape of the generated output (formal gestalt, individual, and repetition), the locus of the generative process (structure, surface, or locus gestalt), the kind of variation the generator uses (style, multiplicity, and cohesion) and the relationship between coherence and the content used as input for the generator. Rather than being mutually exclusive categories, generators can be considered to exhibit aspects of all of these at once.