[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82652-en":3,"doc-seo-82652-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82652,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Evolutionary Wave Function Collapse","Wave Function Collapse (WFC) generates large procedural content by learning local adjacency constraints from example inputs. This paper studies an evolutionary alternative where the algorithm evolves the small WFC input examples rather than evolving complete levels. WFC is used as a genotype-to-phenotype mapping, and each generated level is scored using domain-specific fitness functions. Experiments target maze connectivity maps and Zelda-style dungeon layouts. Results show evolutionary optimization improves quality when objectives emerge from local relationships, while global-constraint domains remain difficult.","Evolutionary Wave Function Collapse  \nDipika Rajesh  \nUC Santa Cruz Santa Cruz, USA [dipika.rajesh@gmail.com](dipika.rajesh@gmail.com)  \nAhmed Khalifa  \nUniversity of Malta Msida, Malta [ahmed@akhalifa.com](ahmed@akhalifa.com)  \nJulian Togelius New York University  \nNew York, USA [julian@togelius.com](julian@togelius.com)  \narXiv :2607 .02082v 1 [ cs .NE] 2 Jul 2026  \nAbstract—Wave Function Collapse (WFC) is a widely used procedural content generation method that learns local adjacency constraints from example inputs to generate larger outputs. In this paper, we explore combining WFC with evolutionary search by evolving the small input examples used by WFC rather than directly evolving complete levels. In this approach, WFC acts as a genotype-to-phenotype mapping. The generated levels are then evaluated through domain-specific fitness functions. We evaluate the method in two domains with different relationships between local and global structure: Maze connectivity maps and Zelda-style dungeon layouts. Our results show that evolutionary optimization over WFC inputs improves generation quality in domains where properties emerge from local relationships, while domains requiring global constraints remain challenging. These findings suggest that evolutionary search can effectively guide WFC generation when target objectives align with local structure.  \nIndex Terms—Procedural Level Generation, WaveFunctionCollapse, Self-Supervised Learning, Constraint-Solving, Evolutionary Algorithms, Video Games  \nI. INTRODUCTION  \nThe wide range of Procedural Content Generation (PCG) methods in existence contains not only different algorithmic foundations, but also different use cases. For example, the Wave Function Collapse (WFC) algorithm [1], which can be seen as constraint solving or self-supervised learning, is widely used in indie games. It is self-contained, requires little input, and rapidly generates small levels, although it cannot guarantee solvability and does not scale well to larger levels.  \nBy contrast, search-based PCG sees content generation asan optimization to be solved with evolution, meaning that complex objectives and constraints can be satisfied. While search-based PCG is the subject of hundreds of papers, it isnot widely used in actual games, probably because of the long generation time and/or complexity of specifying objectives.  \nIn AI, as in other fields of engineering, the best methods are often hybrid methods that combine the advantages of multiple algorithms. What if we could combine some of the advantages of WFC and search-based PCG? For example, allowing authoring by specifying objectives. In this paper, we investigate whether the compact representation of WFC can be combined with the controllability of evolutionary search. Specifically, we evolve the inputs provided to WFC rather than directly evolving complete levels. This can be seen  \nas using WFC as a genotype-to-phenotype mapping for the evolutionary algorithm.  \nWe evaluate this approach in two game domains with different relationships between local and global structure. In the Maze domain, where desired properties such as connectivity come out of local spatial relationships, evolutionary optimization successfully utilizes WFC toward higher-quality outputs. In the Zelda domain, where the game depends on global constraints such as exactly one player, key, and door, the limitations of local patterns become more apparent. Our results suggest that evolutionary optimization over WFC genotypes is most effective when target objectives are compatible with local structural regularities.  \nII. BACKGROUND  \nProcedural content generation [2] is getting a lot of attention from the game industry in the past couple of years 1. The problem is that most of the techniques that are used in the industry are based on human knowledge and heuristics, which makes the algorithm not generalizable between games, as each game requires a different algorithm. Wave Function Collapse (WFC","cbCaiobJbdGz48Jv","https://ap.wps.com/l/cbCaiobJbdGz48Jv","pdf",208213,2,1,4,"English","en",105,"# Introduction\n# Background\n## Wave Function Collapse\n## Related Work","[{\"question\":\"How does the proposed evolutionary method interact with Wave Function Collapse (WFC)?\",\"answer\":\"The evolutionary search evolves the small input examples used by WFC. WFC then maps each evolved input (genotype) to a generated level (phenotype), which is evaluated by fitness functions.\"},{\"question\":\"What types of domains were used to evaluate the method?\",\"answer\":\"The method was evaluated in two game domains: maze connectivity maps and Zelda-style dungeon layouts, which differ in how local structure relates to global requirements.\"},{\"question\":\"When does evolutionary optimization with WFC input improvements work best?\",\"answer\":\"It works best when the target objectives are compatible with local structural regularities, where desired properties emerge from local relationships. 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WFC then maps each evolved input (genotype) to a generated level (phenotype), which is evaluated by fitness functions.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What types of domains were used to evaluate the method?",{"text":79,"@type":75},"The method was evaluated in two game domains: maze connectivity maps and Zelda-style dungeon layouts, which differ in how local structure relates to global requirements.",{"name":81,"@type":72,"acceptedAnswer":82},"When does evolutionary optimization with WFC input improvements work best?",{"text":83,"@type":75},"It works best when the target objectives are compatible with local structural regularities, where desired properties emerge from local relationships. 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