Wave Function Collapse (algorithm)
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Wave Function Collapse (algorithm)
Model synthesis (also wave function collapse or 'wfc') is a family of Constraint solving, constraint-solving algorithms commonly used in procedural generation, especially in the video game industry. Some video games known to have utilized variants of the algorithm include ''Bad North'', ''Townscaper'', and ''Caves of Qud''. The first example of this type of algorithm was described by Paul Merrell, who termed it 'model synthesis' first in his 2007 i3D paper and also presented at the 2008 SIGGRAPH conference and his 2009 PhD thesis. The name 'wave function collapse' later became the popular name for a variant of that algorithm, after an implementation by Maxim Gumin was published in 2016 on a GitHub Repository (version control), repository with that name. Gumin's implementation significantly popularised this style of algorithm, with it becoming widely adopted and adapted by technical artists and game developers over the following years. There were a number of inspirations to Gumin's ...
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Constraint Solving
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research f ...
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