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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Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ...
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Procedural Generation
In computing, procedural generation is a method of creating data algorithmically as opposed to manually, typically through a combination of human-generated content and algorithms coupled with computer-generated randomness and processing power. In computer graphics, it is commonly used to create Procedural texture, textures and 3D models. In video games, it is used to automatically create large amounts of content in a game. Depending on the implementation, advantages of procedural generation can include smaller file sizes, larger amounts of content, and randomness for less predictable gameplay. Overview The term ''procedural'' refers to the process that computes a particular function. Fractals are geometric patterns which can often be generated procedurally. Commonplace procedural content includes Texture mapping, textures and polygon mesh, meshes. Sound is often also procedurally generated, and has applications in both speech synthesis as well as music. It has been used to creat ...
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Video Game Industry
The video game industry is the tertiary industry, tertiary and quaternary industry, quaternary sectors of the entertainment industry that specialize in the video game development, development, marketing, distribution (marketing), distribution, video game monetization, monetization, and customer satisfaction research, consumer feedback of video games. The industry (economics), industry encompasses dozens of job disciplines and thousands of jobs worldwide. The video game industry has grown from niche to mainstream. , video games generated annually in global sales. In the US, the industry earned about in 2007, in 2008, and 2010, according to the Entertainment Software Association, ESA annual report. Research from Ampere Analysis indicated three points: the sector has consistently grown since at least 2015 and expanded 26% COVID-19 pandemic, from 2019 to 2021, to a record ; the global games and services market is forecast to shrink 1.2% annually to in 2022. The industry has i ...
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Bad North
''Bad North'' is a real-time strategy video game developed by Plausible Concept (a game studio in Malmö, Sweden, founded by Oskar Stålberg and Richard Meredith) and published by Raw Fury. The game was released on August 20, 2018, for the Nintendo Switch, then for PlayStation 4 and Xbox One on August 28. A Microsoft Windows version was released on October 16, 2018. Versions for Android and iOS followed on October 16, 2019. Gameplay ''Bad North'' focuses on real-time tactics gameplay. The main goals are to defend the player's kingdom from the attacking Viking invaders who killed the king and to guide the island's people to evacuate. The procedurally generated In computing, procedural generation is a method of creating data algorithmically as opposed to manually, typically through a combination of human-generated content and algorithms coupled with computer-generated randomness and processing power. I ... islands are divided into multiple tiles and have houses with Vikings a ...
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Townscaper
''Townscaper'' is a city builder game by Oskar Stålberg. It was released for Windows and Mac in August 2021. A port to the Nintendo Switch was released in August 2021 when the Steam version left early access. The mobile version was released in October 2021. It was later ported to Xbox One, Xbox Series X/S, and web browsers (as a demo) in December 2021. It features low poly graphics and a simple, minimalist user interface. Gameplay ''Townscaper'' has no inherent objective or story and has been described by developer Stålberg as "more of a toy" than a game. Users construct an island town by placing and removing colored blocks on an ocean. Various "rules" dictate these blocks' appearances, with some appearing as spires and others as balconies. This method of rule-based decoration allows arches, gardens, and stairways to be created without specific user instruction. Setting ''Townscaper'' takes place on a large distorted grid set in an infinite sea. This allows for towns that fee ...
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Caves Of Qud
''Caves of Qud'' is a roguelike role-playing video game developed by American studio Freehold Games set in an open world that is partially pre-made and partially randomly generated. The game takes place in a post-apocalyptic science fantasy setting and is inspired by the pen-and-paper role-playing games ''Gamma World'' and ''Dungeons & Dragons''. Development Freehold Games began development on Caves of Qud in 2007, with the first public beta released in 2010. Caves of Qud was released on Steam in 2015, under their early access model. Content was gradually added through weekly updates. In July 2023, Kitfox Games, the publisher of the Steam version of ''Dwarf Fortress'', announced that they would be publishing the 1.0 version of Caves of Qud the following year. The game was fully released on December 5, 2024. Gameplay Unlike other traditional roguelikes such as NetHack, Caves of Qud has a quest system as a core mechanic. Some quests are scripted, while others are procedurall ...
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SIGGRAPH Conference
SIGGRAPH (Special Interest Group on Computer Graphics and Interactive Techniques) is an annual conference centered around computer graphics organized by ACM, starting in 1974 in Boulder, CO. The main conference has always been held in North America; SIGGRAPH Asia, a second conference held annually, has been held since 2008 in countries throughout Asia. Overview The conference incorporates both academic presentations as well as an industry trade show. Other events at the conference include educational courses and panel discussions on recent topics in computer graphics and interactive techniques. SIGGRAPH Proceedings The SIGGRAPH conference proceedings, which are published in the ACM Transactions on Graphics, has one of the highest impact factors among academic publications in the field of computer graphics. The paper acceptance rate for SIGGRAPH has historically been between 17% and 29%, with the average acceptance rate between 2015 and 2019 of 27%. The submitted papers are ...
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Repository (version Control)
In version control systems, a repository is a data structure that stores metadata for a set of files or directory structure. Depending on whether the version control system in use is distributed, like Git or Mercurial, or centralized, like Subversion, CVS, or Perforce, the whole set of information in the repository may be duplicated on every user's system or may be maintained on a single server. Some of the metadata that a repository contains includes, among other things, a historical record of changes in the repository, a set of commit objects, and a set of references to commit objects, called ''heads''. The main purpose of a repository is to store a set of files, as well as the history of changes made to those files. Exactly how each version control system handles storing those changes, however, differs greatly. For instance, Subversion in the past relied on a database instance but has since moved to storing its changes directly on the filesystem. These differences in stor ...
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Convolutional Neural Network
A convolutional neural network (CNN) is a type of feedforward neural network that learns features via filter (or kernel) optimization. This type of deep learning network has been applied to process and make predictions from many different types of data including text, images and audio. Convolution-based networks are the de-facto standard in deep learning-based approaches to computer vision and image processing, and have only recently been replaced—in some cases—by newer deep learning architectures such as the transformer. Vanishing gradients and exploding gradients, seen during backpropagation in earlier neural networks, are prevented by the regularization that comes from using shared weights over fewer connections. For example, for ''each'' neuron in the fully-connected layer, 10,000 weights would be required for processing an image sized 100 × 100 pixels. However, applying cascaded ''convolution'' (or cross-correlation) kernels, only 25 weights for each convolutio ...
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Superposition Principle
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input ''A'' produces response ''X'', and input ''B'' produces response ''Y'', then input (''A'' + ''B'') produces response (''X'' + ''Y''). A function F(x) that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties: additivity F(x_1 + x_2) = F(x_1) + F(x_2) and homogeneity F(ax) = a F(x) for scalar . This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathemat ...
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Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ...
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