Procedural Content Generation methods enable the creation of varied content algorithmically. Wave Function Collapse (WFC) is one such method. It is a tile-based local constraint solver commonly applied to world and map generation for grid-based content; it is able to create varied output from the same set of rules. While WFC is versatile, content generated with it is i) limited to one grid, ii) based on uniform tiles and iii) must use the same tile set and constraints throughout the grid. Due to these limitations, large classes of content are excluded, such as structured objects. Structured objects consist of an assembly of multiple components, each possibly based on a different tile set. We therefore propose Expressive Wave Function Collapse (XWFC), a major extension of WFC that enables solving and combining multiple grids with different Non-Uniform Tile (NUT) sets. Additionally, we can guarantee NUT shape and size preservation even under WFC’s Overlapping Model. With these generalizations, new domains are within reach for structured objects based on NUT sets, such as Tetris or LEGO.

AI-generated music is a huge research field with many different approaches and models being the result of it. One such model is the ProceduraLiszt model, which utilizes the Wave Function Collapse algorithm, an algorithm similar to constraint programming, to generate its music. This research builds upon that model. It does so by trying to reverse engineer a given piece of music into a set of satisfied constraints that the model is compatible with. We present an approach that allows for the inference of constraints of a given music file that adheres to the MIDI format called MidiAnalyser. We run our model on a set of music files and analyze the inferred constraints. The constraints include aspects like key and note range.

Procedurally generating a coherent and emotionally resonant piece of music can be very challenging. The Wave Function Collapse (WFC) algorithm is very effective when it comes to generating randomized patterns and maps that resemble an input sample. A version of this algorithm using a hierarchy of sections, chords and melody was used to create a model capable of generating music. In this paper, we extend the capabilities of this model to improve its utility and help composers more effectively utilize this music generation method to create engaging pieces. Our model offers improvements over previous methods by allowing composers to retain desirable elements of the music output while regenerating others, thus streamlining the iterative nature of music composition. We consider and compare different music visualization techniques and explore various user interface (UI) interaction methods to facilitate the effective selection of elements from the output. We designed and implemented this model with the conclusion that it significantly enhances the user experience and allows for creating a much more sound and complete piece of music compared to the original.

Wave Function Collapse (WFC) can be described as a family of algorithms, meant for content generation through constraint solving. One variant is Hierarchical WFC, where a hierarchical structure is given to the tileset used in WFC. This variant has seen use in a mixed-initiative procedural music generation model, where pieces of music simulating a single instrument playing chords and a melody are generated. In this paper, we explore how this model can be adapted to generate (coherent) pieces of music simulating several instruments playing in parallel. To achieve this, three model properties had to be defined: a new canvas structure, a set of constraints that instruments impose on each other, and the manner in which cells of all canvasses are collapsed. A hierarchical structure has been defined of a single section canvas, of which every cell has an inheriting chord canvas, of which every cell has an inheriting melody canvas for each instrument. The section cells impose constraints on inheriting chord and melody cells, and the chord cells impose constraints on inheriting melody cells. Besides this, melody cells impose constraints on cells belonging to other melody canvases (i.e. other instruments). With this canvas structure and these sets of constraints, the cells could be collapsed, such that coherent pieces of music simulating several instruments playing in parallel were generated.

Procedural Content Generation (PCG) is a method to automatically generate content with little to no human assistance required. It emerges as a promising tool to generate educational content tailored to individual learning needs, a fundamental aspect of effective teaching.
This review aims to provide an overview of existing research on the educational applications of PCG across disciplines. The key objectives of this paper include identifying the range of domains that have profited from the educational use of PCG, the challenges faced by specific disciplines as well as discerning the similarities and differences in their approaches. By addressing these objectives, this literature review seeks to identify areas for further research and provide insight into understanding the obstacles preventing the adoption of PCG in certain educational domains. By carefully surveying a sample of research conducted on the educational use of PCG in a broad range of disciplines, we found that computer science and mathematics have extensively leveraged PCG to enhance learning experiences, while natural sciences and social sciences could benefit from further research. To the best of our knowledge, fields like geography, physics and biology as well as arts, business and economics remain largely unexplored. Furthermore, challenges such as adjusting content difficulty, generating coherent exercises, and educational accuracy issues have been identified as significant barriers in various fields.

Music, a profound expression of the human experience, is built upon intricate patterns that humans have spent centuries trying to understand and recreate. Consequentially, Hierarchical Wave Function Collapse was proposed as a novel model for procedural music generation, which organizes musical constraints within a three-level hierarchy. However, music with melody but no rhythm, is like a text with all characters but no spacing. This research aims to create rhythm procedurally by exploring existing representations and combining the most effective elements to propose a simple but comprehensive rhythmic model. Though not all-powerful, the proposed model accommodates varied measures and motifs. By implementing it, the research evaluates its efficiency and limitations, identifying the types of music it cannot generate. This study aims to contribute a tool for mixed-initiative music creation, expanding procedural music generation with a nuanced approach to rhythm.

Procedural Content Generation (PCG) is a powerful content generation technique that can be used to automatically generate content (an example would be exercises for a quiz or a game). As it stands, PCG is able to create content with zero human interaction which makes it a technique worth exploring for educational purposes. In the context of PCG, this research focuses on how PCG is used to orchestrate the simultaneous generation of content of various types and identify what could be done more, possibly towards educational use. The method chosen for this research is literature review. As such, this paper provides a summary of "orchestrative" PCG approaches found in recent literature and evaluates said approaches through the lens of "PCG for education". Findings are presented in an exhaustive manner with each piece of literature occupying a subsection. A discussion section that explores how these approaches could benefit education and/or what could be done to facilitate that is also present.

This paper investigates the use of Adaptive Procedural Content Generation (APCG), a form of procedural content generation that is adjusted to a player model, to tailor educational content based on individual learner profiles, thereby improving engagement and consequent learning outcomes. Key research questions include how to measure the success of APCG, its impact on academic performance, and the comparative advantages over traditional PCG methods. Through a literature review, this study identifies current trends, methodologies, and challenges in the application of APCG in educational settings. A list of existing papers has been synthesized on the knowledge body that exists on APCG implementations. We present these findings together with their most relevant methods, domains, target demographics and conclusions to gain an in- sight in which research currently exists on it. The findings aim to provide insights for educators, game developers, and researchers on effective implementations of APCG, paving the way for more personalized and impactful educational technologies.

Wave Function Collapse (WFC) is among the most well-known and beloved procedural content generation algorithms. WFC solvers can be understood as a specific type of constraint solver, and as such, backtracking is an integral part of exploring the space of possible solutions. Recent advancements were inspired by this algorithm to model procedural music generation, using a hierarchy of many canvases, each with its own semantic domain within music composition (sections, chords, melody). In the model, due to the structural dependencies between canvases, constraints that involve cells from different canvases make exhaustive backtracking a challenge. Existing backtracking methods only consider a single set of variables, but if a specific value on one canvas can affect the entire structure of another canvas, we need more elaborate ways to deal with conflicts.

This paper presents the basic principles that backtracking models for this hierarchy should abide by, and additional guidelines for evaluating them. Two approaches are proposed, and their runtime efficiencies are compared. Depth-first traversal of the canvas hierarchy results in significantly shorter runtimes than its breadth-first counterpart.

Navigation is a core aspect of exploring virtual environments. To assist players, a mini-map is a commonly used navigational tool. Navigation in an unknown space can be difficult. This difficulty is only increased when a player finds themselves in a non-Euclidean space. This paper explores the effect the mini-map's positioning has on the player's navigational performance in Virtual Reality using hyperbolic space. For this two positions are used: the first mini-map is positioned on the Heads-Up Display and the second is positioned on the player's right hand. Two player groups are randomly created to take part in a player experiment. Players get to read an information sheet and complete a small tutorial before having to complete 3 levels. Players are measured on how much time and how many steps it takes them to complete each level, how much their time and steps improve over the levels, their total time, and their total amount of steps. Combined these results indicate that there is no clear effect on the player's performance navigating a hyperbolic space in Virtual Reality.

Virtual Reality allows for the ultimate immersion in environments not naturally encountered. Still, hyperbolic environments are extremely difficult to get used to. This paper explores whether immersion in virtual hyperbolic environments can be enhanced by introducing a procedurally generated world. We propose a Wave Function Collapse (WFC) algorithm that can divide the hyperbolic plane into distinct areas and populate the space with dynamically generated objects. This can assist players in recognising areas visited prior, which can create an intuitive feel for how hyperbolic space operates. Although 5-order square tiling is used in this paper, the proposed algorithm can be extended to other tiling approaches. Evidence suggests players in a populated hyperbolic environment need on average fewer steps to reach their objective compared to a control group with an empty environment, although the time taken for both groups is roughly the same. From this and a qualitative analysis we infer that players feel more immersed in the environment when it is procedurally generated instead of mostly empty.

Non-Euclidean spaces are spaces that do not satisfy all of Euclid’s postulates. An example of such a space is hyperbolic space. In this paper, a method is discussed to draw a tessellation of hyperbolic space in a manner that fits with the virtual reality game "Holonomy", a game which takes place in hyperbolic space. The main result shows that the new approach is better in terms of simplicity than the old approach and is able to draw the game world more faithfully than the old approach. The features of the new approach could still be significantly expanded upon.

It is possible to use a different representation of space in a Virtual Reality (VR) game, instead of using the euclidean representation we are used to. The reason why that is interesting is that it opens up the possibility of traversing infinitely far in the virtual space while being confined to a relatively limited space in the real world. But for this to be a useful use case, people will need the ability to traverse this new space in an intuitive or at least competent way. One way to help people with navigation in such a space would be to show the person what the fastest path from point A to point B is. This paper researches the possible ways to calculate this path so it can be used to help people while they are traversing this different type of space. Concluding that a trade-off needs to be made between the speed and accuracy of the result depending on the situation, and that no algorithm exists which is the best in both speed and accuracy. Meaning that the context determines what algorithm should be used.

Simulating non-Euclidean geometry in virtual reality is of interest to a wide variety of fields of research. However it is still quite a challenge. Various methods are already known, but they vary greatly in performance and applicability. This paper compares some methods of rendering a non-Euclidean space. We focus on the order-5 square tiling that can be found in the hyperbolic plane, but the methods used are also relevant to other non-Euclidean spaces. We render this space using portals with two different implementations: one using render textures, an one using stencil polygons. Through an experiment where we measured and compared the frame rate of each method, we have found that, even with a small number of portals, the stencil polygon approach is more than two times as efficient. However, this method is limited in the number of portals, whereas render textures can be used for any number of portals.

Virtual worlds are rapidly increasing in size, enabled by advancements in computing technology, which puts a large burden on designers creating them.
Procedural Content Generation can help alleviate this burden, though lacks precise control, to the detriment of designer intent. Some PCG algorithms, such as Wave Function Collapse (WFC), known for generating tile-based content adhering to certain constraints, are able to induce this control through mixed-initiative editing opportunities, combining the efforts of humans and machines while capturing designer intent. However, stock WFC operates on a flat set of tiles with all their semantics blurred together, which unnecessarily strains designers with additional cognitive load when working with such detailed tiles.



We therefore propose Hierarchical Semantic Wave Function Collapse (HSWFC), a generalized approach to WFC that augments the tileset with a new type of tile, the meta-tile, which represents semantic traits, and then organizes the tileset into a hierarchy akin to a taxonomy induced by such semantic representations: the meta-tree. A cell once collapsed to any tile high up in the meta-tree (such as "forest" or "village"), can further collapse to concrete tiles at the bottom (such as “tree” or “wall”).


We investigate how this extension in data organization affects the original algorithm, and explore several novel editing facilities, including e.g. sketching with semantic tiles, controlling tile distributions, regenerating areas that represent specific semantics, and more. A prototypical HSWFC-driven tile-editor was developed and evaluated through a user study, confirming that such an editor indeed reduces cognitive load compared to its stock WFC counterpart, and that the newly enabled features are highly valued by environment designers.

Wave Function Collapse (WFC) is a powerful generative algorithm, able to create locally-similar output based on a single example input. One of the inherent limitations of the original WFC is that it often requires users to understand its inner workings, and possibly make their own ad-hoc mods to achieve satisfactory results. Besides distracting from your creative task, this strongly reduces the algorithm's effective usefulness to a small group of technical users.

We propose a novel mixed-initiative approach to WFC, aimed at overcoming these drawbacks. These methods focus on providing intuitive control to its users, in a way that matches their usual creative workflow.

Among its main features, this approach provides (i) interactive navigation through design history, including controlled backtracking, (ii) precise manual editing of the output for direct expression of design intent, (iii) interactive manipulation of the tiles, and (iv) an initial layered approach towards post-processing algorithm output. These methods combined provide the required tools for users to tweak the global appearance of the output.

We evaluated a prototype implementation of our approach among game artists and other creative professionals, and concluded that its features were largely considered intuitive and supportive to express their creative intent.

In this paper, one of the challenges that comes with defending in AI soccer is highlighted and an attempt is made in finding a solution for the problem. In soccer, defense is an important part of the game and the research question in this research is formulated as follows: what are the most effective methods to take by surprise and dispossess the attacking opponent player who carries the ball? To find the most optimal solutions for this problem, the Webots AI Soccer environment is used, which simulates a game of five versus five soccer. To be able to answer the research question, several approaches and strategies are implemented in the environment and their success is compared. This has led to the conclusion that, in this particular environment, defensive actions like slide tackling cannot be performed and thus cannot be used to defend. Therefore, other solutions are necessary, as a result, a combination of approaches is the most important way of making the dispossession strategy as successful as possible. This combination consists of predicting where the opponent is moving to with the ball and determining the optimal side to approach the opponent from.

Robot soccer competitions have been around for a while and have been a great environment to develop AI algorithms in. One of these environments is the AI world cup. The AI world cup environment is a virtual environment where two teams with five robots each play a soccer match. This paper focuses on defending the attacker that is carrying the ball in the AI world cup environment. This is achieved by comparing two approaches, a rule-based algorithm, and a Deep Deterministic Policy Gradient rein- forcement learning algorithm. The two algorithms are based on a coaching framework build by the TU Delft. This framework implements the actions of the robots, such as moving, jumping, and kicking the ball, and the communication between the robots. The two approaches have been evaluated and the rule-based outperforms the reinforce- ment learning algorithm. Furthermore, a teamwork strategy between the goalkeeper and defender has been developed, where this teamwork is a significant improvement over the non-teamwork algorithm.

Virtual robot soccer competitions have been rising in popularity in recent years, due to their easier accessibility than physical robot soccer. This is also the reason these virtual competitions were created. The goal is to compete in the AI world cup, one of the virtual soccer competitions. A coach-based framework has already been built, and the aim is to create strong defensive capabilities for the robot team. This paper in particular focuses on covering opponents without the ball. The marking strategy and specific opponent covering that have been devised for this are explained. Both are completely rule-based, and opponent covering has been thoroughly tested with an in-house developed batch-runner. In short, opponent covering consists of standing at the optimal position between the passer and receiver, and when the ball is passed going to the closest intercept point. This optimal position is learned with the batch-runner. Opponent covering performs well in the generated test cases. Some specific algorithms counter attacking strategies which have not been implemented yet, therefore it was not possible to evaluate those algorithms. They are theoretically optimal however.

Nebulae are colorful astronomical phenomena that have a mesmerizing appearance. Researching them is difficult, since they are many light-years away. As a result of this, we can only observe them from one viewpoint: Earth. The appearance of nebulae is almost always unique, because of the many factors that influence it. Still, there exist a class of nebulae with a pronounced axial-symmetry in their appearance. The axial-symmetry in these nebulae gives us an indication on how particles in the nebulae will be distributed. We can exploit this symmetry and represent the 3D volume of such a nebulae using a 2D map that is rotated around the symmetry axis. Previous methods converted the 2D map into a 3D volume before rendering, but we propose a novel visualization technique whereby only the 2D map is used. A benefit of representing the nebula using a 2D map is that it is easier to modify than a 3D volume, making it easy to model plausible looking nebulae. We also propose new techniques for reconstructing the 2D map of existing nebulae from telescope images. Combining our achievements in visualization and reconstruction makes it possible to view real axial-symmetrical nebulae from novel viewpoints. Finally, we propose methods to reintroduce asymmetries in volumes of the axial-symmetrical nebulae. These irregularities are also found in real axial-symmetrical nebulae and make the visualizations appear even more realistic.