Our tiles can each have a relative weight (eg, one tile is 5 times as likely as another) so using a weighted random selection we pick a Tile for our lowest entropy Cell and assign it, this process is called collapsing a given Cell. The last point is that this algorithm isnt magic. Applications. I invite everyone interested in some coding challenges to implement one yourself and see if it can be useful for your games. But lets say we have a few more tile types that could potentially fit. Essentials. The tile to the north of the primary tile: Since the primary tile wont change we know that the rules for the southern edge will be [water, water], The tile to the north, whatever it may be (lets say it is all grass for now) will not change either so the northern edge will have a rule of [grass, grass]. Reddit and its partners use cookies and similar technologies to provide you with a better experience. If they accidentally kill an innocent NPC, fabricate a couple skeletons in the closet. This is the first place where things started to get somewhat obscured in the references I found. By recording a stack of undo snapshots and backtracking when the second strategy would later require the third strategy, the algorithm will always solve perfectly without violating any constraints, if such a thing is possible. The algorithm then procedurally populates the output on the right using these rules and weights. This leads to some tiles being evaluated before they should have been, and this causes misses in other areas with constraint solving. With my first implementation of the algorithm I ran around my tiles placing water everywhere and suddenly an error flashed up. This just means we find the cell in our matrix with the fewest possible valid tiles in our tileset (the original algorithm uses a more complicated approach but for our purposes its unnecessary.) 26 minutes ago. Wave-Function-Collapse. Audio. In the 3d preview, the up and down keys can be used to cycle through slices of the Z axis. For example, a cell's possible values might be constrained by the cells adjacent to it, or there might be a global limit like only allowing one boss room and 2-4 treasure rooms per floor. Coding Train video covering JavaScript arrow (=>) function. Target is Wave Function Collapse BPLibrary. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page. At this point if any superpositions still contain more than one possibility, you can just arbitrarily select any options from within it and it should fit. We'll take a look at the kinds of output WFC can produce and the meaning of the algorithm's parameters. Wave Function Collapse is a neat little algorithm for generating images locally similar to the input. This is useful when you want to derive neighboring tile data from a WFC-solved actor to be used for post processing. In the original version its just a single edge tile. The basic idea behind Wave Function Collapse (or WFC as I will refer to it going forwards) is, as best as I understand it, as follows: Each tile type has a set of rules that describe each edge. Define coefficients. On first glance this approach seems difficult to translate into 3D models and is what tripped me up the most. This may reduce the possibilities for other locations around that initial one, or, depending on the tileset, even completely determine what tiles we must pick in some places. By adjusting the weighted probabilities of different tiles we can get pretty reasonable buildings, however we still sometimes generate completely cut off or trivial structures that arent really contributing to a play experience. The AdjacencyConstraint data structure allows certain offsets to be ignored, but by only recognizing two-way links it either cannot interact with or excessively limits texture complexity, rather than having a full matrix for each potential output. You can see it in action here (2D overlapping model) and here (3D tile model). Theoretically we could apply some constraints to our building generation that are somewhat outside the scope of the initial algorithm. This superposition of possibilities serves as a starting point which I can then iterate through in order to collapse my possibilities until they resolve into exactly the right configuration (or near enough) to ensure a continuous connection between my tiles. The northern tile as we have seen has constants to the north and south. In our limited use case there is only one possible match for each, which is the edge tile. Download. The original implementation tracks a frontier and updates the most-easily solved cell, but my implementation walks each cell in XZY order first attempting to trivially solve and then using probability as a fallback. 3Blue1Brown video with more detailed context about entropy and information theory. Check out this impressive implementation of the wave function collapse algorithm in Unity by marian42 @ https://marian42.de/Wikipedia: In quantum mechanics, . Wave Function Collapse Demonstration Created by Oskar Stlberg in unity, an interactive demonstration of the WFC algorithm. Since this is not a proper engine, I have had to find some lateral solutions. The first step in my process was to establish which tiles should be taken into consideration during the process, which will change as the result of a tile placement, and which will remain constant. Add files via upload. The tiles that are directly adjacent from it are the secondary tiles as they have border edges with the primary and finally the diagonally adjacent tiles are the tertiary tiles. Weighting will change if the algorithm accounts for a tiles weight when picking which tile to collapse into. Garazbolg's GitHub issue describing a solution for assymmetric tiles. You could create a hash function of the vertices or something to resolve to the same number and use that as an indication of connectivity, but I found a list wound up being more stable for my level of precision with 3D modelling and for debugging. Im using WFC as a means to automate alignment of manual tile placements. However these are computationally expensive operations and even with using some backtracking to unwind collapsed states it could take a long time to generate a meaningful structure that satisfied all our constraints. VFX. the northern edge of the fourth tile would be expressed as [grass, water] and would match up to a southern edge that corresponded to [grass, water]. Wave Function Collapse algorithm in Unreal Engine. Since this is using a very small tile set we already know what our secondary tiles should be so we can go ahead and grab those edge rules as well. When working on this project I felt like this algorithm was the hardest simple algorithm I ever implemented, since the overall function is very straightforward but the details can really hang you up. I found this to especially be the case with those few that had translated this image processing algorithm into 3D model generators. This makes WFC perfect for level generation in games and pixel art, and less suited for large full-color textures. Wave function collapseis a draftprogramming task. The end result of all of this is that you can place tiles with impunity and they will all align neatly! WFC is a non-backtracking, greedy search algorithm that enables large output generated from a small number of constraints determined by a window of input media. So we have our aim, and we have our building blocks, how do we automate this process on the fly? . I mentioned earlier that I eventually found out I was missing a tile type. Most Popular Programming Languages In 2022, MY JOURNEY AS A DEVELOPER Join the Coding Train Discord to chat with the community and get help with your code from the Station Managers. The entire matrix starts with every cell empty but with the possibility of having any tile in our tileset occupy it. borgel on Sept 30, 2016 [-] If you enjoy pondering on that, you may enjoy reading Permutation City [1] by Greg Egan. You can see it in action here (2D "overlapping model") and here (3D "tiled model"). selfsame. If the players wander to the wrong town, move the current narrative to that town. If its possibility space is reduced to a size of 1 it can be trivially solved, since there is only one possible solution. Like I said, the local similarity aspect has been tossed which feels disingenuous and I would like to find a way to better incorporate it. Demo Unity project (2019.2ish) 13 MB. I found a pretty good video describing one of the ways to create these adjacency lists here. As far as I can tell this isnt really true, but we can achieve this effect by making tiles in our tileset that connect to exactly one (or two) other tiles, so collapsing a cell with one of these will automatically collapse the appropriate number of neighbors, giving the illusion of a tile that spans multiple cells, which is a nice side effect. Once you have defined your tiles and rule set, you can gather all potential tiles for any given location in a sort of superposition. First we need to think about the shape of the tiles themselves and how they will actually connect to each other. Tools. 3d. However, I think this is a problem with the analyzer, since by default distance=2 leaves cannot be generated without leaves on both sides of its distance=1 parent. So, what is the Wave Function Collapse algorithm (WFC)? ( Source) silent. The rest is actually just as simple. This helped me identify a few common shapes. To propagate a single set of adjacency constraints in a cube of radius 2 tiles, 5*5*5-1 = 124 tiles are addressed. If you've come here hoping to learn about quantum physics, you are going to be disappointed. What makes this algorithm different from most procedural generation algorithms I've read about is that it is extremely simple. src/me/Josh123likeme/ WaveFunctionCollapse. Controls: WASD for walking, Shift to run, Ctrl to jetpack. Time to start out with good intentions but get bogged down in an interesting coding challenge that has little effect on the game itself! . Well, describing these edge patterns means that each tile type has a limited set of possible tiles that can fit in any given configuration. It is an algorithm written in 2016 by Maxim Gumin that can generate procedural patterns from a sample image or from a collection of tiles. WFC is easy to set up - you give the algorithm a sample map, and it generates more maps that look like the original map, by re-using small snippets from it. // there are a few ways to calculate entropy, but essentially its a function of the number of available tiles that can fit into a single cell, fewer options means lower entropy. The closest thing I could find for Unity (my engine of choice) was its tile rules for 2D tiles. It can be run in 2d or 3d, even on hexagonal or irregular grids. Learn on the go with our new app. For tertiary tiles this means the two ancillary tiles that border them. We can resolve this by going through exactly the same steps as before, but instead we collect all of these potential tiles in superpositions which we will then test tertiary tiles against. 3D models areless wonderful to work with, since they are made of vertices and triangles with a host of image, color and other vertex data wadded up into a big confusing ball of numbers.