First task is to find a port of WFC in your language of choice. NOTE: For this tuturial, we'll be focusing on the Overlap Model, as it's easier to create input for. . There's also an aspect of collaboration with the machine, as the resulting output can be surprising and sometimes lead you to change your design. In order to post comments, please make sure JavaScript and Cookies are enabled, and reload the page. Quite often though, this idea is rejected because a restricted concept of Markov chain is discussed. What about the Copenhagen interpretation? For simplicity, we'll just create a cube and drag it into the resources directory to turn it into a prefab. Instead, to account for a rate of occurrence, TWFC requires this information to be some tile frequency or tile weight in the meta-data file. The js version uses ImageData for input and ouput. There's also an aspect of collaboration with the machine, as the resulting output can be surprising and sometimes lead you to change your design. Adding prefabs to it's palette property will display them below the image area, where they can be sampled by clicking them with the S key. They also only work with unidirectional tiles, and are undesirable when your final game tiles have direction dependent graphics or functionality. While you can tweak your input to increase the chances for full solutions, another strategy is to retry the algorithm until it can complete. This greatly reduces the time involved as there is no need to perform texture synthesis to infer constraint data. Create an empty named output and add an Overlap WFC component to it. Or the many-world one? Start a new unity project and either import the .unitypackage or clone the github repository into the Assets directory. In mathematical terms, this corresponds to saying that the collapsing of the wave function corresponds to a Markov chain. From the Fourier transform that provides a mapping of every wavenumber with an amplitude, we can easily deduce a mapping of every momentum with an amplitude. Instead, the MkWFC model uses the kernel identification advantages of OWFC, while maintaining the control and performance advantages of TWFC. Download a copy of wfc.js into your project folder. It has been widely taught worldwide. But anyways, the greatest applications of Schrdinger equation rather concern the calculations of stationary states. By feeding the constraints and possible tiles in manually generated meta-data to TWFC, the kernel generation step is not required hence reducing the computational load involved of TWFC as opposed to that of OWFC. Then we'll walk through setting up WFC in javascript and the Unity game engine. It may happen that during propagation all the coefficients for a certain pixel become zero. As far as I understand, these interpretations provide explanations of why probability is involved. Does the quantum wave function represent reality? If you can, please write an article to explain in more details what Im saying here succinctly. Check out this awesome video: Yes! NOTE: Oskar Stlberg's interactive web demo is a great way to get a feel for how the algorithm works. Whats more the Euclidean norm of the coordinates is equal to 1. In other words, what triggers the collapse? The final feature is backtracking. I'm interested in porting this to Haxe but am struggling to understand the math behind the algorithm (keep falling down the rabbit hole of complex mathematical concepts). In particular, this is what happens if we consider wave functions confined in a box. The procedural content generation algorithms are a well-known concept in the game industry. Introduction to Wave Function Collapse. You can also find the tutorial on GitHub, constructing a new model instance from input and parameters, saving or reading the output image and making use of it. WFC consists of two parts, an input Model and a constraint Solver. What people often refer to as quantum weirdness is the wave function being transformed by its mere observation. It rather aims at providing you an image of what the intimate relationship between position space and momentum space wave functions. Does the quantum wave function represent reality? Wave Function Collapse (WFC) by @exutumno is a new algorithm that can generate procedural patterns from a sample image. Part of the generation task is to say "I want a sentence with words . To eliminate this scalability tradeoff, MkWFC performs an automation step to infer the constraints rather than use a manually generated meta-data file. Although this introduces an overhead in terms of execution time, by automating the non-trivial step of constraint identification, MkWFC simplifies the meta-data required making the algorithm scalable. This, however, comes at the cost of manually generating a meta-data file that feeds the relevant constraint information to TWFC which is non-trivial, this affects the scalability of TWFC as increasing the complexity of the input can result in the need for increased investment of resources in determining the constraints required to generate desired results. END. This trick also works for the general structure of your patterns. Even though I can prove it mathematically, I have no understanding of the fundamental reason why Schrdinger equation links average position and average momentum. Had some trouble getting the Unity portion to work, but the following bits ultimately made things work nicely: Clone with Git or checkout with SVN using the repositorys web address. NOTE: The Tile Painter component can speed up input creation, letting you click and draw tiles from a palette of prefabs. Similarly to energy, the possible values of the physical measures correspond to the eigenvalues of the operators. A measurement then collapses the wave into the wave function corresponding to the measured value. If you're designing a dungeon, floor variants can be included to encourage the emergence of larger rooms. You signed in with another tab or window. From this data, we can infer that MkWFC can do better than TWFC in all cases when identifying constraint information from a set of input sample images as opposed to curating the meta-data manually. more replies. You can even drag a folder of prefabs onto it's palette property to load them all at once. It's also configured with components, so there's no code required for basic use. This spectrum has absolutely nothing to do with the physical spectrum of frequencies of light. It's especially exciting for game designers, letting us draw our ideas instead of hand coding them. my article on the essence of quantum mechanics, The Most Beautiful Equation of Math: Euler's Identity, Fourier Analysis: Signals and Frequencies. This corresponds to the following formula: From Schrdinger equation can be derived the fact that the average position varies according to the average momentum. That'd explain why when I couldn't find an explanation of what wave function collapse meant. Heres the best explanation Ive come up with. Each grid location holds an array of booleans for what tiles it can and cannot be. No life, none of us. Basically, the Fourier transform provides a description of any wave, like the one on the left, by an infinite combination of trigonometric waves, like those on the right: In this figure, the greater the wavenumber, the more arrows I have put on the trigonometric functions. Wavefunction Collapse can even accomodate additional constraints, like "this tile must be sea", or "this pixel must be red", or "there can only be one monster in the output." As a result, the wave function becomes very localized, which implies that the momentum space wave function is greatly spread. Heres an image illustrating the some of the tiles provided as input to TWFC and the corresponding outputs generated in different sizes: To achieve this, TWFC needed some changes in its logic, specifically using the constraints provided by meta-data as opposed to identifying said constraints from input sample images. Child prefabs that are placed within the Training bounds will be read by the algorithm. The eigenvalue, which is the real proportionality coefficient, is then the energy of the wave. The position of this localized wave function follows a probabilistic distribution whose density is the square of the norm of the wave function before it collapses. Whats particularly weird about this kinetic energy is that it can have a complex value. Keywords: Wave Function Collapse, Procedural City Generation, Machine Learning, Generative Adversarial Network, 2.2 Artificial Intelligence application to Wave Function Collapse, 2. We'll also need a Resources directory for our tile objects. A Markov chain is a stochastic process, but it differs from a general stochastic process in that a Markov chain must be "memory-less."That is, (the probability of) future actions are not dependent upon the steps that led up to the present state. According to this, any wave is uniquely decomposable into an infinite superposition of trigonometric waves of different frequencies. Because of their time efficiency, there is more effort put into developing new algorithms. First, add this function to get a pixel value from the ImageData: Next let's make a lookup table to translate from a color value to a single integer. On each step the number of non-zero coefficients decreases and in the end we have a completely observed state, the wave function has collapsed. Approaches which seem more promising to me on a mathematical viewpoint involve quantum information theory or particles going back in time. Then we'll walk through setting up WFC in javascript and the Unity game engine. You can get around this problem by either uploading your project somewhere, or running a local server on your computer. Thesis: Markov-Chain based Wave Function Collapse, Percentage Increase of identified constraints, Language/Tools: C++ programming on the Prodigy Engine. Because the spacing is larger than our N setting, all the algorithm knows is that coins are surrounded by empty space, and our output has a random scattering of coins. But to understand this, Id need to introduce operators, which would take too much time. But the amplitude of the wave function is rather a complex number. When running the trials highlighted above using MkWFC and comparing the performance against TWFC, there was some interesting phenomenon worth noting. At least, that's how I like to think about this, since, apparently, at least on the web, this is controversial. Because the spacing is larger than our N setting, all the algorithm knows is that coins are surrounded by empty space, and our output has a random scattering of coins. Viewed through the lense of the overlaps N pattern chunks, the algorithm knows that sometimes variant1 is above a platform tile, variant2 is always above variant1, and a coin is always above variant2. In mathematical terms, this means that the wave function should be an eigenvector of the Hamiltonian. Heres an example of the output generated when we dont allow the kernels to reflect along the y-axis: Heres some of the logic involved in generating this image using OWFC: Apart from having an OWFC class that handles all the information pertaining to OWFC, we also have a WFC class that performs entropy resolution based on constraints received, a WFC wave class which contains the generated output image as well as a WFC Propagator class which propagates the information across neighboring pixels as entropy resolution takes place. It's Training component should hook up to the input you've created. Implies the local constraints, a probabilistic approach and Maxim Gumin's passion for Markov's work. This means that the green position is one of the most likely position where the wave may collapse to if observed. This reduces the entropy of that pixel to 1 and it is assigned 1 of the observed pixel colors. Lets assume that the wave function has collapsed around the green position. This means that a rotation of the complex plane change nothing to the physical nature of the wave. limit (int) is how many iterations to run, providing 0 will run until completion or a contradiction. In this setting, waves are commonly represented as signals through space, as follows. For instance, the Hamiltonian is the operator associated to energy. Wavefunction collapse is most accurately treated through decoherence theory (see quantum decoherence, einselection, etc.) Indeed, at the scale we are looking at, distances are so short that stationary states are reached in such a small fraction of time that we can only observe these equilibria. By doing so, the tiling model can benefit from not having to use per-pixel entropies, instead, it can have a tile that can comprise some set of pixels that fit on a fixed tile grid. Finally in our start function we construct an array of arrays the same dimensions as our ImageData, pushing the integer code for each pixel: Let's take a quick look at using WFC with the Unity game engine using unity-wave-function-collapse. Inefficient iterative check-in MkWFC model that does some repetition on the input sample during constraint identification. artist Maxim Gumin proposed the wave function collapse (WFC)[23] algorithm in 2016, which is one of the texture synthesis techniques. So far, we have described the position of the particle. It let's you play the part of the observation phase and animates the propagation after you select a grid value. No, because they dont start nor end at 0. But there are other observations which cant be explained without the other half of quantum mechanics. Cryptography and Quantum Physics Cryptography and Quantum PhysicsBy Scott McKinney | Updated:2016-02 | Views: 2697Recent discoveries in the branch of physics known as quantum mechanics have powerful applications in the field of network security - they have the potential to break forms of internet security based on mathematics such as the RSA algorithm, and also present new ways to safely send information. This article follows my article on the essence of quantum mechanics, where I pointed out that everything is made of elementary waves. This information is then propagated to its neighboring pixels. Now we'll need a tileset. Its a much more significative concept in physics because of the law of conservation of momentum, which states that the momentum of a closed system is always conserved. This boils down to the question of what a measurement does. Markov Chains - Simplified !! More precisely the energy of the wave is the number of turns it makes in a second multiplied by Plancks constant. We're using a modified version of kchapelier's javascript port, which has been edited into a single file to make things a little quicker to set up. This is called the Markov property.While the theory of Markov chains is important precisely because so many "everyday" processes satisfy the Markov . We'll also need a Resources directory for our tile objects. Download Citation | On Jan 1, 2021, Pronay Peddiraju and others published Procedural Image Generation Using Markov Wave Function Collapse | Find, read and cite all the research you need on . Recall that these waves are fields which map each point of space with a number. This is a big assumption of quantum mechanics, which then describes how these waves behave through time. Whats extremely weird is that this probabilistic distribution depends on whats being measured. Instead of using image files for input and output, it works with arrangements of prefab GameObjects. Wave Function Collapse (WFC) by @exutumno is a new algorithm that can generate procedural patterns from a sample image. Basically, yes! It will remain in a superposition. This article does. If you look carefully at what weve discussed until now, no probability is involved. If it went clockwise, it would be negative. Technically, the spreading of a wave function is measured by the standard deviation of the probabilistic distribution of position induced by the wave function. Your can now load your index with the url http://localhost:8999, Now let's feed the ImageData into an OverlappingModel. This concept is useful for predicting data in many different fields. But have you ever stopped to really sense the meaning of this incredible formula? This is powerful but time consuming, and your original vision can sometimes get lost during the process. Im not sure what the Fourier transform stands for in this picture? Enforcing the patterns building desirable content, Figure 2 On the left: Input image that indicates areas with specific desirable values, on the right: the solution that corresponds to the input image, Figure 3 Examples of the 2D patterns generated by Max Gumin with a use of WFC, Figure 4 Island generated with Wave Function Collapse in Bad North. By splitting an image into some uniform chunks called Kernels, the WFC algorithm can identify patterns that exist in the input sample and their rate of occurrence. The lower energies refer to stationary wave functions localized closer to the nucleus. This has been done by Derek Muller on Veritasium in a very simple experiment! Heres some of the code showing how TWFC was implemented using a templated class: When comparing the 2 models, OWFC model takes a sample image as input while the TWFC model takes a meta-data file as input which contains a set of tiles that can be used as subsets of the image or tiles that complete an image and some constraints that determine what tiles can be placed next to each other. You can also click the generate and RUN buttons to see the output in edit mode. There are also several physical measures which are combinations of momenta and positions, like angular momenta. Let's try this out for our demo, converting the ImageData into a simple array of arrays, which hold a single number representing their tile type. Viewed through the lense of the overlaps N pattern chunks, the algorithm knows that sometimes variant1 is above a platform tile, variant2 is always above variant1, and a coin is always above variant2. Click here for instructions on how to enable JavaScript in your browser. Below is an example of the meta-data fed as input to MkWFC: By simplifying the meta-data being used, we are able to eliminate the non-trivial meta-data data generation process of having to determine the constraints manually. We can add a feature for this at the end of the start function like so: WFC usually creates some sort of image data type for it's output. It is an algorithm written in 2016 by Maxim Gumin that can generate procedural patterns from a sample image. name/input input data. In this article well see how a physics-based method can be used to secure online information. Thanks for this, it's very informative. Yes! The js version uses ImageData for input and ouput. Drag prefabs onto the object on the heirarchy window. Most WFC versions work with some sort of image format, for both input and output. And the decomposition is given by the Fourier transform. This may at first be considered a bug with the algorithm but is actually a valid output due to constraint identification allowing the placement of castles next to the adjacency scenarios exhibited by the neighboring tiles on the map. Note that the trigonometric function in the figure turns anti-clockwise. You do not need any other kind of equation. For the original algorithm it's a string representing a file name ($"samples/{name}.png"), width,depth (int) dimensions of the output data. NOTE: For this tuturial, we'll be focusing on the Overlap Model, as it's easier to create input for. In the case of 2D, the OWFC model splits an input image into smaller NxN sized kernels. With python, this can be as simple as opening a terminal in the project directory and running python3 -m http.server 8999 or python2 -m SimpleHTTPServer 8999. For example you could sprinkle some trees at random coordinates, draw roads with a brownian motion, and add rooms with a Binary Space Partition. The following figure displays the possible collapses of a wave function, where bolder arrows correspond to more likely collapses. To simplify our understanding of wave functions, lets consider a 1-dimension space. Finally, call img_url_to_data with your image url and the start callback: If everything works, you should now see your output drawn to the canvas: NOTE: Depending on the input pattern, it's possible that WFC will not be able to finish solving an output. Wave Function Collapse (WFC) is a constraint solving algorithm named after the quantum physics wave superposition concept. In this setting, whats surprising is that the measurement of the position of a wave localizes the wave around a position. In the figure above, the most likely collapses correspond to positions blue, green and red, because the distances from the origin to the value of the wave function at these points are greater. You calculate the evolution of the density matrix (instead of the wavefunction), and it's always a deterministic PDE, even during "measurement". It's similar to a 2D markov chain. Yes! NOTE: For this tuturial, we'll be focusing on the Overlap Model, as it's easier to create input for. 1. It builds on the approach of model synthesis by dividing the model into smaller pieces and propagatingtheconstraintstoconstructacoherentmodel. Made for PROCJAM 2017 | Thanks to our Kickstarter backers . I wonder how this algorithm could be applied to higher-order aspects of music notation. So a vertical localized wave would be essentially identical to the one above! Save my name, email, and website in this browser for the next time I comment. And this half accounts for plenty of counter-intuitive observations. But, overall, I really dont understand the measurement problem. Quite often though, this idea is rejected because a restricted concept of Markov chain is discussed. 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