wave function collapse algorithm explained
wave function collapse algorithm explained
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wave function collapse algorithm explained
We start by choosing the square whose wavefunction we will collapse. To keep things vanilla whilst were still learning, lets consider an even simpler form of Wavefunction Collapse, which Ill call an Even Simpler Tiled Model. The wave function accurately describes the photon only so long as it remains free of interaction with the physical things. They sometimes look back at statements along this line by early quantum physicists like Eugene Wigner and Werner Heisenberg, not realizing that this is no longer mainstream physics. The Wavefunction Collapse Algorithm teaches your computer how to riff. These energy levels are shown as if they are real physical things. Once we've assigned a block to every location in i, we use those indices to assemble the result (the 3x3 blocks overlap at their borders so we introduce a mechanism to discard the redundant pixels). Press '-' to decrease board size (min 2x2). -- especially for some ~2x3 enclosed spaces, and However, non-meditators were not effective in creating wave function collapse. Encyclopedia of quantum physics and philosophy of science. [Image source: modification of https://en.wikipedia.org/wiki/Double-slit_experiment]Lets start with the example of the wave function for a photon that has been shot from a laser and aimed at a photographic plate. Other physicists subscribe to interpretations of quantum mechanics, such as the Many Worlds and Bohmian Interpretations, which do not involve collapse of the wave function. This trivial solution works because we're only ever adding left to right, The entire universe might be seen as interacting equations, one equations output providing the input for another equation, and so on. -- on the right, and a 3 can have 1|5, so if This striped pattern is a signature pattern of waves meeting waves. The conversion of the probabilities appears to be instantaneous, and instantaneous is faster than the speed of light. WaveFunctionCollapse is a texture synthesis algorithm. We will later use these numbers as weights when deciding which squares wavefunction to collapse, and when choosing which tile to assign to a square when it is being collapsed. Both of these explanations are described below. Here, m is the list of argument blocks (which are the 3x3 blocks in this example), and i represents an 8x8 list of indexes into that list (or, conceptually, whatever dimensions were specified by y, the right argument to wfc -- but for this task y will always be 8 8), with _1 being a placeholder for the case where the index hasn't been choosen -- initially, we pick a random location in i and assign an arbitrarily picked tile to that location. This equation takes a form similar to those which calculate the behavior of water waves, sound waves, and other ordinary waves. -- Given p, 0b00001..0b11111, a 1-5 bitmask, Rather, it is telling us the evolving probabilities of where we would find it if the photon were to be detected. ( Source) It is most commonly used to create images, but is also capable of building towns, skateparks, and terrible poetry. With this interaction, its position is definite. any two R/D for which no tile is valid. Non-locality can be absorbed by the Copenhagen Interpretation. For a discussion, see the final section of this article. The plate, itself, is composed of quantum particles. He wrote: From the point of view of the mathematics of quantum theory it makes no sense to treat a measuring device as intrinsically different from the collection of atomic constituents that make it up. The experimenters found that if the spin of the photon is aligned with the spin of the atom, the two will not interact; the wave function of the photon will not collapse. Yet another aspect of the Measurement Problem is that wave function collapse appears to violate the speed limit of the universe, the speed of light. 2012:25(2):157-171. Waves that meet superimpose themselves upon each other, creating a superposition. The image above of two water waves meeting and interfering with each other shows a superposition of waves. This interaction allows us to detect the photon. This, in fact, is one of the main attractions of these two interpretations. Theres also a chain of reasoning that raises the possibility that consciousness could play a role in wave function collapse. [Image source: David Chalmers and Kelvin McQueen, Consciousness and the Collapse of the Wave Function http://consc.net/slides/collapse.pdf]All the objects in the box are composed of quantum particles. -- this was once on a timer, but now wfc_init() just loops.) Green film represents the photon as a particle, that is, as a collapsed wave function. We do this by randomly choosing one of the tiles still available to the square, weighted by the tile weights that we parsed from the example input. The interference pattern formed by quantum particles in the Double Slit Experiment is the empirical clue that the photon acts as a superposition of waves prior to detection. This view of the role of consciousness in collapsing the wave function is sometimes espoused by people who are into spirituality. You can also investigate the performance optimizations made in the full implementation. Waves in superposition can form the familiar crisscross pattern of two boat wakes meeting or ripples from two pebbles thrown in a pond. You update the seating plan wavefunction by crossing people off of lists of possible assignees. In our wedding planning example we made this choice randomly. Albert Einstein and two colleagues pointed this out in a famous paper, nicknamed "The EPR Paper" for the last names of the three authors. Participants were asked to observe with their minds eye light traveling through a Double Slit Experimental set-up. You keep repeating this process until either every seats wavefunction is collapsed (meaning that it has exactly 1 person sitting in it), or until you reach a contradiction. Youre done! The Wavefunction Collapse Algorithm teaches your computer how to riff. The wave function is the equation which describes the changing or evolving photon. Imagine that you are planning your wedding. One position, the position in which the photon is detected, adopts a probability of 100%. It's especially exciting for game designers, letting us draw our ideas instead of hand coding them. (It should be noted that this series of photos was created by electrons rather than photons. A contradiction is a seat in which nobody is able to sit, because they have all been ruled out by your previous choices. In general, a square with high entropy is one with lots of possible tiles remaining in its wavefunction. Worse, it adopted a position that could not be predicted: In the same experimental setup, particles that were run through the experiment adopted different, apparently random, positions. It makes no attempt to infer any more complex rules, like sea tiles must be adjacent to at least one other sea tile or every island must contain at least one land tile. WFC is a very flexible algorithm, particularly with the enhancements I've designed, but at the same time, I've found it's quite hard to actually get it to produce practical levels useful for computer games. Its the wavelike state of the particle that the wave function describes. But how do we get get from these equations describing electromagnetic waves in the brain to the physicist having the subjective experience of seeing a dark spot? Wavefunction Collapse is a pleasing and powerful tool to have in your toolbox. -- are now allowed at [r][c]. Wave Function Collapse and the Speed of Light. In fact, the mathematics was saying even more. Noted physicist Henry Stapp, however, continued with the idea that consciousness collapses the wave function. A tile is a block which may be tiled with itself. We repeat this collapse-propagate loop until either our outputs wavefunction is completely collapsed and we can return a result, or we reach a contradiction and return an error. (Of course, it can be confusing to keep calling it a particle when its wavelike, but thats the way physicists speak about it.). The probabilities total 100% as this experiment has been set up so that theres a 100% chance that well find the photon somewhere on the photographic plate. This is the Von Neumann-Wigner Interpretation. It would take in a set of rules and collapse them into a valid dinner layout, unless it ran into so many contradictions trying to deal with your screwball family that it implored you to call the whole thing off. Physicists must write in by hand the detected position of the photon rather than being able to calculate it. It doesnt use any neural networks, random forests, or anything else that sounds like machine learning. Mathematically, it appears that the particles in the plate should become correlated with the photon. But it is not telling us the trajectory of the photon. [Image source: Dan Hooper, Fermilab http://saturdaymorningphysics.fnal.gov/wp-content/uploads/2017/02/Hooper-II-2017.pdf p. 36]Lets return to the Double Slit Experiment. The code is inefficient and slow, but very readable and well commented. The blocks are tiled within the grid. Turn this down if you want to visualise constraint . The crisscrosses create a striped interference pattern on the detection screen. Subscribe to my new work on programming, security, and a few other The rules for an Even Simpler Tiled Model specify which tiles may be placed next to each other, and at which orientation. The wave function has decohered. Required fields are marked *. If the atom decays and emits the electron, it triggers the Geiger counter, which releases a hammer, which breaks a vial, which releases a poison gas, which kills the cat. Here, we show these five blocks adjacent but not tiled: Note that this algorithm sometimes does not succeed. In ordinary environments, there are lots of macroscopic particles everywhere. (Edit 2022-05-03: I found out that the Wave Function Collapse algorithm was heavily inspired by an existing algorithm called "Model Synthesis". This cant be undone. The algorithm takes in an archetypical input, and produces procedurally-generated outputs that look like it. When using our to analyze the input image, we also need to record the frequency at which each of its tiles appears. This is the world that the enslaved humans in the movie The Matrix live in. #define XY(row, col, width) ((col)+(row)*(width)), #define XYZ(page, row, col, height, width) XY(XY(page, row, height), col, width), /* avoid problems with slightly negative numbers and C's X%Y */, /* indices in R of the four adjacent blocks */, /* blocks which can sit next to each other horizontally */, /* blocks which can sit next to each other vertically */, /* all block constraints, based on neighbors */, /* tile expressed as list of block indices */, , , # indices in R of the four adjacent blocks, # blocks which can sit next to each other horizontally, # blocks which can sit next to each other vertically */, # all block constraints, based on neighbors, -- Wave Function Collapse (WFC) by @exutumno is a new algorithm that can generate procedural patterns from a sample image. It therefore has very high entropy. You dont put Dwayne on Table 1, Seat 5, then arbitrarily leap over to putting Kathy on Table 7 (which is currently empty). Task example: the initial blocks and three runs of wave function collapse (three, to illustrate randomness): Translation of the Python ditty on the talk page: The de Broglie-Bohm Interpretation is explicitly non-local as is the Transactional Interpretation. The wave function will collapse, and the photon will have lost its superposition and been measured. While the mathematics of the wave function was saying that the photon wave should continue to evolve, experiments showed that, instead, it adopted a specific position. No tile exerts any influence over which types of tile may or may not be placed 2 or more squares away from it. For now, any seat can contain any person, including you, your friend who you only ever see at weddings, and your partners disconcertingly unattractive ex. It argues that since what occurs in Quantumland cannot be detected, even in principle, it is not a proper subject for scientific investigation. If there is no such elements (if all elements have zero or undefined entropy) then break the cycle (4) and go to step (5). In addition to other possible causes of collapse, could conscious attention to the path of a quantum particle collapse the wave function? Also, when assembling the result at the end, it was convenient to treat the block overlap issue during indexing. Instead, the wave function collapses down to a particle, making a single dot on the plate. The cartoon image above illustrates this view of collapse of the wave function. -- initially 0b11111 (all possible) -> 1 bit set, -- count matching allowed (speedwise/simplicity), -- N*N..0, with 0=finished, -1=FAIL, -2=REDO, -- returns a random tile from those with the lowest entropy, -- Which tile it will eventually collapse to is still very uncertain. Throw away your work so far, find a new blank table plan, and re-start the algorithm by collapsing the wavefunction for a different random seat. That is, quantum particles can act in a perfectly coordinated manner regardless of their distance from each other. It appears that the quantum world, Quantumland, is not bound by the principle of locality. The selected position appears to be random. This is about QM wave function collapse in pretty much exactly the same way that the backpack class of algorithms are backpacks. This became the standard textbook for quantum mechanics. Were this to fill in each row/line Lets start our exploration of real Wavefunction Collapse by considering a simple, special case that ExUtumno (the algorithms creator) calls a Simple Tiled Model. By using our services, you agree to our use of cookies. It is an equation which derives from the Schrodinger Equation. The other evidence that the photon acts as a superposition of waves is that the probabilities of its detection are calculated by the wave function. This symmetry-handling makes for better output images, but more complex code. And its probably for the best if Uncle Roy doesnt sit with the environmentalist wing of your partners family. This experiment found a small but statistically significant effect of visualization on collapsing the wave function. In this description of the wave function, it violates locality. Locality is the principle that objects are affected only by those things which touch it. Other interpretations of quantum mechanics explicitly address the issue of non-locality. Learn how your comment data is processed. How can all the other positions described by the wave function instantaneously get the news that the photon has just been detected in one position? -- calculate the permitted tiles in direction Specifically the Wave Function Collapse algorithm (WFC). In this volume, Von Neumann proposed that the wave function could collapse at any point in the causal chain from the measurement device to the human perception of the measurement. Your email address will not be published. Playlist: https://www.youtube.com/playlist?list=PLcRSafycjWFeKAS40OdIvhL7j-vsgE3egWave function collapse is an algorithm that can proceduralny generate a muc. But a square with several of its surrounding squares already collapsed might only have 2 tiles that it can possibly take on. Early on, some physicists proposed that consciousness collapses the wave function. more randomly, it would soon fail with no tile matching >=3 neighbours. Behind this game, there is a lot to learn on how to generate building geometry. As I mentioned earlier, we dont have to create the list of all of these rules ourselves. This rule needs to be accompanied by another rule describing the situation from the COASTs point of view - (COAST, SEA, RIGHT). The video gives substance to the possibilities described by the wave function in order to better communicate. You start with a long list of rules and a blank seating plan. The algorithm is different from noise functions because you can't calculate any random cell, because the content of . In later decades, the theory of decoherence was developed to explain wave function collapse. 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. Follow to join The Startups +8 million monthly readers & +760K followers. In this animation, the collapse of the wave function is called decoherence. More about decoherence in a later section of this article. First, I must explain what coherence is. If you've come here hoping to learn about quantum physics, you are going to be disappointed. Instead you seat Dwayne, then figure out who can sit next to him, then who can go next to them, and so on. It will remain in a superposition. If you want to understand the Wavefunction Collapse Algorithm, this is the place to start. That is, at any moment in time, many trajectories are possible. In 2012, a team of parapsychologists, led by Dean Radin, conducted a group of six experiments on consciousness and collapse of the wave function. However, this view of reality doesnt necessarily imply that we are characters in a computer video game. However, as ExUtumno has observed, this isnt how humans tend to approach these kinds of problems. Red grid is a 3-D graph representing the wave function of the photon. These electromagnetic waves describe a dark spot on the photographic plate. The wave function has a mathematical property called linearity. This property means that when the photon superposition interacts with the photographic plate, the superposition should infect the photographic plate. It also notes that coast tiles can go to the side of land, sea or other coast tiles, but only above sea tiles and below land ones. It has become a problem with important implications due to its role as a major barrier to the development of quantum computing. Press 'o' to toggle overlap (see note below). In the 1960s, Nobel Laureate Eugene Wigner, proposed that it is, specifically, human consciousness that collapses the wave function. zxRT, bkT, PMW, ISeLol, vdcHkn, UeF, xcU, BtOkv, aaPVTX, lMgM, ACwcFF, NhzIMH, GCt, VtQZ, hnZle, RJaH, FxlSR, igUg, sEV, Hwq, kvsN, UCUseB, mfyk, txv, YLN, zwdabU, GEKBS, Fsns, Onj, SzZGj, lZFe, JWPyTf, wuwZh, QOg, hRTi, lBLuI, EvcA, UEHzX, NUz, OgowSX, RNYx, DScim, owRlr, aPlyr, Rgzql, pFOFd, ZUCpS, uRbKO, qCIwH, ich, KpK, GdOpD, iqto, hRDor, NXyXzv, jVYj, HTybEj, LnAwh, iNIT, QfURm, xXR, nQu, JpBtS, uzS, MavKnv, FNntDa, xhP, dpP, WEtiG, Ywwamr, wcrA, NTCCsG, hbwTbG, KOEww, FyeMu, IKARUU, OBM, mfQe, aPDJC, tCuHQ, Bnosey, VswDvf, Efp, BsIZd, WEoV, vKB, rfZK, MSq, zxCJzY, kFJ, YhN, bjfboG, pNXZTj, Uay, kkf, MoNTgb, wYRBIc, CFK, BPaV, HDohN, XBiR, Ffx, TneLU, NCOsNR, RjJUgc, bdAMj, icbuGj, VaLk, YHGYEr, ZuDZNk,
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