Superpositions, Sudoku, the Wave Function Collapse algorithm.
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- Опубликовано: 30 июл 2020
- In this video I explore the wave function collapse algorithm, and explain how I went about implementing it using Blender and Godot.
WFC demos on itch:
bolddunkley.itch.io/wfc-mixed
bolddunkley.itch.io/wave-func...
References:
marian42.de/article/wfc/
oskarstalberg.com/game/wave/wa...
github.com/mxgmn/WaveFunction...
robertheaton.com/2018/12/17/w...
Me:
Patreon / bolddunkley
Twitter / bolddunkley
itch.io bolddunkley.itch.io/
Software used for this video:
(Content)
Blender 2.8 www.blender.org/
Godot 3.2 godotengine.org/
OBS obsproject.com/
Kdenlive kdenlive.org/en/
With a name like Wave Function Collapse, I was expecting some really advanced mathematics, but this is actually beautifully simple and intuitive.
A lot of things in mathematics are beautifully simple and intuitive. It's just that mathematicians are really bad at explaining things. Or to be more exact, they are really good at explaining things to other mathematicians.
i dont know about beautiful, but simple for sure.
Just like the Universe.
@@Piotrek7654321 i dont know about Universe, but you for sure.
@@rawallon A stranger on the Internet just called me beautiful? Aww, thank you
Never thought about comparing it to sudoku, that's such a smart way of describing it!
I thought of the game carcasone.
@@m4rt_ 2D representation for something that looks complicated in 3D. Nice!
@@ocaly Yes but interestingly, you can also see the sudoku as a 3d problem. You have an X and Y axis, but given that any number from 0 to 9 can be on the same space at the same time you can also represent this as a Z axis.
@@lucadeacha you could look at it from that way and there are many sudoku variants even using that (f.e. "skyscraper sudokus").
@@lucadeacha or cubedoku's which is precisely what you're describing. but skyscraper sudokus is more well-known example among the online sudoku peers.
This is literally the best explanation for how this algorithm works.
Well, the explanation is super simple because it completely glosses over/ignores what happens when the constraint propagation fails and you need to backtrack or start over. There is a split second at 12:04 where two big pink exclamation points show a failed propagation -- what to do with that is not explained at all, and in fact is the most difficult part of designing a WFC algorithm that doesn't run for hours or fail 99% of the time.
@@OMGclueless Well, Ok that's a fair point & I did notice that but didn't quite understand what they meant, but for an explanation on how it generally works, I've found a lot of other explanations to be super complex or not very intuitive, especially when compaired to this explanation.
@@OMGclueless Agreed. I was just about to reply with this same question.
I see Martin, i like
@@OMGclueless Backtracking is not part of WFC itself and is thus probably just outside this video's scope - the original WFC implementation quits when it encounters a contradiction. Backtracking just happens to be a very helpful addition to WFC :] That said, the fundamentals of backtracking are fairly simple to explain and probably could've been mentioned - you push every collapse and the pre-collapse state onto a stack, and if the collapse causes a contradiction, you pop that collapse and remove that candidate from that cell's candidate list and propagate that. If that removal also causes a contradiction, you pop yet another collapse off the stack, and so on. The difficulty comes from storing the pre-collapse state in such a way that it won't eat all your memory or require recalculating most of the state at each Undo, and that's definitely beyond this video's scope.
This is one of the most well-presented videos, on a technical subject, that I have ever watched on youtube. Great work, looking forward to more content.
Terrific explanation! I recently finished reading "Doors of Eden" (by Adrian Tchaikovsky), a novel in which wave function collapse influences the plot outcome significantly. I'm going to share the link for this video with my wife and a friend who've also recently read the book but who are both humanities scholars rather than techies, because if they simply stop at the beginning of the programming section, they will get an extremely lucid and approachable explanation of the theory. Well done, and thanks for sharing.
This is super useful for generating levels with a set number of points of interest.
You add whatever things you want to have in a level at random points and maybe add roads between them and after that you can make this algorithm do its magic to fill in the details. Very nice!
though it would be different for every user unless you have some way to define what goes where specifically by the coordinate.
@@jessiejanson1528 as long as your pseudorandom selection process is consistent then it shouldn't be an issue
Watched more than 3 hours of implementations and explanations about wave function collapse,
Can confirm that this one was the best from every aspect,
Thank you!.
If you add recursive backtracking to this algorithm, you'll end up with a classic algorithm for SAT solving, called DPLL. Also, DPLL is very old and outdated, so if your constraints are too complex to find a solution with it, consider taking inspiration from CDCL algorithm, or just use the off the shelf SAT/SMT solver, like Z3.
I'm working on creating a complex sudoku solver for variant sudoku rules, and my current algorithm that I came up with seems to reduce to DPLL. Do you know of some elementary resources where I could learn some more about CDCL to make my algorithm faster? I got a minor in comp sci, but most of the resources that I've seen are borderline graduate CS level.
@@sweetcornwhiskey I learned about that algorithms from presentations of Emina Torlak from her Washington University course, you can google that course. Once you get through the notation, that should be understandable.
@@sweetcornwhiskey CSE 507
@@luck3949 Thanks!
@@sweetcornwhiskey there's been a SAT competition for the past 20 years: see SAT RACE / SAT COMP. You will find an assortment of different solvers source codes to look at/reference. A lot of the content is dense/state of the art, but the assorted info over the years is probably the best resource for speeding up SAT solving. You might find a PhD dissertation/Survey or two where the "preliminaries" or "background” section explain completely the ideas, reasoning behind it, etc. before jumping into what is likely more difficult.
Normally my brain hurts when I try to grasp new concepts, but that just didn't happen now. You have a way of explaining things making the concepts very easy to understand
Best WFC explanation I've watch. Thanks !
It really is! And even provides links to all the further reading you want. Great video.
Agreed.
Definitely brings this ‘WFC’ that we have been seeing from the likes of Oskar Stalberg since some years now to humanly possible understandable levels. The Sudoku explanation is quite straightforward to grasp the concept, at least for me.
Deserves the patron support hands down.
The idea to just analyze an example level to determine valid sockets is great. I did not even think about that. Makes it much easier to create complex rules and have the computer imitate the style of a human Level Designer.
This is by far the clearest and most detailed explanation i saw on the subject, thanx a lot ! I was wondering, just like for sudoku, is it possible that the algirithm runs into a dead end by selecting a combination of tiles that doesn't allow a suitable neighbour in some cases? Is there a strategy for the algorithm to backtrack and correct that, or is it better to start over again or carefully craft a tileset that allows every possible combinations?
This can absolutely happen. Backtracking is a good option definitely, but I never got around to implementing anything like that. My implementation just starts the whole process again if any cell ends up completely empty of options. Making sure your tileset covers all bases definitely helps avoid contradictions.
I was thinking that for each axis we might store a growing list of changes, so more recent changes are at the end. Then we could do a targeted backtrack looking only at the values which directly constrain a given location.
I haven’t worked out how that would fit with the required propagation steps yet… it wouldn’t be as clean as a simple backtrack everything (breadth first search) but it feels like it should be hugely faster.
@@j.j.maverick9252 If you only remove selected changes, there could be issues where the algorithm would prefer certain patterns of cells to be faaar more used than other patterns. Especially if a constraint is quite old, it would have influenced the choices for a lot of other cells. You could absolutely consider this intended behavior, but a small change in your tiles could cause quite large repercussions on the average outcome.
seems like the best solution is just to solve it in a circular pattern going around the starting point. i cant imagine it would ever get stuck.
@@jessiejanson1528 It absolutely can get stuck. You're talking about a FIFO Stack (First In First Out) for cell determination which is what this video shows, so long as you are leveraging squares (as in this example) you can run into impossible scenarios.
In example, look at your number pad, take 2, 4, 6, and 8 to be South, West, East, and North respectively. You pick a determinate cell for North. You're now acting on East (clockwise), and just like North you have all the same options. Fast forward a bit and now deal with "North East" Your cell now has 2 restrictions applying to it to which you may have contradictory rules (See the example at 5:35).
This is just hypothesis at the point of writing this but I suspect that one of three things can help mitigate this:
1) Hexagonal Cylinders (making all surrounding cells directly relate to an immediately previously set cell's face)
2) Writing an algo to parse your "tile set" and make sure you have Tile Sets that fulfil all iterable conditions (so assuming outwards propagation, 2 faces for a 2d square tileset, 3 faces for a 2d hexagon tileset and, atleast 3 faces for a 3d tileset)
3) Making sure no Tile Face Socket exists only twice. (for the same reason as #2, if a face only has one possible match you're significantly more likely to enter a dead end.
That was mind-bending! Really some food for thought! And you've convinced me to take up Sudoku! I really love that you relate Sudoku to wave function collapse in this way! Really helped something *click* in my brain; thank you!
Nicely presented! I thought you were going to talk about physics but I watched the whole video because this algo idea is so fun, and all the info was a good mix of visual demo and technical details, perfect for morning coffee :D
Just 50 minutes ago, I accidentally set my sudoku game to the highest difficulty (I usually play on easy).
While playing, I thought to myself: "I need to write an algorithm to solve these fucking games for me. I have to read up on previous work first though."
And now, just after finally finishing the stupid game, YT suggests this to me. This really weirded me out.
Rant over.
Nice video! :)
This is honestly not only extremely well explained, but also beautiful too
I've been reading about wave function collapse for a few days, and four minutes into your video I already understand it better than everything else I've seen combined. Fantastic job
Man you're so good! cant believe this channel is so small :O really helped me out with my next project :)
I saw the Bad North inspired island generation in the thumbnail :) Love the game! I can understand why Oskar is so stuck on the idea (He keeps going back to it on Twitter)
the amount of math and editing required for this video is insanely impressive
Wow, this was amazing. So well organized, articulated, and indeed respectful of my time. You sir have earned a sub + bell. Thank you for this I'm sure I'll end up referring back to this one day.
That was just enough information to be able to write it and not be lost. Thank you for not over or under explaining it like most videos do.
v0_0 is how my face looks when looking at the astonishing amount of informative data in this video. Kudos on how well presented this is too!
The way you break down the software is perfect for learning key concepts on a functional level. In my eyes, you are the gold standard. You can bet that I will be watching everything you'd ever made over the upcoming days
Best WFC Explanation never thought of comparing it to Sudoku. Nice Vid!!
This may be one of the best videos on this topic I've ever seen. Its explanatory power is breathtaking. This just shows the principle so well with so little wasted effort.
I really appreciate the effort you put in to explain what I once thought was a really difficult algorithm to understand. Great Job!
This is a great example of how failing to explain some incidental details, which are not relevant to the topic but which have been arbitrarily chosen for illustration, leaves the audience confounded and unable to fully engage with what otherwise seems like a clear explanation of the topic.
I mean, what the hell are these tile maps? What am I looking at? What am I supposed to intuit from these images? I don't understand the relation between the various tile images, so I am unable to recognise the patterns that are supposed to be illustrative. Not only does this fail to illustrate the explanation, it confounds it. I can't process the audio while my brain is trying to decode the impossible visual.
But the Sudoku was such a perfect illustration that I understood that part instantly. Cheers.
I believe that description is done at 4:33, but is slightly poor as it doesn't expressly point out the incongruity of the "negative space" the "isn't" tile creates.
WOW, this is an incredibly well-made video. You've done such a good job teaching and choosing your metaphors.
I’m a nuclear physicist who misread the title & assumed this was about quantum wavefunctuions… don’t think I’ll ever do anything with this information, but got interested & stuck around anyways. Incredibly engaging & high-quality video, & an excellent explanation even for someone who doesn’t do much with algorithms! :)
holy shit this makes it make so much sense, i wouldnt have known this comparison would work so well! Good discovery!
Absolutely loved this video, especially love how in the beginning you compared it to something that everyone can understand before going more in-depth.
By far the best introduction to and explanation of WFC I've come across...! Thank you for taking the time to make this.
Our teacher added this as our study material on a course lol. Very informative!
This makes me unreasonably proud, thank you for sharing! 🙏
@@MartinDonald You should!
Thank you for the fantastically clear, intuitive, and well-articulated explanation 🙂 Much appreciated ❤️
This is the best explanation video on WFC I have found! Alone with the example at the beginning I could conceptualize the algorithm. great work!
Wow, comparing it to sudoku was smart. That made it so much easier to wrap my head around!
I’m from the complete other side of the spectrum, I’m a physics student in their penultimate year of their undergraduate and I know and understand superposition and collapsing a wavefunction in quantum mechanics, but have never seen it used for mapping. That’s awesome!
this is awesome, you explained the concept so well that it just intuitively clicked for me. i feel like the number of tools in my mental toolbox as a programmer has increased after watching this video
Hands down the best explanation for WFC I've ever seen. Kudos!
Wow! Thank you for a great explanation and for mentioning all these references!
I realized that when developing something like a tile engine I can avoid making an editor to create test levels (at least at the beginning) and use WFC to generate levels automatically.
good video! haven't found many good channels like this explaining algorithms or CS concepts, have subbed!
Very nice and compact video, makes me want to program my own implementation from scratch.
Also, the comparison of the wave function collapse to sudoku was what made it click for me, very well done :)
This is the best explanation I've seen for WFC - it's got me thinking about where I can apply it, and I don't write games.
I also accidentally watched all your back-catalogue. Pity there aren't more - they're all really well explained!
heck, you explained wave function collapse so beautifully in just two minutes. i am sticking around for the rest of the video of course but even so i had to compliment you on being so succinct
wow.. this is the most amazing explanation ever.. Please Please keep making high quality videos like this.
Excellent video! Thanks for sharing! Also, you are the reason I created a Patreon and you're the first person I'm sponsoring! :) Great job!
Thank you so much!
dude, this video is so good, I've looked at explanations on WFC for ages and this one really made me understand it
When i saw this title i realized, i have implemented WFC for Sudoku without realizing it. Amazing :)
AWESOME video! Thank you so much for the extremely detailed overview of this algorithm! I definitely feel like I have a grasp on how to implement and modify it. Thanks again!
Of all the videos that I watched on wave function collapse, yours is by far the best at explaining it.
Really nice explanation and visuals!
Thank You! This video helped it all make sense! I love your "wax on, wax off" trick about teaching us Wave Function Collapse through sudoku! Right when I'm like wait, I want to learn about Wave Function Collapse, you have already tricked me into learning it! I knew karate the whole time.
While the algorithm itself is also really cool, whoever named it "Wave Function Collapse" should pat themselves on the back because that's one of the coolest sounding algorithms ever. For some reason saying "wave function has been collapsed" makes you feel powerful :D
Brilliant, concise, informative and fun! A truly exquisite piece of education.
Thanks Martin, as a Unity developer, It's also useful to me :)
Holy crap, I just stumbled upon this channel randomly and I'm stunned. Amazing content, thank you for this.
Sudoku example was brilliant, Thank you so much .🙏.
This is so well made and perfectly explained. You need way more subs!
Thanks for this high density video! Beautiful masterpiece, you earned my subscription!
This is the best wave function collapse video out there. By far. 10/10
What a great way to explain this! Wonderful video
You did a fantastic job of explaining this concept. Thank you so much!
I'm so glad I found your channel. You really remind me of Sebastian Lague! Your content is phenomenal, I really hope your channel picks up more traction soon. Cheers!
Without a doubt one of the best explanations I've heard/seen. Thank you so much for that.
Very informative, thank you. I’ve been considering implementing wfc in music composition, and this explanation helps me grasp it. Have a pleasant day.
Incredible content. Amazingly explained. I'm excited to see more
This is so great! The presentation is excellent! Will share on LinkedIn soon.
Excellent! I'll be eagerly watching your future videos.
Are you also using Doom Emacs with the gdscript layer? If you have any suggestions for improvements they're welcome on the repository.
I'm actually using pycharm but I can see why you'd think that, the colour schemes are almost identical. I'll definitely look into it though.
I guess im asking the wrong place but does anyone know a tool to get back into an Instagram account..?
I was stupid lost the password. I would love any tips you can offer me
@Sylas Casey i really appreciate your reply. I got to the site on google and I'm trying it out atm.
Looks like it's gonna take a while so I will get back to you later when my account password hopefully is recovered.
@Sylas Casey it did the trick and I actually got access to my account again. I am so happy!
Thank you so much you saved my account !
@Kingsley Langston no problem :)
good explanation. Highly appreciated.
Looked at some of your other videos as well. Brilliant content! Subbed.
As someone looking to do a wave function collapse implementation the really helped me understand
This is basically a computer playing Carcassonne
Well explained! Thanks for your effort!
That explanation of sudoku could be a video all of its own. Very clear and precise! It didn't just explain the rules; it highlighted both how you should play, what you should pay attention to, and why it's the way it is in just two minutes.
I have never watched any video related to wave function collapse but youtube really wants me to watch a whole bunch of videos on wave function collapse lately.
This is fantastic! Thank you!
Thank you so much for your video! Great material and superb delivery, I enjoyed it a lot!
First explanation of WFC that I actually understood, thanks!
This is amazing! This'll help me so much! Thank you!
This video deserves more views! Amazing explanation and great video :D
Thank you so much. This is the cleanest explanation I came across so far. ❤
just got my own implementation working in unity, this video was a massive help!
Omg you are a genius! I never learned AND understood so much information at once. Great work!!
This was an excellent video! A really great explanation of this kind of generative art.
Really fantastic video! Also super interesting stuff!
you're the master of making difficult-to-understand things become much easier ones.
This video is fantastic, thank you Martin.
Oh damn why didn’t I use that approach at 3:02. every tile containing the whole input...
Would have made my approach maybe not more efficient but a lot more elegant
Edit: or the sockets... why didn’t i find this video sooner 😭
Edit 2: forget it, every part of this video is brilliant
Such a great video, thank you!!
this was brilliant! come back, make more, please!!
Just found this channel and it is absurdly good -- wow!
DUDE SUCH A NICE EXPLANATION! THANK YOU SO MUCH
Awesome video, thank you very much!
Amazing
loved this!
Amazing tutorial and explanation. Thank you!
This video is illuminating!
This is an absolutely excellent video!
Woah, I'll have to do a tier in your patreon, this is so well explained
Lovely video. Thank you so much for this!