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WaveFunctionCollapse: Generates bitmaps that are locally similar to the input (github.com/mxgmn)
281 points by lnyan 13 days ago | hide | past | favorite | 39 comments

One cool property that I haven’t seen anyone else use is that you can use time itself as another tiling dimension.

I did some experiments with creating looped animations a few years ago:




Can it create temporally-similar patterns as well? Something that is bounded by a similarity metric over each time period?

Yeah seems like that should be possible, since at the end of the day WFC is a system of constraints, so you can add any other arbitrary constraints you want on top of it.

With the examples I posted above, since they wrap/loop in the time dimension, there is always some similarity/consistency. For example, in the one with the rabbits, if a rabbit dies, that means there will have to also be a birth to get back to the correct number of rabbits before it loops.

Interesting, I thought there might be something built-in for randomness. Great animations!

I used this algorithm to generate minigolf courses [1].

I used this repo [2].

The algorithm is literally just a constraint solver. I'm pretty sure it's pretty similar to the sudoku solver I wrote in prolog for a university course.

It's kinda pretentiously named and described, probably because its more academic to do that. It's just a constraint solver.

1: https://twitter.com/00jknight/status/1249091532071645184

2: https://github.com/math-fehr/fast-wfc

I played around a lot with this library:


Fun stuff, but I struggled to get a lot of value out of using it for level gen. You get cool patterns, but levels need structure and intent to be interesting. Adding constraints to the algorithm becomes a big-oh nightmare and you end up with frequently unsolvable paths as the algorithm recurses.

The game Bad North used it to good effect, so depending on the game it may be a very useful tool in the toolbelt.


I wonder if it could be combined with a tool like Path of Exile uses. They draw very rudimentary maps (River here, N bridges, etc) and then the tooling generates the level around those constraints.


How slow does an algorithm have to be before it stops saving time on level design, realistically? Obviously if it straight up fails for complex sets of constraints that’s one thing but even running for a day, if it yields usable results that seems like a timesaver.

Seems like it might be worth taking some lessons from SAT solvers. e.g. backjumping and clause learning.

I can imagine it for textures so the cobblestone and brick don’t end up repeating.

wouldn’t you be using perlin noise based textures for that?

The maps in Bad North are frequently quite weird (although never actually broken), but that's part of their charm.

TownScaper is a game built around WaveFunctionCollapse.

You specify which cells in a 3D grid are occupied by clicking, and it fills in the details to make a charming little town.


The creator Oskar Stålberg has a great overview talk of Wave Function Collapse and how he applied it to his previous game Bad North - it’s absolutely worth a watch! https://youtu.be/0bcZb-SsnrA

And he has a prototype of WFC city building online! https://oskarstalberg.com/game/house/index.html

https://oskarstalberg.com/game/house/Release/UnityLoader.js(...: Invoking error handler due to Uncaught RangeError: Array buffer allocation failed ERROR> blob:https://oskarstalberg.com/5b6b4a87-7358-438a-a06d-fd70825093...: Uncaught RangeError: Array buffer allocation failed

I would highly recommend this video as a good starter


This was great, I feel like I have a good understanding of how it works now. Thanks for sharing.

I've struggled with implementing my own version of this algorithm - so I know I don't understand it properly. I get lost because of the "quantum mechanics" aspect - I am kind of suspecting it's just an analogy for the actual algorithm (maybe it's not?)... but I'd love to see if this could be re-written without the "entropy" and "superposition"-type wording, just to see if I can finally make it click in my brain!

It's been discussed numerous times that this is simply a constraint satisfaction problem with hand-wavey BS applied over the top.

Here's a good (free) explanation: https://www.boristhebrave.com/2020/04/13/wave-function-colla...

Specifically read the 'Least Entropy' section: It's broken down very simply:

Pick a random tile which is the 'least random', because (due to already having resolved the constraints we can), this is most likely to be a cell that won't cause problems (ie. unsatisfiable constraints) later.

You might also like to read this (also) free paper on implementing WFC using a constraint solving library: https://canvas.ucsc.edu/files/109152/download?download_frd=1, which I quote here:

> The heuristic of selecting the most constrained variable or equivalently the variable with minimum remaining values (MRV) is well known in constraint solving.

> Since there is more than one valid pattern for that location—or it would already have been set to zero entropy in the previous loop—one of those patterns needs to be chosen. One of the patterns is chosen with a random sample, weighted by the frequency that pattern appears in the input image.

> This implements Gumin’s secondary goal for local similarity: that patterns appear with a similar distribution in the output as are found in the input [12].

I agree that the quantum mechanics terms are often more confusing than helpful here. To the point that I wrote a journal article to try to demystify how the algorithm works [1].

If you're familiar with constraint solving, "superposition" is just "the remaining possible choices in the domain" and "entropy" is just describing how to select the next node.


Do you get a commission from this?

No way to read online for free?

Here's an open access link: https://escholarship.org/uc/item/3rm1w0mn

Academics don't make any money from sales of paywalled journal articles. If you click a link to a journal article and hit a paywall, it's usually because whoever shared the link has institutional access to the journal and forgot that the paywall was there (since it effectively isn't for them.)

I wondered why you would link to magazines a while ago, as they're often behind a paywall and the author doesn't get a cut as I understand. Maybe it's for the citations? Do authors mind sharing the article for free next to the publication link?

Check out sci-hub.

I looked at the WFC recently ("Level generation and style enhancement - deep learning for game development overview", https://arxiv.org/abs/2107.07397).

Yes, it is a big inspiration, and there are numerous beautiful examples of its results. However, the QM wording is at best an extremely loose analogy (one that a hacker would use). If you want to compare it to other methods, see "WaveFunctionCollapse is constraint solving in the wild" https://dl.acm.org/doi/10.1145/3102071.3110566.

"WaveFunctionCollapse is constraint solving in the wild."

https://reddit.com/r/proceduralgeneration has content like this come up from time to time. Useful if you are interested in similar items.

I assume that a lot of people have played around with this concept, it's one of those things that are not too complicated to implement.

But I guess I am the only one who used the Zelda, a link to the past overworld as the training input ;-)

Examples: https://imgur.com/a/R1OleXp

My problem with that was that the algorithm basically always ran into unsolvable states. The WFC solution to that is to just start again, but most WFC implementations use only few (<10) tiles. The Zelda map had several hundred, you can actually see the algorithm searching for valid solutions in the videos I linked.

the algorithm is much simpler than I thought it would be. It basically takes an image made of tiles (think the levels of an NES game) and it searches for a permutation of those tiles with the property that each tile is immediately surrounded by the same types of tiles as in the original image.

Reminds me of the PatchMatch algorithm.


Love how the 3D images looks like they're taken straight out of Labyrinth, never mind M. C. Escher. Wonder what it would take to make those render more efficiently.

The game Caves of Qud uses this to generate maps:


as someone who did game dev for a while, i sure hope this plays well with semi-hires photos(1000x1000) as it seems better than conventional algorithms for unique texturing

Only "seems". It's excellent at small scales literally because it's optimized for small scale local similarity, it's useless for large scale.

https://github.com/EmbarkStudios/texture-synthesis this was on HN a couple of years ago, and seems to use a similar approach for photorealistic textures.

It does not. It is for very small-scale similarities.

The smallest possible scale, in fact: a pixel and its neighbors.

Maybe VQGAN would be good for you

wow this is awesome i would love to use this as a webapp

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