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vintermann 3 hours ago [-]
It's beautiful. But also pretty unsatisfying in a way. Roads don't make sense. Rivers barely make sense. There's no higher-scale structure - the reason why most games with incremental procedural generation usually feel stale after a while, and always static. Every planet is different, yet feels the same.
(Dwarf Fortress is the one procedural game I know - besides maybe its more faithful clones - which isn't static. But the procedural generation there is also mostly not incremental, it generates the whole world beforehand and only some of the fill-in details are incrementally generated).
The holy grail has to be a graph-based refinement/embellishment system, where it generates just the nodes, temporally and spatially, which matter for the situation the player is in.
porphyra 16 hours ago [-]
The post glosses over the "backtracking" and says they just limit it to 500 steps but actually constraint programming is an extremely interesting and complicated field with lots of cool algorithms and tricks. In this case we could solve it with Knuth's Algorithm X [1] with dancing links, which is a special kind of backtracking. Algorithm X should, in theory, be able to solve the border region described in the article's "Layer 2" with a higher success rate as opposed to 86%.
Furthermore, various heuristics can speed up the backtracking a lot compared to a brute force approach. As anyone who has implemented a Sudoku solver can attest, a brute force backtracking is easy to implement but will immediately get bogged down with slowness.
there's also a bunch of dedicated constraint programming solvers / high level modelling languages for these kinds of constraint-y combinatorial optimisation problems
e.g. https://www.minizinc.org/ offers a high level modelling language that can target a few different solver backends
might be pretty good results to completely ignore writing a custom algorithm and drop in an existing industrial-grade constraint programming solver, model your procgen problem using a high level language, and use the existing solver to find you random solutions (or exhaustively enumerate them). then more time to iterate on changing the problem definition to produce more interesting maps rather than getting bogged down writing a solver.
porphyra 14 hours ago [-]
Yeah, you can also use Clingo [0] which is pretty popular and people have tried it specifically with WFC content generation [1]. You can even run it in the browser easily [2].
I have a (very slight) beef with the name Algorithm X, as it is more of a data-structure to manage undo-information for the backtracking than an algorithm. It is a very fun, useful, and interesting data-structure, but it doesn't really change what steps are performed in the backtracking search.
felixturner 8 hours ago [-]
Thanks for the feedback. Feel free to drop a PR :)
Hard-coding the constraints skips the whole point of the algorithm (which is also badly named by the way).
nextaccountic 6 hours ago [-]
Note that the original algorithm is model synthesis. WFC is just a minor tweak on it
djray 12 hours ago [-]
The demo runs at 5 FPS on my laptop (11th gen Core i5 and Iris Xe graphics, Chrome Latest as the browser, with the GPU being the bottleneck). I was hoping for something rather more efficient given the write-up saying it ran at 60 fps on mobile.
The maps are pretty, but the per-tile build constraints of the WFC build approach means that pretty unnatural generations end up happening because non-local influence is difficult to take into account. I think this may be OK for games where you discover tiles one at a time, but for a full map generator it's not great, and better solutions exist. Red Blob Games did a writeup of a noise-based method which looks superior imo. You can use moisture-tracking approaches for rivers, lay roads, bridges and other artificial elements in a separate pass, and it will likely end up faster and more robust. I think WFC is an interesting programming problem, though, so it was likely fun to implement.
Nonetheless, this was an excellent write-up and impressive demo.
wmil 6 hours ago [-]
You should be able to use chrome://gpu/ or about:gpu to tell if Chrome is doing software rendering.
rafram 7 hours ago [-]
It runs quite smoothly on my iPhone 15, so I think there’s something wrong with your graphics setup.
socalgal2 11 hours ago [-]
your on windows or linux or ... maybe your on CPU rasterization?
refulgentis 12 hours ago [-]
I’m stunned - works fine on mobile for me. I’m curious how you determine FPS, I was hoping the site had an indicator, but either I’m missing it, or it’s Chrome Dev Tools (and thus it’s presumably impossible for me to get on iOS/Android)
jesse__ 17 hours ago [-]
Love this.
As an aside, if the author reads this, did you consider using bitfields for the superposition state (ie, what options are available for a tile)? I did a wfc implementation a while back and moved to bitfields after a while.. the speedup was incredible. It became faster to just recompute a chunk from scratch than backtrack because the inner loop was nearly completely branchless. I think my chunks were 100 tiles cubed or something.
zimpenfish 13 hours ago [-]
> I did a wfc implementation a while back and moved to bitfields after a while.. the speedup was incredible.
Yeah, my WFC bot (which happens to generate Carcassonne maps in an amusing coincidence) eventually ended up using https://github.com/bits-and-blooms/bitset which improved things hugely.
> It became faster to just recompute a chunk from scratch
Kinda what mine does - every now and again[0] it stacks the current state and if it gets stuck, just pops the last one and continues from there.
[0] Just checked and it's every `tileCount / 20` iterations, hilariously in a variable named `tenper`. I hate past me.
netdevphoenix 25 minutes ago [-]
Is there anything special about using the wave function collapse algorithm in this particular context? I feel this is like when experimental musician make music with plant electrical signals, wind flow or sea wave movements, etc. The idea sounds great but the execution not so much.
jcalx 16 hours ago [-]
Reminds me of Jasper Flick's Unity tutorial on hex terrain [0] which is similarly wonderfully detailed. Interesting contrast: this project uses premade tiles and constraint solving to match tile boundaries, while that one dynamically generates tile boundaries (geometries, blending, etc.) on the fly. Both enjoyable reads!
the game dorfromantik is a fun twist on this idea - the game generates random tiles and you have to fit them in with matching edges. you produce some beautiful pastoral landscapes while playing a pretty fun and challenging game.
It seems like a lot of the difficulty is in finding arrangements that satisfy constraints. I wonder if an alternative approach would be to use a SAT solver. I suppose the problem with that approach would be that the solver might always find an 'easy' solution that doesn't look random. I know that some SAT solvers let you randomly assign the initial assignments of the variables, but that doesn't mean you get a random solution. Has anyone tried a similar approach?
teamonkey 15 hours ago [-]
I think the problem with SAT solvers is that they’re complicated, in terms of computation and also how easy it is to understand by someone who didn’t study formal methods.
WFC is brute-force-simple, but because it’s simple it’s quite computationally inexpensive (unless it hits a lot of dead-ends) and I wouldn’t be surprised if it could often find an adequate solution quicker than a SAT solver. At least for games, where a result doesn’t need to be perfect, just good enough.
gmueckl 12 hours ago [-]
Less than perfect solutions can make certain types of video games more interesting because the domain of potential results is generally larger and can include many more variations of challenges to the player.
xipho 17 hours ago [-]
Inspirational stuff, with lots of great references to the OGs at the bottom, and source available. Now can it be merged with the look/feel of https://heredragonsabound.blogspot.com/. ;)
Oh, wow, TIL. Both were released in 2022 but the video game already had an alpha release in 2021.
foota 14 hours ago [-]
I realize this comes up every so often, but I was just looking at this the other day :) A related idea is wang tiles, which are a way to construct a tileset such that you can place them without ever running into a contradiction.
In the level data, the start/goal tiles (approx 10x10 blocks of solid ground under the player and goal) and slopes aren't represented by their tile offset in the level data -- whilst all other "ground" tiles are. Instead, for slopes you're only told the start and end coordinates, and they often overlap.
So to render the slopes correctly I had to work out all the rules for which tiles were allowed next to each other, and solve some ambiguity rules -- I figured out that shallow slopes take precedence over steep ones. Eventually I cracked it, but it took quite a week or so of iteration to figure it out.
ionwake 16 hours ago [-]
This is absolutely beautiful, I could even tell I was going to like it from the title. Good job.
jcul 16 hours ago [-]
That "Carcassonne" game sounds really fun. I'd never heard of it before.
It’s one of the great board games IMO. Everyone has fun. Pretty light on the rules and satisfying.
juleiie 10 hours ago [-]
Interesting. In my little project I only need one generation of hex tiled terrain but based on certain lore and vision for thousands of objects with different lore. I tell LLM to research the lore and paint the terrain using json in chunks. Some results are shit, some results are great. Still, it would be impossible manually. I can always do another pass for unsatisfying results with different prompt engineering.
hananova 12 hours ago [-]
AI;DR. Can the author please just post the prompt?
iamjs 12 hours ago [-]
This sentiment is quickly becoming the most annoying low-effort comment on HN. If you don't want to read it, don't read it. If something about the writing offends you, then describe it, so we can talk about it.
_bent 8 hours ago [-]
It's extremely distracting to read heavily ai edited texts like these because every single aism throws me a curveball.
It doesn't help that the figures of speech ai loves to use are those that stress things and create tension and drama. And it uses one in every single paragraph, rendering the text into the literal equivalent of a deepfried faux HDR jpg (or a dialogue scene in a Michael Bay movie).
And beyond those practical concerns it's just hard to gauge how much the author truly understands of what he's writing about (and transitively if it's worth to continue reading)
btbuildem 16 hours ago [-]
I really like the part where you can "reroll" sub-areas of each tile. Consider exposing some of the weight knobs (eg, I'd like to tweak it to favour mountainous terrain)!
MattRix 14 hours ago [-]
Fun fact: because WFC is graph-based, you can do stuff like creating a graph where it uses time as a dimension, so you can create animations that “wrap” in time.
In this rabbit example I made 8 years ago, the WFC solver ensures that the animation must loop, which means you will always end up with an equal number of births and deaths.
"WebGPU is not available on your device or browser.". Other 3d demos works fine though. Tried Firefox and Opera on mobile.
socalgal2 11 hours ago [-]
what's your device? guessing android? new? old? Has Firefox shipped WebGPU on Android? MDN says no, though it does claim Opera has.
profer602 12 hours ago [-]
Interesting exploration of WFC on a non-square grid. The constraint propagation challenges must be significantly more complex than the 'canonical' example. Makes me wonder if a different constraint solver (e.g., constraint logic programming) might offer advantages in terms of expressiveness and performance for these more complex topologies.
nickandbro 17 hours ago [-]
This looks amazing man, seriously good job with this.
jbmsf 14 hours ago [-]
Years and years ago (pre-smart phone), I built a mobile map and navigation product. Labeling streets was one of the more interesting side quests and the solution I found took a similar approach of generating a large number of candidates, picking one solution, and iterating. It worked quite well in practice.
kevinsync 17 hours ago [-]
Super awesome, love the tilt-shift camera effect!
I was also wishing I could zoom in to human size and run around HAHAHA
matthewfcarlson 14 hours ago [-]
I started on a simple coop top-down pirate game yesterday when this popped up. I will probably switch the map generation to be using something like this tbh
contextfree 17 hours ago [-]
"Stop playing your AI garbage and get to bed!"
"Mooooom! It's not AI garbage, it's classical procedurally generated content!"
behnam_amiri 17 hours ago [-]
This is cool. Curious if you plan on keep it as a map generator or turn it into something more interactive too.
hermitcrab 11 hours ago [-]
The maps look beautiful.
llm_nerd 13 hours ago [-]
This is fun and neat, and looks fantastic, but the generated maps are basically nonsensical, aren't they? Landmasses and waterways and roads and buildings and forests and so on that don't make any logical sense for their placement.
I say this having had a couple of fun "hex-based strategy game hobby projects" over the years (sidenote -- trying to cover a sphere in hexes is actually a non-trivial matter). Invariably I ended up with "to make a map from scratch, first you create the universe" where I'd go through all of the ages, compute waterflows and precipitation, and on and on. Maybe I made the requirements too unreasonable and that's precisely why I never yielded a working game from it.
zimpenfish 12 hours ago [-]
> This is fun and neat, and looks fantastic, but the generated maps are basically nonsensical, aren't they?
WFC lets you address that though with extra constraints. e.g. my bot today generated a church inside a river loop[0] - completely useless! But I could add a rule that says "if you place the church-above-river tile, the tile above that cannot be anything horizontally blocking" (obviously after tagging any relevant tiles as "horizontally blocking" in the tileset) and that would prevent "church in a river loop" situations.
(I've already been working on some extra rules because, e.g., I don't like the one-edge-castle-wall tiles being placed next to each other - you get tiny pasty shaped castles and I hate them.)
"Though hidden from the sea, the castle controls access to Loch Shiel" says Wikipedia. Which is a sensible thing for a castle to do back in the olden times.
Plus it's a tidal island - you can just walk across. Don't even need a drawbridge (although I guess that makes defending attacks from inland a bit tricky.)
Related (?) has anyone else been following the Hytale Worldgen v2? They've built a visual node editor so anyone can create biomes, structures, or complete worlds. I believe there is a competition going on right now.
They are essentially making the entire game based on similar concepts and then using them to develop their core content. Simon is an inspiration and has said they won't be taking investor money so they can stay true to the users and creators.
MattDamonSpace 18 hours ago [-]
Gorgeous
bobek 17 hours ago [-]
Made me smile. Thank you!
deterministic 10 hours ago [-]
Excellent beautiful work. And a great write up. Thanks!
> Model synthesis (also wave function collapse or 'wfc') is a family of constraint-solving algorithms commonly used in procedural generation, especially in the video game industry.
> [...] One of the differences between Merrell & Gumin's implementation and 'wave function collapse' lies in the decision of which cell to 'collapse' next. Merrell's implementation uses a scanline approach, whereas Gumin's always selects as next cell the one with the lowest number of possible outcomes
At what point is this style going to become human style? Kids use LLMs to learn, pick up their patterns, repeat them.
_bent 8 hours ago [-]
just a quick example from the backtracking section:
"Here's the dirty secret of WFC: it fails. A lot. You make a series of random choices, propagate constraints, and eventually back yourself into a corner where some cell has zero valid options left. Congratulations, the puzzle is unsolvable."
BretonForearm 5 hours ago [-]
Besides what others said. The "The Numbers" section is a dead giveaway. LLM likes to generate random summary stats in a metrics grid without any prompting.
coolcoder9520 7 hours ago [-]
The discussion about bitfields vs backtracking here is fascinating. I’ve found that in procedural generation, the moment you move from 'trying to make it work' to 'optimizing the inner loop,' you stop fighting the algorithm and start treating it as a constraint-satisfaction machine.
Moving to bitsets/bitfields is almost always the 'Aha!' moment for WFC performance. It feels like moving from interpreted code to compiled code—you remove so much branching that you're no longer backtracking; you're just pruning a state space. It’s a great example of where 'simple' code often hides massive performance bottlenecks that only show up when your tile set grows.
(Dwarf Fortress is the one procedural game I know - besides maybe its more faithful clones - which isn't static. But the procedural generation there is also mostly not incremental, it generates the whole world beforehand and only some of the fill-in details are incrementally generated).
The holy grail has to be a graph-based refinement/embellishment system, where it generates just the nodes, temporally and spatially, which matter for the situation the player is in.
Furthermore, various heuristics can speed up the backtracking a lot compared to a brute force approach. As anyone who has implemented a Sudoku solver can attest, a brute force backtracking is easy to implement but will immediately get bogged down with slowness.
[1] https://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X
e.g. https://www.minizinc.org/ offers a high level modelling language that can target a few different solver backends
might be pretty good results to completely ignore writing a custom algorithm and drop in an existing industrial-grade constraint programming solver, model your procgen problem using a high level language, and use the existing solver to find you random solutions (or exhaustively enumerate them). then more time to iterate on changing the problem definition to produce more interesting maps rather than getting bogged down writing a solver.
[0] https://potassco.org/clingo/
[1] https://adamsmith.as/papers/tog-wfc.pdf
[2] https://potassco.org/clingo/run/
The goal of the original algorithm ( https://github.com/mxgmn/WaveFunctionCollapse ) is to infer the constraints from a sample, and then run a constraint solver.
Hard-coding the constraints skips the whole point of the algorithm (which is also badly named by the way).
The maps are pretty, but the per-tile build constraints of the WFC build approach means that pretty unnatural generations end up happening because non-local influence is difficult to take into account. I think this may be OK for games where you discover tiles one at a time, but for a full map generator it's not great, and better solutions exist. Red Blob Games did a writeup of a noise-based method which looks superior imo. You can use moisture-tracking approaches for rivers, lay roads, bridges and other artificial elements in a separate pass, and it will likely end up faster and more robust. I think WFC is an interesting programming problem, though, so it was likely fun to implement.
Nonetheless, this was an excellent write-up and impressive demo.
As an aside, if the author reads this, did you consider using bitfields for the superposition state (ie, what options are available for a tile)? I did a wfc implementation a while back and moved to bitfields after a while.. the speedup was incredible. It became faster to just recompute a chunk from scratch than backtrack because the inner loop was nearly completely branchless. I think my chunks were 100 tiles cubed or something.
Yeah, my WFC bot (which happens to generate Carcassonne maps in an amusing coincidence) eventually ended up using https://github.com/bits-and-blooms/bitset which improved things hugely.
> It became faster to just recompute a chunk from scratch
Kinda what mine does - every now and again[0] it stacks the current state and if it gets stuck, just pops the last one and continues from there.
[0] Just checked and it's every `tileCount / 20` iterations, hilariously in a variable named `tenper`. I hate past me.
[0] https://catlikecoding.com/unity/tutorials/hex-map/
https://en.wikipedia.org/wiki/Dorfromantik
WFC is brute-force-simple, but because it’s simple it’s quite computationally inexpensive (unless it hits a lot of dead-ends) and I wouldn’t be surprised if it could often find an adequate solution quicker than a SAT solver. At least for games, where a result doesn’t need to be perfect, just good enough.
[0] https://store.steampowered.com/app/1455840/Dorfromantik/
https://boardgamegeek.com/boardgame/370591/dorfromantik-the-...
In the level data, the start/goal tiles (approx 10x10 blocks of solid ground under the player and goal) and slopes aren't represented by their tile offset in the level data -- whilst all other "ground" tiles are. Instead, for slopes you're only told the start and end coordinates, and they often overlap.
So to render the slopes correctly I had to work out all the rules for which tiles were allowed next to each other, and solve some ambiguity rules -- I figured out that shallow slopes take precedence over steep ones. Eventually I cracked it, but it took quite a week or so of iteration to figure it out.
see https://boardgamegeek.com/boardgame/822/carcassonne
It doesn't help that the figures of speech ai loves to use are those that stress things and create tension and drama. And it uses one in every single paragraph, rendering the text into the literal equivalent of a deepfried faux HDR jpg (or a dialogue scene in a Michael Bay movie).
And beyond those practical concerns it's just hard to gauge how much the author truly understands of what he's writing about (and transitively if it's worth to continue reading)
In this rabbit example I made 8 years ago, the WFC solver ensures that the animation must loop, which means you will always end up with an equal number of births and deaths.
https://xcancel.com/MattRix/status/979020989181890560
I was also wishing I could zoom in to human size and run around HAHAHA
I say this having had a couple of fun "hex-based strategy game hobby projects" over the years (sidenote -- trying to cover a sphere in hexes is actually a non-trivial matter). Invariably I ended up with "to make a map from scratch, first you create the universe" where I'd go through all of the ages, compute waterflows and precipitation, and on and on. Maybe I made the requirements too unreasonable and that's precisely why I never yielded a working game from it.
WFC lets you address that though with extra constraints. e.g. my bot today generated a church inside a river loop[0] - completely useless! But I could add a rule that says "if you place the church-above-river tile, the tile above that cannot be anything horizontally blocking" (obviously after tagging any relevant tiles as "horizontally blocking" in the tileset) and that would prevent "church in a river loop" situations.
(I've already been working on some extra rules because, e.g., I don't like the one-edge-castle-wall tiles being placed next to each other - you get tiny pasty shaped castles and I hate them.)
[0] https://social.browser.org/fileserver/01E5NFWNPGZWNJ0DS1WE88... - bottom 3 rows, just past halfway across
That said, there's an Apple TV video of a castle on an island where my first thought was "why does this exist?"
https://vimeo.com/657386068
"Though hidden from the sea, the castle controls access to Loch Shiel" says Wikipedia. Which is a sensible thing for a castle to do back in the olden times.
Plus it's a tidal island - you can just walk across. Don't even need a drawbridge (although I guess that makes defending attacks from inland a bit tricky.)
https://en.wikipedia.org/wiki/Castle_Tioram
They are essentially making the entire game based on similar concepts and then using them to develop their core content. Simon is an inspiration and has said they won't be taking investor money so they can stay true to the users and creators.
> Model synthesis (also wave function collapse or 'wfc') is a family of constraint-solving algorithms commonly used in procedural generation, especially in the video game industry.
> [...] One of the differences between Merrell & Gumin's implementation and 'wave function collapse' lies in the decision of which cell to 'collapse' next. Merrell's implementation uses a scanline approach, whereas Gumin's always selects as next cell the one with the lowest number of possible outcomes
And then `## Developments` mentions:
"Hierarchical semantic wave function collapse" (2023) Alaska, Bidarra: .. citations of: https://scholar.google.com/scholar?cites=1671019743611687613...
"This map isn't flat — it has 5 levels of elevation."
"The ocean isn't just a blue plane — it has animated caustic sparkles"
"The fundamental issue:" and "The key constraint:"
I still enjoyed the article.
[0] https://github.com/felixturner/hex-map-wfc/commit/1679be
"Here's the dirty secret of WFC: it fails. A lot. You make a series of random choices, propagate constraints, and eventually back yourself into a corner where some cell has zero valid options left. Congratulations, the puzzle is unsolvable."
Moving to bitsets/bitfields is almost always the 'Aha!' moment for WFC performance. It feels like moving from interpreted code to compiled code—you remove so much branching that you're no longer backtracking; you're just pruning a state space. It’s a great example of where 'simple' code often hides massive performance bottlenecks that only show up when your tile set grows.