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/. ;)
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.
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.
> 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.
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."
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.
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
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 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.
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.
> 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
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)!
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?
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.
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.
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.
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.
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.
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.
> 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.)
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.
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.
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)
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.
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)
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.
I didn't want to nitpick terminology, but yes, the tile-placement algorithm here is just a way of solving constraint satisfaction problems with DFS using a "minimum remaining values" heuristic [0]. The original use case for generating textures [1] is different in that the constraints are implicit in the input bitmap, but this project is a more straightforward tile placement with explicit constraints.
I think this algorithm is more efficient for generating maps with only local (adjacency) constraints, but setting this up as an integer linear program and plugging it into a constraint solver is more generalizable (say, if you wanted to enforce a constraint that rivers had to flow across the whole map and could not loop).
But I agree "wave function collapse" is not really the best name, for two reasons:
- the original repository mentions "it doesn't do the actual quantum mechanics, but it was inspired by QM", but it implies something QM-related.
- as an ORIE major in college that loved optimization, I think constraint satisfaction problems are really cool and actually somewhat approachable! So calling the heuristic something else like "wave function collapse" might limit people from finding previous work and known improvements (e.g. forward checking).
Colloquially this is what gamedevs mean when they refer to WaveFunctionCollapse (though the constraints may or may not be inferred from tiles or 3D models, depending on the implementation). It may not match the academic terminology exactly
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.
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.
Situation-adaptive generation also gets predictable and boring once you can read it easily. Classic procedural generation is good for perceived variety and breaking small patterns, but it doesn't introduce novelty on its own, it just shifts it from the asset design to the algorithm design.
I think it helps in Dwarf Fortress that you are not really exploring the world (well, unless you play adventurer mode, but that seems far less popular), you pick a site and settle and start building. You see far less of the world than in something like Minecraft. Yes, you get to see more of the world over multiple runs, but it is still far more limited.
Rimworld is interesting here, as it is what I would consider a DF style game. And I would have said the same for it, except that the latest expansion (Oddessy) added space ships that you can build, and fly to another area. While fun this has made the procedural generation show its weaknesses.
(That said, DF world gen is top notch, but probably not quite as good as it may seem due to what I mentioned.)
That's a general problem with procedurally generated content.
Remember that wave function collapse focuses on local optimization. The algorithm can’t take a step back and look at the whole map. That’s why you won’t get a sensible road network. Rivers are only slightly better when the follow height gradients.
What you can do, and this is also a general advice for procgen, is to mix in some templates before WCF runs. Often, a bit of post-processing is needed as well.
The templates can be hand-designed, or generated with simpler procgen code. Place a few towns on the map, connect them with roads, and then let WFC fill in the gaps to create a more interesting landscape.
As I recall, a lot goes into DF's world generation, including erosion simulation and the like to achieve a realistic result. That game is the embodiment of over-engineering, after all.
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.
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.
Hex math is weird. Since there are 6 directions instead of 4, there's no simple mapping between hex positions and 2D x,y coordinates.
There is, a hexagonal grid is isomorphic to a [skewed] rectangular grid, i.e. it can also be indexed with a coordinate pair (u, v). The neighbours are at offsets (+1, 0), (-1, 0), (0, +1), and (0, -1) - just as in a rectangular grid - and the two additional neighbours are at (+1, -1) and (-1, +1). The coordinates in the plane are (x, y) = (√3(u + v/2), 3v/2) or some variation of this, depending on how exactly one lays out the hexagons and picks axes.
It is surprisingly hard to find a good illustration for this, or maybe I am using the wrong search terms, but here [1] is the best one I could quickly find.
That is one of the first results I found and it is probably a great resource if you want to dive into the topic, but it also lacks an image of the rectangular - or rhombic - grid on top of the hexagonal tiling which I think is visually much clearer than those interactive maps highlighting only the axes of the cell under the cursor. But I understand why they made the choice, other coordinate systems do not admit the same type of visualization while the interactive maps are universal in that sense.
As others have said, this is more of a constraint programming system than Wave Function Collapse. Whatever one wants to call it, I liked it.
For guiding the search, you might want to consider search steps that select only one feature, for example that a pair of adjacent tiles should be connected by a road, and just propagate that information. That could be used as a way to guide the search on high-level features first, and then later realize the plans by doing the normal search.
Wave Function Collapse keeps showing up in fascinating places.
What I like about this approach is that it feels less like procedural generation and more like constraint propagation shaping the map
MattDamonSpace | a day ago
gedy | a day ago
contextfree | a day ago
xipho | a day ago
verdverm | a day ago
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.
nickandbro | a day ago
jesse__ | a day ago
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 | 22 hours ago
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.
bobek | a day ago
moi2388 | a day ago
[OP] imadr | a day ago
zparky | a day ago
"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
socalgal2 | 20 hours ago
_bent | 17 hours ago
"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 | 14 hours ago
ArcaneMoose | a day ago
tomtomistaken | a day ago
[0] https://store.steampowered.com/app/1455840/Dorfromantik/
bhaak | a day ago
https://boardgamegeek.com/boardgame/370591/dorfromantik-the-...
the_mitsuhiko | a day ago
bhaak | a day ago
kevinsync | a day ago
I was also wishing I could zoom in to human size and run around HAHAHA
matthewfcarlson | 23 hours ago
schemathings | a day ago
zparky | a day ago
schemathings | a day ago
behnam_amiri | a day ago
rhdunn | a day ago
jcalx | a day ago
[0] https://catlikecoding.com/unity/tutorials/hex-map/
meander_water | 18 hours ago
jcul | a day ago
shoo | 23 hours ago
see https://boardgamegeek.com/boardgame/822/carcassonne
rafram | 16 hours ago
porphyra | a day ago
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
shoo | 23 hours ago
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 | 23 hours ago
[0] https://potassco.org/clingo/
[1] https://adamsmith.as/papers/tog-wfc.pdf
[2] https://potassco.org/clingo/run/
felixturner | 17 hours ago
mzl | 13 hours ago
westurner | a day ago
> 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...
ionwake | a day ago
btbuildem | a day ago
OscarCunningham | a day ago
teamonkey | a day ago
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 | 21 hours ago
jbmsf | 23 hours ago
z3t4 | 23 hours ago
socalgal2 | 20 hours ago
foota | 23 hours ago
MattRix | 23 hours ago
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
llm_nerd | 22 hours ago
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 | 22 hours ago
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
socalgal2 | 20 hours ago
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
zimpenfish | 19 hours ago
"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
profer602 | 22 hours ago
djray | 21 hours ago
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.
refulgentis | 21 hours ago
socalgal2 | 20 hours ago
rafram | 16 hours ago
wmil | 15 hours ago
hananova | 21 hours ago
iamjs | 21 hours ago
_bent | 17 hours ago
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)
hermitcrab | 21 hours ago
deterministic | 19 hours ago
juleiie | 19 hours ago
linkdd | 19 hours ago
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).
nextaccountic | 15 hours ago
jcalx | 6 hours ago
I think this algorithm is more efficient for generating maps with only local (adjacency) constraints, but setting this up as an integer linear program and plugging it into a constraint solver is more generalizable (say, if you wanted to enforce a constraint that rivers had to flow across the whole map and could not loop).
But I agree "wave function collapse" is not really the best name, for two reasons:
- the original repository mentions "it doesn't do the actual quantum mechanics, but it was inspired by QM", but it implies something QM-related.
- as an ORIE major in college that loved optimization, I think constraint satisfaction problems are really cool and actually somewhat approachable! So calling the heuristic something else like "wave function collapse" might limit people from finding previous work and known improvements (e.g. forward checking).
[0] https://www.cs.cornell.edu/courses/cs4700/2011fa/lectures/05...
[1] https://github.com/mxgmn/WaveFunctionCollapse
swiftcoder | 5 hours ago
andrewingram | 18 hours ago
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.
vintermann | 12 hours ago
(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.
orbital-decay | 8 hours ago
antonvs | 7 hours ago
It feels a bit like the graphical equivalent of Markov chain text generation.
VorpalWay | 7 hours ago
Rimworld is interesting here, as it is what I would consider a DF style game. And I would have said the same for it, except that the latest expansion (Oddessy) added space ships that you can build, and fly to another area. While fun this has made the procedural generation show its weaknesses.
(That said, DF world gen is top notch, but probably not quite as good as it may seem due to what I mentioned.)
bhaak | 6 hours ago
Remember that wave function collapse focuses on local optimization. The algorithm can’t take a step back and look at the whole map. That’s why you won’t get a sensible road network. Rivers are only slightly better when the follow height gradients.
What you can do, and this is also a general advice for procgen, is to mix in some templates before WCF runs. Often, a bit of post-processing is needed as well.
The templates can be hand-designed, or generated with simpler procgen code. Place a few towns on the map, connect them with roads, and then let WFC fill in the gaps to create a more interesting landscape.
elestor | 4 hours ago
MITSardine | 4 hours ago
zem | 10 hours ago
https://en.wikipedia.org/wiki/Dorfromantik
netdevphoenix | 10 hours ago
danbruc | 5 hours ago
There is, a hexagonal grid is isomorphic to a [skewed] rectangular grid, i.e. it can also be indexed with a coordinate pair (u, v). The neighbours are at offsets (+1, 0), (-1, 0), (0, +1), and (0, -1) - just as in a rectangular grid - and the two additional neighbours are at (+1, -1) and (-1, +1). The coordinates in the plane are (x, y) = (√3(u + v/2), 3v/2) or some variation of this, depending on how exactly one lays out the hexagons and picks axes.
It is surprisingly hard to find a good illustration for this, or maybe I am using the wrong search terms, but here [1] is the best one I could quickly find.
[1] https://www.researchgate.net/figure/Rhomboidal-and-hexagonal...
swiftcoder | 5 hours ago
danbruc | 3 hours ago
mzl | 4 hours ago
For guiding the search, you might want to consider search steps that select only one feature, for example that a pair of adjacent tiles should be connected by a road, and just propagate that information. That could be used as a way to guide the search on high-level features first, and then later realize the plans by doing the normal search.
priowise | 3 hours ago