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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.

[1] https://en.wikipedia.org/wiki/Knuth%27s_Algorithm_X

Oskar Stålberg used wave function collapse for various games, including Townscaper. He talks about it here: https://www.youtube.com/watch?v=Uxeo9c-PX-w&pp=ygUhdG93bnNjY... (SGC21- Oskar Stålberg - Beyond Townscapers).

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.

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.

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!

[0] https://catlikecoding.com/unity/tutorials/hex-map/

AI;DR. Can the author please just post the prompt?

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?

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.

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/. ;)

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.

OP is probably familiar but this site has a lot of good examples of hex math with code examples - https://www.redblobgames.com/grids/hexagons/

Reminds me of Dorfromantik[0].

[0] https://store.steampowered.com/app/1455840/Dorfromantik/

This is absolutely beautiful, I could even tell I was going to like it from the title. Good job.

"WebGPU is not available on your device or browser.". Other 3d demos works fine though. Tried Firefox and Opera on mobile.

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)!

That "Carcassonne" game sounds really fun. I'd never heard of it before.

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.

https://xcancel.com/MattRix/status/979020989181890560

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.

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.

"Stop playing your AI garbage and get to bed!" "Mooooom! It's not AI garbage, it's classical procedurally generated content!"

This looks amazing man, seriously good job with this.

Super awesome, love the tilt-shift camera effect!

I was also wishing I could zoom in to human size and run around HAHAHA

This is cool. Curious if you plan on keep it as a map generator or turn it into something more interactive too.

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.

Made me smile. Thank you!

Gorgeous

Beautiful work!

Model synthesis: https://en.wikipedia.org/wiki/Model_synthesis :

> 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...

Real engineering skills, I love it.

This entire article reads like it was fully written by AI unfortunately