Since developing DeBroglie and Tessera, I’ve had a lot of requests to explain what it is, how it works. The generation can often seem quite magical, but actually the rules underlying it are quite simple.
So, what is the Wave Function Collapse algorithm (WFC)? Well, it’s an algorithm developed by Maxim Gumin for generating tile based images based off simple configuration or sample images. If you’ve come here hoping to learn about quantum physics, you are going to be disappointed.
WFC is explained briefly in Maxim’s README, but I felt it needed a fuller explanation from first principals. It is a slight twist on a much more broad concept – constraint programming. So much of this article is going to explain constraint programming, and we’ll get back to WFC at the end.
WFC is a very flexible algorithm, particularly with the enhancements I’ve designed, but at the same time, I’ve found it’s quite hard to actually get it to produce practical levels useful for computer games. The key difficulty is WFC doesn’t have any global structure to it, all it does it make the output generation look like the input locally, i.e. when viewing small rectangles of output at a time.
In this article, I share what I’ve learned to take your constraint based generators to the next level.
I recently released an addon in the Unity asset store. It’s actually two addons: Tessera Pro is a fully featured copy, with complete source code, and Tessera which has cut down features, and you just get a precompiled .dll.
I quickly discovered a big problem – if you upgrade from Tessera to Tessera Pro, then all your scenes become broken. You get this error, which is likely familiar to veteran Unity developers.
I’ll go into what’s happening in general, and how I dealt with it.
I’ve been playing a lot of Enter The Gungeon recently. It’s a great, brutally hard, twin stick bullet hell that reminded me a lot of Binding of Isaac. But as I’ve been playing it more and more, I realized that the dungeon design actually shows some subtle genius.
There are many procedural generators out there that produce sensible level layouts that manage pacing and rewards correctly, and there are other generators out there that provide levels that include loops and compact layouts. But it’s hard to find both in a single game. Really, the only other game I’ve heard attempting this is Unexplored.
So, naturally, I broke out the decompiler to reveal all of Gungeon‘s secrets to me. I’ll share with you what I found.
Diablo 1 is a classic 1996 hack and slash action RPG. It was one of the first popular attempts at bringing roguelikes to the masses, from the niche ascii art. It’s spun a host of sequels, and imitators. It’s known for a dark, moody atmosphere that intensifies as the player descends into the dungeon beneath the town of Tristram. It was one of the first games I played with procedurally generated maps, and it blew me away that generating such convincing areas was even possible.
I recently discovered that thanks to the discovery of various debug symbol files accidentally left lying around, several fans took it upon themselves to reverse-engineer the source code and clean it up into a good guess at what the original game is like. Thus began a week long deep dive into how exactly did lead developer, David Brevik, actually craft these levels. It may have taken away some of the magic of the game, but I learnt lots of techniques I think are applicable to anyone developing a similar game, which I share with you below.
The algorithm is simple. Start with the entire area covered in path tiles, then and remove tiles one by one until only a thin path remains. When removing tiles, you cannot remove any tile that will cause the ends of the path to become disconnected. These are called articulation points (or cut-vertices). I use a fast algorithm based on DFS to find the articulation points. I had to modify the algorithm slightly so it only cares about articulation points that separate the ends, rather than anything which cuts the area in two. After identifying articulation points it’s just a matter of picking a random tile from the remaining points, and repeating. When there are no more removable tiles, you are done. Or you can stop early, to give a bit of a different feel.
I call it “chiseling” as you are carving the path out of a much larger space, piece by piece.