Sans titre

Before I get into the meat of my argument, let me set the stage. I've been dabbling in procedural dungeon generation for RPGS/roguelikes for a few years now. While I've been rather successful at creating somewhat good procedures, I've always worked "by feel", never fully being able to point at what make dungeons, dungeons. Now, I just recently got my hands on a basic topology book at a local second hand bookstore and started reading through it.

Now, I'm probably not the first one to point this out but dungeon design, more particularily, dugeon layout design, is, at its core, a topological problem. I think what really opened my eyes to this fact was the "dungeon" layout in Slay the Spire and how it's basically just a graph in the topological sense of the word.

The dungeon space of Slay the spire is quite unique in that it is not equally navigable in all direction: once you go forward, you cannot go back. However, it is, from a topological perspective, the only way it differs from dungeon spaces in games such as the binding of isaac or even the OG rogue.

This really opens up a few doors both in terms of dungeon design and game studies. First, by modeling dugeons as topological spaces, we open the door to some very non-euclidian dungeon design, something that intuitive dungeon design hasn't, to my knowledge, done yet. (In my experience, and, admittedly, very lackluster knowledge of topology, most video game dungeons are homeomorphic to a (bounded or unbounded) sphere, but imagine dungeons homeomorphic to a torus, a klein bottle, or any time of strange topological space you can imagine: this really opens the door to some experimental level design)

In terms of game studies, topology provides a framework to analyse video game dungeons. Moreover, while this concerns dungeon layout design, i do believe it to be applicable to level design in general. This has typological consequences that might have not been considered before: homeomorphic level design might be the key to firm definitions for some genres. It also provides a way to analyse and measure level design complexity and provides a way to treat 2D and 3D games in comparable terms.

In my opinion, the possibilities are endless and I'm sure people more knowledgeable about topology will be much more able than me to truly gauge the potential of this.