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The mind-bending joys of Non-Euclidean Platform Puzzlers or “Up is down. It’s bigger on the inside”.

Gamingtodaynews1f - The mind-bending joys of Non-Euclidean Platform Puzzlers or "Up is down. It's bigger on the inside".

I just finished the incredibly artistic (if a bit short) Manifold Garden and it made me realize that there is a small but budding genre of puzzle game that I don't think most people even know exists.

The Non-Euclidean Platform Puzzler*

*possibly even higher dimensional worlds

Just to get everyone onto the same page, What do I mean by Non-Euclidean?

There's a lot of great Math videos out there, but I think

does it best in relation to

. The short take of what makes a game world fall into this are the following:
  • Buildings being larger inside than outside
  • Walking in a straight line and returning to where you started
  • Moving downwards to get up higher.
  • Allowing the player to Access

    (movement in the 4th or 5th dimension relative to our 3d world)

As mentioned at the start, the recently released Manifold Garden Is a non-euclidean space, where travel in a single (straight) direction loops back onto itself. You can look out into an infinite world, and see yourself stretching out to infinity. Jump off the ledge and you'll just fall down on top of where you leapt from. Run long enough forward, and you'll find that you're running towards the area left behind.

I think the wonderful Antichamber was the first game to really bring this concept out of tech demo and into a complete game product. It is almost abusive in how it subverts the players natural instincts of how physics and geometry should work in creating a wonderful puzzle platformer unlike anything that had been seen before.

There is another game that I lump into this category, but isn't really non-euclidean, and that is Superliminal. It takes the way that your viewing perspective can make objects smaller or larger, appear flat, or round, and projects that into the game space, allowing you to shrink or grow objects depending on what way you are looking at them, flatten them into a texture, or pulling a painting out into the 3rd dimension. Unlike Anti-chamber and Manifold Garden, Superliminal does feel a bit more like a tech demo than a game, but I think it's a must-buy if you can snag it for less than $10USD. It also has a devkit/level editor available, so there are hundreds of user levels to play through (although truthfully, only about 50 on the workshop or so are good).


I linked to this developer's youtube earlier, but Miegakure is a game that's trying to take 4th dimensional travel (Not including time, 5D if you count that too) and turn it into a game. There is still no release date, so unfortunately there are no truly 4D games out on the market yet.

Why I find these fun

At it's core, these game's use of non-euclidean space for the player to re-think the most basic ways they are interacting with the game-world. You may be able to see your destination just a few feet away, but walking there in a straight line will take an infinite amount of time, so you must navigate along another direction which is much shorter than it appears. Similarly, you know that the switch you need to hit is just around the corner, but you if you go around the corner, you're right back to where you started, so you must take another route, or maybe push another switch which changes how the geometry works and allows you to now go around the corner "normally"

It's this distortion of reality that makes moving around the world into a puzzle. We are hard-wired to instinctively know how to move around in normal, Euclidean 3D space. When the world around us no longer conforms to that you have to actively think about how your movements are being transposed into this new reality. It's not completely alien though. Things like Gravity, momentum/inertia, and Movement in short distances (usually) work the way we expect, so there's a grounding to everything. It's very eerily normal in these games, until it's not.

As was shown in Anti-Chamber, the way the world works can change as needed for the game. Maybe in one section, the total degrees in a circle is only 270, and in another it's 720. As a player you will need to constantly observe how the world is behaving and adjusting your own internal sense of "the way of things" It's this constant mental stimulation of wondering "Am I getting closer to my objective when I move in this way? Has gravity changed?" is what I find so mentally engaging.

I'd love to see more developers explore into this world space, and maybe even break it out of the puzzle platformer and into the action/FPS realm. However I also know this is a very technical challenge and would not be trivial to implement multiple players/entities interacting with the world. The maths behind these worlds are relatively simple, but when you start rendering the same object hundreds or thousands of times from different angles, the way that object is artistically designed and calculated in engine really matters to allow playability. Manifold Garden's William Chyr


In summary, there's a very small group of games out there that play with how reality works on a geometric level, and It's always a blast to play these physics defying games when I find them.

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