HyperRogue – A non-Euclidean roguelike | Hacker News Reader

HyperRogue – A non-Euclidean roguelike

roguetemple.com

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HyperRogue is specifically hyperbolic (and very cool! See also RogueVis), but of course there are a number of non-Euclidean roguelikes. One of my favourites is Smart Kobold [1], which really amazed me at the time, particularly as it was made in just 7 days for the 7DRL! It's so called because pathing through a non-Euclidean map is very difficult for a human but trivial for a computer or a kobold. The map looks 2D, but is made out of small pieces that are (seamlessly) joined together at their seams to connect in unexpected ways. Jeff Lait also used the code for other 7DRLs (I honestly wouldn't know which is best to recommend) [2]

[1] http://www.zincland.com/7drl/kobold/

[2] http://www.zincland.com/

You posted similar reply 10 years ago:

https://news.ycombinator.com/item?id=9744353#9746212

:-)

Hah! Thanks, I'd forgotten. I think my older reply was better.

> It's so called because pathing through a non-Euclidean map is very difficult for a human but trivial for a computer or a kobold.

That sounds like an artifact of the display. Pathing through a non-Euclidean map is, for example, a major game mechanic of Super Mario Galaxy; it's not difficult at all.

Super Mario Galaxy is not non- euclidean; it's just a regular 3D projection onto a 2D screen. The spheres you travel on are technically non-euclidean if you consider the surface in a vacuum, but you aren't playing on the surface, you're playing in a full 3D space.

Additionally, 2D sphere surfaces are very understandable because they can actually exist in our 3D world and we're used to them; hyperrogue has a hyperbolic non-euclidean 2D geometry which is impossible in real life, much more confusing, and impossible to display with no confusion. I don't know what Smart Kobold is, but I presume it's also not just a regular 3D game like Super Mario Galaxy.

> but you aren't playing on the surface, you're playing in a full 3D space.

That is not true in any meaningful sense. You can jump. But you can't move through the 3D space. You're stuck to the surface of the closest sphere. All of your pathfinding problems are non-Euclidean pathfinding problems.

If you were a sprite embedded within the surface, moving from sphere to sphere by using pipes, that would add nothing to the difficulty of pathing around the sphere.

Good point, the movement is more isomorphic with a fully spherical 2D geometry game than I was thinking. But I still wouldn't say it qualifies as non-euclidean in the same sense as hyperrogue at all, given that you aren't fully stuck on a sphere (and they don't give any way to change the view to a top down 2D spherical geometry view; because it's actually just a regular 3D game).

More relevantly to your original comment, it is always going to be far easier to understand 2D spherical geometry (possible to create in 3 dimensions, we see it every day) than 2D hyperbolic geometry (not possible to create in 3 dimensions, completely foreign to us), so I don't think it is a 'display' issue at all.

> 2D hyperbolic geometry (not possible to create in 3 dimensions, completely foreign to us)

Foreign to us, yes. It's perfectly possible to represent a hyperbolic paraboloid in three dimensions.

https://mathworld.wolfram.com/HyperbolicParaboloid.html

> so I don't think it is a 'display' issue at all.

...you just complained that moving around a sphere should count as non-Euclidean if it's displayed inconveniently, but not if it's displayed conveniently. But you don't think that's a display issue?

The hyperbolic paraboloid is not an isometric embedding of the hyperbolic plane H2 in Euclidean space E3, because it does not have constant negative Gaussian curvature.

In general it is impossible to have an isometric embedding of H2 in E3, although it is possible to have isometric embeddings of fragments of H2.

If I understand you correctly, the game geometry is actually euclidean but world contains many seamless portals?

I think geometry being euclidean or not is specifically about parallel lines, and the term "non-euclidean" is sightly misused for other kinds of spatial gimmicks. At least that's what I learned after watching several ZenoRogue videos (HyperRogue channel) :)

Yeah, Jeff calls it "non-Cartesian". He changes the topology but the geometry is Euclidean. There are also lots of roguelikes doing other experiments with topology, tilings, dimensions (Verdagon 7DRLs, geometry episode of Roguelike Radio, etc.)

Wouldn't any geometry that violates any of Euclid's five postulates be non-Euclidean? Yes, the parallel lines one is the most famous, but surely a geometry that violates any of the other four would be too.

How would you violate one of the other four?

Postulate 1 defines what a line is.

Postulate 2 defines what a direction is.

Postulate 3 defines what a circle is.

Postulate 4, in modern terms, doesn't say anything at all. (We aren't even sure why the Greeks felt it was necessary to state it!)

Well, for 1, consider spherical geometry. In Euclidean geometry, there can be only one line between any two points. But consider the lines on a sphere between the antipodes (like lines of longitude on Earth) -- there are infinite lines of longitude that connect the North and South Poles, not just one.

That's postulate 5, parallel lines meeting. Postulate 1 says that a line can be drawn between any two points. Drawing more than one line between a certain pair of points doesn't contradict that. If you can draw two lines, you can draw one line.

No. Postulate 1 says that for any two points A and B, there is a line AB connecting them. While you could argue that "infinite lines" are a superset of "a line" it is pretty obvious that Euclid meant one and only one line (which is true in Euclidean geometry)

You don't seem comfortable with math.

You might observe that the way Euclid uses postulate 1 is to provide geometric constructions of shapes. If you want to argue about what he meant, what he meant was "you have a straightedge". Similarly, postulate 3 says "you have a compass", and postulate 2 says... "you have a straightedge".

You've described drawing several parallel lines that meet at two opposite points of a sphere. Postulate 1 has no problem with that - all of those lines are straight. Postulate 5 has a problem with it, because they meet.

If your geometry has portals, the parallel line postulate will no longer hold. If your portals can have different angles between the entrance and the exit you can straight up cross "parallel" lines, and even if you require them to be oriented at the same angle you'll lose "when given a line and a point exactly one parallel line can be drawn".

Euclidean geometry is an extremely precise geometry, and there is nothing wrong with calling any deviation from it "non-Euclidean". Since Euclidean geometry is a fairly specific point in geometry-space, the only real objection is that calling something "non-Euclidean" doesn't tell you much about what it is, but Euclidean geometry isn't a bad choice for a "default" geometry and at least it tells you it's not that. There is no requirement for it to be continuously curved in some spherical or hyperbolic manner to be "non-Euclidean". Even just permitting a single portal into an otherwise Euclidean geometry would utterly shred Euclid's Elements from top to bottom.

By my examination of the original postulates, not only would portals wreck the parallel line postulate, it in fact ruins 4 out of 5 of them, leaving only that a line can be continuously extended (and that line can still self-intersect, which may in fact violate the definition of a "line" and mean all 5 axioms are busted if you really dug in). It means it is no longer possible to draw a line between any two points (portals can shadow portions of the space such that some points are not connectible), cicles lose a lot of their properties that we rely on (imagine the unit circle, and a portal starting x = .5 and going straight up... they're no longer necessarily continuous), right angles may not be equal to each other any more (portals can change the apparent angles, or give two interpretations rather than one), and of course the parallel line doesn't hold. Putting portals into a geometry fairly comprehensively makes it non-Euclidean.

> It means it is no longer possible to draw a line between any two points (portals can shadow portions of the space such that some points are not connectible

This feels a bit like saying that putting a wall in a room makes it non-euclidean since there's now a barrier in the way.

I know where you're coming from, but this is confusing geometry and topology. (Curvature vs. how the space is connected.)

> This feels a bit like saying that putting a wall in a room makes it non-euclidean since there's now a barrier in the way.

Maybe that's what H. P. Lovecraft meant about non-Euclidean architecture in R'lyeh. ;D

(It probably isn't - the quote from The Call of Cthulhu says "the geometry of the dream-place he saw was abnormal, non-Euclidean, and loathsomely redolent of spheres [...]".)

If you define "a line" as "blocked by another line (standing in for a wall)", it would be non-Euclidean, by virtue of breaking the axiom that says a line can be infinite extended, so that's not a particularly compelling argument.

I don't need to "confuse" geometry and topology. Euclid's axioms require both flat geometry and no "connections" in the space. It's right there in the axioms, if you can read them properly. They have no accommodations for "topology", and it is certainly not just a handwave "oh, whatever, it's no big deal" to extend them to handle it.

By that logic, the game Portal is non-Euclidean. Which might be true in a certain interpretation. But nobody looks at portal and thinks it’s anything but a normal 3D world with portals.

Here the geometry is very unusual. But using the existence of portals to define that seems insincere.

It is non-Euclidean. 4 out of 5, if not 5 out of 5, of the postulates that define Euclidean space fail. It can't fail any harder.

This isn't a matter of emotion or feeling like "oh, gee, I don't want to, like, demote the space or make it feel bad for calling it 'non-Euclidean'." This is math. The postulates won't work. The proofs won't hold. Even a single portal in the space make it non-Euclidean. It doesn't fall down a little bit. It doesn't "mostly hold, you know, except for a few exceptions". It breaks the axioms from top to bottom.

I think we both love Math. But I respectfully disagree. These are games. In a game like Portal, standard intuition about geometry mostly applies, as long as there isn’t a portal in the portion of space you’re considering. The boundaries between reality and magic are what make it interesting. And the fact that it’s mostly normal but sometimes not is exactly what makes it interesting. Because for the player, it doesn’t matter if the proofs are invalid, their intuition mostly holds.

In HyperRogue, normal Earth intuition is mostly inapplicable because of the hyperbolic geometry. The fact that it has portals and therefore proofs fail shouldn’t IMHO be the defining features of the world. Unless you think the key audience of the game is topologists or something, but if you care about non-mathematicians getting into the game, I’d say focus on intuition not axioms.

Considered in three dimensions, I would guess that most Rogue-likes (in a narrow, classical sense) are non-Euclidean (in that broad sense): the down stairs on one level don't necessarily line up with the up stairs on the next.

At least in Angband, the game explicitly tells you that you pass through a maze of staircases. The level you just left still notionally exists, but you can never find it again.

(This is also true of the recall effect, for no reason stated by the ingame text. But then again, the ingame text never claims anything other than that you'll recall to a particular depth, as opposed to a particular place.)

No, you are confusing geometry and topology here. Topology does not change when you stretch the space but changes when you cut/glue it. Geometry does not change when you cut/glue but changes when you stretch. So portals change the topology but the geometry is Euclidean (you get a Euclidean manifold). This are the meanings used by mathematicians working in these areas.

(The original meaning is of course about breaking 5th postulate while all the others hold, showing that it was possible was a celebrated result in mathematics, while it is trivial to break the postulates in some arbitrary way.)

The modern meaning of "geometry" may not change, but cutting and gluing space definitely break Euclidean geometry, as in, specifically the one defined by Euclid. You can't break a mathematical system much harder than to kill it at the axiomatic level. 4 out of 5, if not 5 out of 5, axioms do not hold if you include portals. That's pretty dead.

For an analogy: an Abelian group is a structure in which four axioms hold. A non-Abelian group is a structure in which three of these axioms hold, and the fourth does not. It is not a structure in which some random proper subset of axioms holds, because such a notion would be useless. While structures where specific subsets of axioms hold (non-Abelian groups, semigroups, monoids, etc.) are useful.

Jeff Lait is a major source of inspiration to me. I will one day ascend with the black heart of Beazl'bub!

Previously:

How to create a game using hyperbolic geometry? (2020) - https://news.ycombinator.com/item?id=36448270 - June 2023 (44 comments)

HyperRogue: A puzzle roguelike in a non-Euclidean world - https://news.ycombinator.com/item?id=26073813 - Feb 2021 (34 comments)

HyperRogue – a non-Euclidean roguelike - https://news.ycombinator.com/item?id=17432974 - June 2018 (38 comments)

HyperRogue – A non-Euclidean roguelike - https://news.ycombinator.com/item?id=9744353 - June 2015 (33 comments)

Actually highly recommend this game. I got a lot of fun out of it when I discovered it a few years back, and it especially works well as an airplane time waster game. I'm not generally one for roguelikes but this one really is incredibly fun.

You can buy it on steam too if you want to support the developer!

I played this on android a couple of years ago but eventually uninstalled it. Now it appears to be missing from the Play store?

Google Play is not very friendly to small developers who do not want to share their home address (not their fault, it is some recently introduced EU law), but the Android version can be downloaded from itch.io

It's also available in the official F-Droid repo: https://f-droid.org/packages/com.roguetemple.hyperroid

> some recently introduced EU law

Is it?

you can get it here: https://f-droid.org/packages/com.roguetemple.hyperroid/

I like the concept, but from the video it feels a bit claustrophobic.

Nah. It's ultra boring in comparison to nethack, pathos or more complex games like revengate(!) or greedy cave.

My listing of similar games:

- Grim Omens 3/5 - Revengate 4/5 - Dungeon Crawl Soup (on pc) 4/5 - The greedy cave 5/5 - Pathos 4/5

>ultra boring

Of course, this is just your opinion, presented as an objective fact.

HyperRogue is one of the few roguelikes that I got sucked into. In comparison, I never "got" DCSS and despite several tries I always got bored immediately.

I like hyperrogue but I think it is arguable that it is not very good as a roguelike; I like it more as a puzzle game. The thing is that in hyperrogue each of the worlds is almost entirely self-contained, and the choices you make in one world, or the order you go through the worlds, do not really impact the overall run in any major way. So it lacks the combinatorial explosion of possibilities that many good roguelikes (incl nethack) have.

Everybody understands that it's an opinion, it's a social convention, no need to spell it out. Just like people saying "broccoli are bad" doesn't need to be subtitled with "it's a matter of taste" or this dress looks ugly implies that it's a subjective take on aesthetics.

Brogue (Community Edition) also is awesome!

https://github.com/tmewett/BrogueCE

Nethavk is much much too baroque, a confusion of ideas and one-turn unavoidable deaths (well, avoidable if you know the secret handshake)[0]. It's like a cupcake recipe that has 40 ingredients and is dripping with extra stuff on top.

Brogue, on the other hand, is perfectly simple but perfectly well-executed, a five-ingredient recipe that lets every ingredient shine.

Like other sibling comment said, I think it's just your personal opinion. I don't think The Greedy Cave is that complex or belong to traditional roguelike category, more like MMO's grindy number game with some microtransaction.

ahhh, rainy sunday and i get a recommendation for abstract indie games, today is going to be a good day...

...Project Silverfish[0] is really entertaining so far...

[0]https://store.steampowered.com/app/2941710/Project_Silverfis...

The curse of Hacker News broke the website

AppStore says it’s not available in Canada for some reason.

AppStore only accepts games compiled in a new version of XCode, and I have only a very old Mac on which it does not seem possible to install such a new version.

Imagine this inside miegakure (https://miegakure.com/)

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