Being on a hyperbolic surface instead of strictly flat is certainly non-Euclidean, and this is pretty cool.
Another non-Euclidean approach is that taken by Vicious Orcs: each individual room is Euclidean, and the player can't tell that he's moved from one room to another, but the connections between rooms are arranged such that the overall map doesn't fit in a plane or even a 3 dimensional space. I got very lost and did not finish the game.
That's not all! I know of two other non-Euclidean seven-day roguelikes (7DRLs) Jeff Lait has made. And a very large number of 7DRLs in general. I definitely recommend looking through his games, Jeff Lait has used many wonderful concepts.
For other non-Euclidean space example (although not hyperbolic) there is Antichamber (http://www.antichamber-game.com/). But in general, not only space whole reality was distorted/dream-like in this game.
The game website offers a link to buy the game via Desura - I would urge caution on buying via them as the company who owns them recently filed for bankruptcy [1]. It's unclear what will happen to the site, but it's not worth the risk when you can get it via steam!
I am sad to hear that Desura filed bankruptcy! I try to buy from GOG.com, gamersgate.com or humblebundle.com just so there is some competition in the marketplace.
Thanks for creating the game! I was supposed not to buy any more games this week, but this one clearly deserved an exception. Just two more hours of work, and then I'm gonna play the living hell out of it!
Thanks! I guess there were 11 lands back then, and there are 22 now. And the new ones show many new things in the hyperbolic plane, like wars between huge armies (the Hive), large circles (Camelot, where you have to find the center of a circle of radius 28, and this is challenging), and horocycles (infinite circles -- the Temple of Cthulhu and the Caribbean).
I will think about it :) I am a bit unhappy with gog after buying Spelunky there and seeing that some features (such as the daily challenge) are available only in the Steam version, but I guess this can be done better.
The game looks good, but it makes me wonder are there any clear gameplay advantages/specialties that come from non-euclidean game "board". I mean, as long as the game forms a manifold it is locally euclidean and if we think games like snake where the very euclidean looking board loops around it still has (non-euclidean) geometry of torus.
There is a post on the blog discussing how the hyperbolic geometry affects the map generation and gameplay: http://zenorogue.blogspot.com/2012/03/hyperbolic-geometry-in... It is not up-to-date with some of the newest features, such as the Camelot quest, where you have to find the center of a circle of radius 28, and since such a circle has 31659398 cells inside, this is not trivial.
There is also an Euclidean mode, where you can see for yourself the things which do not work.
Another non-Euclidean approach is that taken by Vicious Orcs: each individual room is Euclidean, and the player can't tell that he's moved from one room to another, but the connections between rooms are arranged such that the overall map doesn't fit in a plane or even a 3 dimensional space. I got very lost and did not finish the game.
http://www.zincland.com/7drl/orcs/