you can have two crossing straight lines neither of which intersects a third straight line, even if the lines are infinitely long.) This is the reason why it's so easy to get lost in HyperRogue people are very used to navigating in terms of directions, and in a world where directions don't exist, it's easy to think of your sense of direction as being wrong. normal) space, they don't have a direction, e.g. (You can draw straight lines in hyperbolic space, but unlike straight lines in Euclidean (i.e. So the things you're walking away from can be seen "bunching up" at the edge of the screen they're the same distance apart, but further away, so they're drawn closer together on the screen.Ī side effect of all this is that things tend to swivel around the edge of the screen constantly, and in particular, directions don't exist in hyperbolic space if you run round in a circle, you'll find that you end up back in the same position but the screen is in a different orientation. The answer is that as you move towards something (thus zooming in on it), the areas you're leaving behind you are being zoomed out on, because they're now further away. Now, you might be thinking "if only the world around me is zoomed in, why does me moving not affect the distance between things further away?". (You can think about this as the wolves "zooming in" by aiming for your location "so that they can move faster" this seems like ridiculous and counter-intuitive reasoning but it actually works in practice.) the place you're aiming for) is to run at your current location, then turn and follow the path you used to flee from them. So the fastest way for them to get from their current location to the point you're fleeing to (i.e. The reason they all end up following you in a line is that the distance from you to them is only 7 spaces or so, but the distance between them is much, much larger than that. So those wolves might look close together to each other, but because they're distant from you, you're seeing a zoomed-out view of them the gaps are actually much larger than they look. One of the best mental models I know of for hyperbolic space is that moving towards something "zooms in" on it, and distant areas are "zoomed out". It would be impossible to complete that land with regular geometry but with hyperbolic geometry, you can simply run away, passing in between the wolves, and they will eventually all line up perfectly for you to kill them, for some reason. One of the things that I love about the game is that initially you will die a lot from enemies that don't move how you expect them to due to the hyperbolic space but as you progress, you will get more and more used to this strange world, and will become actually able to use the non-Euclidean geometry to your advantage.įor example, one of the lands of Hyperrogue, the Hunting Grounds, requires you to evade "ambushes" where everytime you pick up treasure, a few wolves come from the very edges of the screen to surround you, with their number increasing with each treasure pick-up. I had no knowledge of hyperbolic space and the only roguelike I had ever played was DCSS before starting Hyperrogue. Roguelike Radio podcast for all things roguelike-y.
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