I actually purchased Hyperbolic Rogue, a few days ago. I enjoy it quite a bit, but I feel I need to stop and go through the walkthrough, for some of the biomes I've come across. I also feel I might need to map out a few quick methods of finding higher level biomes, if their relationships are fixed (in some way). I enjoy looking for The Crossroads and The Wall, as I'm fairly sure I've worked out why those rather unique areas are the way they are. I'm really looking forward to Hyperbolica. I've been watching it's development, for a while now, and I must admit to being excited by it's potential. These more advanced mathematical concepts, are SO damn unintuitive (for most people), that we really desperately NEED games like that. People are so much more willing to experiement and learn, with games, than they are with classical teaching, that there's no reasonable way around using videogames, as an educational tool.
I agree that games have a unique capacity to teach. I think it's because they model the exploration and experimentation process that kids naturally use when learning. However, I think it's something that will depend entirely on distributed works by independent creators (like the two you mentioned). Governments and other centralized efforts will fail here. Games are just too difficult and expensive to create, and there's no standardized process. Most game projects fail - ie produce something of too low a quality to be appealing to many people.
I really have to applaud the ingenious horror of this creation, I can’t imagine the nightmare that would be solving this, and I’ll be up at night wondering how something this evil could exist. Thank you for sharing!
This is absolutely amazing - a great iteration on the previous form of this idea. Are the frame and tile models publicly available for folks with their own 3d printers, or do you prefer to just offer those on Shapeways?
nightmare fuel. i am still waiting for - a hyperbolic towerr-defense game - a hyperbolic citybuilder (with zombie-like foes) (tower defense with growing borders) - a hyperbolic fascorio-like game (hyperbolic train/pipe/conveyor networks) - a hyperbolic real time strategy game the fun part is, that ranged units cover much more space, that your borders grow more exponentially and that it is VERY likely, that you lose all positions your units in hyperbolic space. the ZenoTheRogue (hyper-rogue is a hyperbolic rogue-like) game channel is a proof of concept for a lot of hyperbolic-space-rendering (and gamification). Some hyperbolic levels have special properties (added symmetries, that mostly locally turn space into endless vortexes/tunnels) The main issue is, that your hyperbolic map tends to get much bigger much faster (without those symmetry-boundaries), and is is much harder to leave a trail of breadcrumbs to return a key to a chest/gate (which is one of the harder challenges in the game), AND hyperbolic procedural generated maps tend to have harsh discontinuities.
I have started experimenting with a hyperbolic tower defense game, but I did not like the result. I do not have much experience with tower defense though, so maybe this is just because I do not know how to design a good tower defense game. Or maybe I should just experiment with it further.
I have a (simplified) graph-based Factorio implementation as a hobby project, so implementing hyperbolic space would actually mostly be a rendering problem... I am intrigued to try this out! It would be cool to have all of your base accessible via a very short walk regardless of how large it gets
I think the game structure I would most like to see using hyperbolic space would be a real time first person multiplayer game where the horizons of players who's game has progressed for a similar length of time are stitched together, so players are constantly running into each other and have to decide whether to fight or team up, but that kind of game seems a long way off.
That's awesome! I can see a bigger hyperbolic puzzle being made where not all of the hinges can be folded flat. I could even see this going to an extreme where the goal now is to move the empty space from one square to another, and the configuration space for doing so is so sparse that it becomes as much of a challenge as solving the 29 puzzle.
i find it very interesting that the 12-puzzle is unusable in a configuration centered on a saddle-shape, which is a common way of representing hyperbolic surfaces in 3D, whereas the semi-convex configuration, which more closely resembles the bell of a hyperbola, _is_ usable, and i find myself wondering if this is because the configuration subspace with that hyperbolic shape can better mimic the hyperbolic rotations needed to perform a basis transformation (bringing any other point on the hyperbola to the "flat" vertex of that "bell")
There is a brilliant Kinetic Sculpture called Dezimova by Nikolaus Weiler that reminds me much of this! You’d love to see it as it moves with geometric and mathematical prowess. Very satisfying.
It just occurred to me that changing the configuration of the puzzle can change its Gaussian curvature, at least for the 3x3 one. The one where the corners all go the same way has positive curvature, while the one where they face away from one another has negative curvature (or at least approximates it in terms of the shape the puzzle seems to make. I'm not well versed enough in differential geometry to have this be anything more solid than a guess). Perhaps the possible configuration spaces of the puzzle and whether the puzzle can be changed from one shape to another or not relate to this? Negative curvature seems less permissive which I imagine has a lot to do with the fact that tiles folding in opposite directions along the same seam arrest all the movement in that seam. So the more you can fold the tiles in the same direction, the easier the puzzle should be to handle, I think.
That’s more or less how the number on dice are made. The 3D printed plastic is very porous, so I’m not sure how much you have to sand down to get through all of the paint. Also I doubt that you’d get a very clean edge to the painted number this way.
It definitely wouldn’t work the same as the hyperbolic one in the video, with hinges and all that. With every corner being an intersection of three, there’d be no way to bend the puzzle to slide the tiles as if on flat space, unless it’s *really* stretchy. I can roughly picture how it would work with 5 tiles and one empty space, basically a very rounded cube where the sides can slide around a solid sphere piece in the center. Puzzles based on platonic solids made from odd-sided shapes would be trickier because the pieces would have to rotate as well as slide.
idea: the recursive 15 puzzle no, not all the tiles being 15 puzzles, but: you can move around 15 puzzle chunks around, each -well, 14 contain 16 tiles, while 1 contains 15 tiles, but you can move these puzzle chunks, and the puzzle tiles to get to... hold on, 14*16... plus 15... eh, i aint grabbing the calculator right now, but probably a lot.
In an actual hyperbolic space, as opposed to an apeirohedron made of flat faces, could rigid tiles physically slide from one position to another? I suspect one would have to shave off a bit at the corners to get them to move without obstruction, to make the edges line up in a smooth curve.
I think you’re correct - each side of the square would have to be an equidistant curve from the midline. These equidistant curves are not geodesics, unlike the edges of the tiling.
@@henryseg Right, they are curves that are equidistant from a geodesic. I initially said they were horocycles but I think they are not. It would make the whole puzzle kind of rattly and fiddly in a way that the one embedded in (nearly) Euclidean space is not.
hey whats the pattern for puzzle size? (aka how big are ‘squares’ in this tiling) it goes 1,5,13,30,61,125 or for this puzzle since there’s one missing 0,4,12,29,60,124 but either way I can’t tell what the pattern is
I can only find a formula if you substitute the 30 in your pattern with 29. If that is the case, the formula is An=2^(n+1)-3. Which is basically starting at the 3rd power of 2 and take away 3 then the next square minus 3 and so on. Very interesting....
@@bongmuon yeah I noticed that as well and I was going crazy counting over and over and I know it has to be what it is based on divisibility by 5 so whatever the pattern is is really tricky
I believe there are five solved states. It’s easiest to see on the Poincaré disk model pictures. You can rotate the tiles by fifths of a turn, but there are no reflections or other symmetries.
@@alexandremuniz9486 Ah, maybe I didn't mention a further restriction: the arrow on tile n points at the left side of the number on tile n+1. Then I think it is restricted to spiralling out.
Honestly the biggest puzzle for me, is trying to decipher the noise you make at the very start of the video. I know they are words, but what words exactly? Haven't a clue.
wow, i see 2021 has driven you to new levels of insanity in hyperbolic 15 puzzles
love it
your profile pic is what most people look like while solving this
damn that day was crazy thank god i managed to get my head together.
*YES* and Zeno the rogue helped! I don't even know why this gets me so hyped.
YEEEESSSSS
Your zeno the rogue is nothing compared to "zeno the assassin" (zeno zoldyck)
@@hshshshshshshshshshs lmao your zeno the assassin is nothing compared to "zeno the omni king" (zeno sama)
I actually purchased Hyperbolic Rogue, a few days ago. I enjoy it quite a bit, but I feel I need to stop and go through the walkthrough, for some of the biomes I've come across. I also feel I might need to map out a few quick methods of finding higher level biomes, if their relationships are fixed (in some way). I enjoy looking for The Crossroads and The Wall, as I'm fairly sure I've worked out why those rather unique areas are the way they are.
I'm really looking forward to Hyperbolica.
I've been watching it's development, for a while now, and I must admit to being excited by it's potential. These more advanced mathematical concepts, are SO damn unintuitive (for most people), that we really desperately NEED games like that. People are so much more willing to experiement and learn, with games, than they are with classical teaching, that there's no reasonable way around using videogames, as an educational tool.
I agree that games have a unique capacity to teach. I think it's because they model the exploration and experimentation process that kids naturally use when learning.
However, I think it's something that will depend entirely on distributed works by independent creators (like the two you mentioned). Governments and other centralized efforts will fail here. Games are just too difficult and expensive to create, and there's no standardized process. Most game projects fail - ie produce something of too low a quality to be appealing to many people.
I really have to applaud the ingenious horror of this creation, I can’t imagine the nightmare that would be solving this, and I’ll be up at night wondering how something this evil could exist. Thank you for sharing!
i KNEW that id eventually come across a mathematical video that uses hyperrogue! both a great game and great tool.
This is absolutely amazing - a great iteration on the previous form of this idea. Are the frame and tile models publicly available for folks with their own 3d printers, or do you prefer to just offer those on Shapeways?
Just on Shapeways for now. I've not tested my hinge/bolt design on a desktop printer at all, no idea if they would work well.
Any chance to buy the files to try?
I love hyperrogue lol, came across this video by chance and i was glad to hear someone mention it
nightmare fuel. i am still waiting for
- a hyperbolic towerr-defense game
- a hyperbolic citybuilder (with zombie-like foes) (tower defense with growing borders)
- a hyperbolic fascorio-like game (hyperbolic train/pipe/conveyor networks)
- a hyperbolic real time strategy game
the fun part is, that ranged units cover much more space, that your borders grow more exponentially and that it is VERY likely, that you lose all positions your units in hyperbolic space.
the ZenoTheRogue (hyper-rogue is a hyperbolic rogue-like) game channel is a proof of concept for a lot of hyperbolic-space-rendering (and gamification).
Some hyperbolic levels have special properties (added symmetries, that mostly locally turn space into endless vortexes/tunnels)
The main issue is, that your hyperbolic map tends to get much bigger much faster (without those symmetry-boundaries), and is is much harder to leave a trail of breadcrumbs to return a key to a chest/gate (which is one of the harder challenges in the game), AND hyperbolic procedural generated maps tend to have harsh discontinuities.
I have started experimenting with a hyperbolic tower defense game, but I did not like the result. I do not have much experience with tower defense though, so maybe this is just because I do not know how to design a good tower defense game. Or maybe I should just experiment with it further.
I have a (simplified) graph-based Factorio implementation as a hobby project, so implementing hyperbolic space would actually mostly be a rendering problem... I am intrigued to try this out! It would be cool to have all of your base accessible via a very short walk regardless of how large it gets
I think the game structure I would most like to see using hyperbolic space would be a real time first person multiplayer game where the horizons of players who's game has progressed for a similar length of time are stitched together, so players are constantly running into each other and have to decide whether to fight or team up, but that kind of game seems a long way off.
Man a hyperbolic GemTD clone would be awesome, I can only imagine how complex the maze would become.
Hyperbolic factorio sounds terrifying
That's awesome! I can see a bigger hyperbolic puzzle being made where not all of the hinges can be folded flat. I could even see this going to an extreme where the goal now is to move the empty space from one square to another, and the configuration space for doing so is so sparse that it becomes as much of a challenge as solving the 29 puzzle.
Go petition the WCA to add this as an speedsolving event
It's not a twisty puzzle though
@@charlieharrison Clock isn't either
i find it very interesting that the 12-puzzle is unusable in a configuration centered on a saddle-shape, which is a common way of representing hyperbolic surfaces in 3D,
whereas the semi-convex configuration, which more closely resembles the bell of a hyperbola, _is_ usable,
and i find myself wondering if this is because the configuration subspace with that hyperbolic shape can better mimic the hyperbolic rotations needed to perform a basis transformation (bringing any other point on the hyperbola to the "flat" vertex of that "bell")
I don’t know why the shape would be super related. I’m guessing it’s just a parity argument.
I love how you treat these obscure math properties like they're normal everyday stuff.
No no no, the world is not ready for it
3:50 Respectively means in the same order already mentioned but you flipped the numbers.
looks and sounds like something i would love to get my hands on
Just so cool.
There is a brilliant Kinetic Sculpture called Dezimova by Nikolaus Weiler that reminds me much of this! You’d love to see it as it moves with geometric and mathematical prowess.
Very satisfying.
Very cool - I wasn’t aware of this. Dezimova looks like it’s based on six squares meeting at a vertex.
Just looking at this puzzle activates my fight-or-flight response.
grab it and run!
This is frankly frightening. Thank you.
i want hyperbolic game of life
Brilliant as always!
I honestly thought i found Liam Neesons youtube channel
keep it up
* i want one of these just to like. fidget with it
I can see a variation of this being 2+ players where players take turns maneuvering pieces and can manipulate the playing field x times per turn
It just occurred to me that changing the configuration of the puzzle can change its Gaussian curvature, at least for the 3x3 one. The one where the corners all go the same way has positive curvature, while the one where they face away from one another has negative curvature (or at least approximates it in terms of the shape the puzzle seems to make. I'm not well versed enough in differential geometry to have this be anything more solid than a guess). Perhaps the possible configuration spaces of the puzzle and whether the puzzle can be changed from one shape to another or not relate to this? Negative curvature seems less permissive which I imagine has a lot to do with the fact that tiles folding in opposite directions along the same seam arrest all the movement in that seam. So the more you can fold the tiles in the same direction, the easier the puzzle should be to handle, I think.
0:06 amgon us.. agongus
sus
there is a guy who is making another game called "hyperbolica" and it looks like a really good game so far.
Wow, crazy but challenging puzzle.
I suppose easily wrapping my head around this one is a first step to being able to adeptly intuit 5D space
could you print the tiles with extruded numbers, paint the whole tile, then simply sand down the extruded number to remove paint from it?
That’s more or less how the number on dice are made. The 3D printed plastic is very porous, so I’m not sure how much you have to sand down to get through all of the paint. Also I doubt that you’d get a very clean edge to the painted number this way.
It sounds kinda stupid but this makes my brain hurt.
i cant resist saying it anymore
This looks like something I'll break out of frustration trying to force a bend.
and break horribly :D
Would it be possible to make a spherical puzzle like this with 3 squares to a vertex? I think that would be cool
Yes, the holonomy mazes use a similar idea but on a sphere. Stay tuned for a 15-puzzle-like puzzle on the sphere.
It definitely wouldn’t work the same as the hyperbolic one in the video, with hinges and all that. With every corner being an intersection of three, there’d be no way to bend the puzzle to slide the tiles as if on flat space, unless it’s *really* stretchy. I can roughly picture how it would work with 5 tiles and one empty space, basically a very rounded cube where the sides can slide around a solid sphere piece in the center. Puzzles based on platonic solids made from odd-sided shapes would be trickier because the pieces would have to rotate as well as slide.
It's so cool
idea: the recursive 15 puzzle
no, not all the tiles being 15 puzzles, but:
you can move around 15 puzzle chunks around, each -well, 14 contain 16 tiles, while 1 contains 15 tiles, but you can move these puzzle chunks, and the puzzle tiles to get to... hold on, 14*16... plus 15... eh, i aint grabbing the calculator right now, but probably a lot.
In an actual hyperbolic space, as opposed to an apeirohedron made of flat faces, could rigid tiles physically slide from one position to another? I suspect one would have to shave off a bit at the corners to get them to move without obstruction, to make the edges line up in a smooth curve.
I think you’re correct - each side of the square would have to be an equidistant curve from the midline. These equidistant curves are not geodesics, unlike the edges of the tiling.
@@henryseg Right, they are curves that are equidistant from a geodesic. I initially said they were horocycles but I think they are not.
It would make the whole puzzle kind of rattly and fiddly in a way that the one embedded in (nearly) Euclidean space is not.
Excellent!
Looks cool
I would buy this
S: make a spherical 15-4 puzzle
Absolutely horrific to comprehend, I love it
hey whats the pattern for puzzle size? (aka how big are ‘squares’ in this tiling)
it goes 1,5,13,30,61,125
or for this puzzle since there’s one missing 0,4,12,29,60,124 but either way I can’t tell what the pattern is
I can only find a formula if you substitute the 30 in your pattern with 29. If that is the case, the formula is An=2^(n+1)-3. Which is basically starting at the 3rd power of 2 and take away 3 then the next square minus 3 and so on. Very interesting....
@@bongmuon yeah I noticed that as well and I was going crazy counting over and over and I know it has to be what it is based on divisibility by 5 so whatever the pattern is is really tricky
I’m not sure off the top of my head. @ZenoTheRogue would know.
Anxiety is my main feeling whenever i encounter hyperbolic space. Weird..
Amazing!!
Z is a great guy
what an amazing world we line in.. ;9)
Muito bom Parabéns nota 10
i hate this. where can i buy one?
Henry Segerman, Mad Genius.
Um. I am sure there is a solved state but how do you easily check it? Should a puzzle be hard to check the solved state?
If the arrow on tile n points at tile n+1, then it is in the solved state.
@@henryseg Have you counted how many distinct solved states there are?
I believe there are five solved states. It’s easiest to see on the Poincaré disk model pictures. You can rotate the tiles by fifths of a turn, but there are no reflections or other symmetries.
@@henryseg It's possible to spiral in from the outside. Could be considered a symmetry on reversing the arrow direction.
@@alexandremuniz9486 Ah, maybe I didn't mention a further restriction: the arrow on tile n points at the left side of the number on tile n+1. Then I think it is restricted to spiralling out.
Now make it, but as a Klein bottle.
I hate the normal puzzle this looks like a nightmare
This is kinda similar to the rubiks magic + klotski
As a complete dumb dumb, this thing scares the crap out of me
have you tried making tiles able to go to the back of the puzzle
Holy shit a rubiks magic/15 puzzle
i like puzzles
See? This is the nonsense you get when you let people study math.
Why is Loks like amongus
H O W ?
Hi seger
Hyper sonic lion tamer
Honestly the biggest puzzle for me, is trying to decipher the noise you make at the very start of the video.
I know they are words, but what words exactly? Haven't a clue.
OH FU--
Who else thought he said hm at the start
rubiks cube, but not
SUS
amogus
Among us 0:06
Sus
Why
@@gigaprofisi the shape of the figure at the beginning of the video...