#rogueviz — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #rogueviz, aggregated by home.social.
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A minor, but still quite large, update to HyperRogue!
Suggest moves after 3 incorrect attempts, grow Ivy through narrow chasms, use compasses, rulers and non-Euclidean tools in the built-in drawing tool, more intuitive touch dragging, bugfixes and more!
https://github.com/zenorogue/hyperrogue/releases/tag/v13.1l #noneuclidean #roguelike #mathart #tessellation #HyperRogue #RogueViz #noneuclideanGeometry
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A minor, but still quite large, update to HyperRogue!
Suggest moves after 3 incorrect attempts, grow Ivy through narrow chasms, use compasses, rulers and non-Euclidean tools in the built-in drawing tool, more intuitive touch dragging, bugfixes and more!
https://github.com/zenorogue/hyperrogue/releases/tag/v13.1l #noneuclidean #roguelike #mathart #tessellation #HyperRogue #RogueViz #noneuclideanGeometry
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A minor, but still quite large, update to HyperRogue!
Suggest moves after 3 incorrect attempts, grow Ivy through narrow chasms, use compasses, rulers and non-Euclidean tools in the built-in drawing tool, more intuitive touch dragging, bugfixes and more!
https://github.com/zenorogue/hyperrogue/releases/tag/v13.1l #noneuclidean #roguelike #mathart #tessellation #HyperRogue #RogueViz #noneuclideanGeometry
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A minor, but still quite large, update to HyperRogue!
Suggest moves after 3 incorrect attempts, grow Ivy through narrow chasms, use compasses, rulers and non-Euclidean tools in the built-in drawing tool, more intuitive touch dragging, bugfixes and more!
https://github.com/zenorogue/hyperrogue/releases/tag/v13.1l #noneuclidean #roguelike #mathart #tessellation #HyperRogue #RogueViz #noneuclideanGeometry
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A minor, but still quite large, update to HyperRogue!
Suggest moves after 3 incorrect attempts, grow Ivy through narrow chasms, use compasses, rulers and non-Euclidean tools in the built-in drawing tool, more intuitive touch dragging, bugfixes and more!
https://github.com/zenorogue/hyperrogue/releases/tag/v13.1l #noneuclidean #roguelike #mathart #tessellation #HyperRogue #RogueViz #noneuclideanGeometry
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An aperiodic tessellation of the hyperbolic plane, found by Toimine in the #tessellations channel in the HyperRogue discord.
These tiles are equilateral, with edge length of 0.56358, which is less than the 0.56626 that was achieved by the regular {7,3} tiling (which was apparently the previous record for a tiling with equilateral convex tiles).
It is also possible to the connect two pentagons by their "bases" to obtain a funky variant of the {8,3} tiling. Then, we can play with the angles -- for "narrow" tiles, the edge length becomes even smaller, about 0.5436.
The animated visualization also shows some new cool features of the RogueViz expression parser: it can now automatically solve for the edge length which makes the tiling work for the given angle \(\alpha\)!
https://github.com/zenorogue/hyperrogue/blob/master/tessellations/sample/aperiodic_pentagons.tes
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Our new video!
In most of our videos, we have been playing with the non-Euclidean spaces. However, we have not played with the time dimension in them so far. In this video, we will combine spherical and hyperbolic geometry with relativistic effects.
#RogueViz #RelativeHell #mathart #NonEuclideanGeometry #RelativitySpace
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Do you want the hexes on a sphere to be regular?
Or do you want them to be of the same area?
Or do you want straight lines be actually straight? (in one of two ways)
And the same idea with squares.
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The animation on the left shows clearly that the shortest path is the straight line. Unbelievably, there are possible worlds where this would NOT be the case!
For example, it is not true in Discworld from Terry Pratchett's novels, which is famously a flat world. In a flat world, the shortest path is NOT a straight line!
(Based on the map of Discworld from https://www.reddit.com/r/discworld/comments/odrog0/wip_discworld_high_res_map/ )
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Ported Seuphorica (Scrabble solitaire deckbuilder) to RogueViz for a more intuitive and powerful interface!
(1) Infinite square grid, with standard Seuphorica special powers. Letters E and R (inverse colors close to the gigantic EE top left) are "reversing", hence "RE" is accepted and "EE" is accepted multiple times. Note the word GEESE which uses a portal to get a multiplier for gigantic 'E' two times in a single word. "PETER" uses a mirror.
But since this is RogueViz, let us make the board geometry abstract, to have even more fun with geometry and topology!
(2) Usually, words can only go "right" and "down". In hyperbolic geometry, we have holonomy, so "right" and "down" are not globally defined. So we have to accept both directions. (Or, optionally, only accept words if they are valid both ways.)
(3) In this one, "right" and "down" are not globally defined either, but "horizontal" and "vertical" are (in a somewhat twisted way), so Seuphorica "horizontal" and "vertical" multiplier powers can work.
Although the hexagons somehow turn a horizontal word into a vertical one...
#RogueViz #NonEuclideanGeometry #mathart #noneuclidean #HyperbolicGeometry #Seuphorica #scrabble
(to be continued...)
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Developer's intention: A beautiful visualization feature!
What the users share: A chaotic art generator! BREAK THE LIMITS! 🎨🔥
#HyperRogue #RogueViz #HyperbolicGeometry #NonEuclideanGeometry #NonEuclidean
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Developer's intention: A beautiful visualization feature!
What the users share: A chaotic art generator! BREAK THE LIMITS! 🎨🔥
#HyperRogue #RogueViz #HyperbolicGeometry #NonEuclideanGeometry #NonEuclidean
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Developer's intention: A beautiful visualization feature!
What the users share: A chaotic art generator! BREAK THE LIMITS! 🎨🔥
#HyperRogue #RogueViz #HyperbolicGeometry #NonEuclideanGeometry #NonEuclidean
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Developer's intention: A beautiful visualization feature!
What the users share: A chaotic art generator! BREAK THE LIMITS! 🎨🔥
#HyperRogue #RogueViz #HyperbolicGeometry #NonEuclideanGeometry #NonEuclidean
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Developer's intention: A beautiful visualization feature!
What the users share: A chaotic art generator! BREAK THE LIMITS! 🎨🔥
#HyperRogue #RogueViz #HyperbolicGeometry #NonEuclideanGeometry #NonEuclidean
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Added some enemy turrets to Relative Hell! (A game in anti-de Sitter spacetime)
These turrets are as accurate as they could possibly be -- they see our ship, and compute the shooting angle so that the ship would be hit if it did not accelerate in the meantime. This can be seen in the last part of the video where the ship does not accelerate.
Note "see" -- of course, the speed of light is limited in this game, so their information is rather outdated... The bullets move at speed close to the speed of light.
The visuals shown here are not what the player would see but rather a slice of the spacetime at t=0 relative to the ship (the turrets are deterministic so let us assume the ship's AI renders the current state). The "wobbling" of turrets seems to be caused by the Lorentz transformations as the spaceship accelerates.
Also new color scheme inspired by pop spacetime explanations, and using a different projection -- this is essentially Beltrami-Klein but it looks conformal because of the map's rotation causing length contraction. Less straightforward but looks better and less cells need to be rendered, which improves the performance.
RogueViz collection: https://store.steampowered.com/app/2271110/RogueViz_Collection/
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And here is another conformal projection. (Obtained from the last one using inversion.)
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A conformal mapping from ℍ²×𝕊¹ to 𝔼³. This is obtained by using the half-plane model for ℍ², let's say {(x,y): y>0}, and then adding the third dimension by rotating it in the 'yz' plane around the 'x' axis.
#NonEuclideanGeometry #NonEuclidean #RogueViz #mathart -
Some improvements in Nil Rider before the Steam release of RogueViz [1]! Previously the game simply ended when you rode off the surface. Now, you can ride off to reach the layer below -- and because of how straight lines work in this geometry, you can drop directly below!
As explained in our video [2] without gravity objects follow helices, with radius smaller when the slope is closer to vertical. With gravity, the slope changes in time, so the projection of a freely falling unicycle is quite a funny curve (pink).
[1] https://store.steampowered.com/app/2271110/RogueViz_Collection/
[2] https://www.youtube.com/watch?v=FNX1rZotjjI#RogueViz #nilrider #NonEuclidean #NonEuclideanGeometry #mathart #gamedev
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Some improvements in Nil Rider before the Steam release of RogueViz [1]! Previously the game simply ended when you rode off the surface. Now, you can ride off to reach the layer below -- and because of how straight lines work in this geometry, you can drop directly below!
As explained in our video [2] without gravity objects follow helices, with radius smaller when the slope is closer to vertical. With gravity, the slope changes in time, so the projection of a freely falling unicycle is quite a funny curve (pink).
[1] https://store.steampowered.com/app/2271110/RogueViz_Collection/
[2] https://www.youtube.com/watch?v=FNX1rZotjjI#RogueViz #nilrider #NonEuclidean #NonEuclideanGeometry #mathart #gamedev
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Some improvements in Nil Rider before the Steam release of RogueViz [1]! Previously the game simply ended when you rode off the surface. Now, you can ride off to reach the layer below -- and because of how straight lines work in this geometry, you can drop directly below!
As explained in our video [2] without gravity objects follow helices, with radius smaller when the slope is closer to vertical. With gravity, the slope changes in time, so the projection of a freely falling unicycle is quite a funny curve (pink).
[1] https://store.steampowered.com/app/2271110/RogueViz_Collection/
[2] https://www.youtube.com/watch?v=FNX1rZotjjI#RogueViz #nilrider #NonEuclidean #NonEuclideanGeometry #mathart #gamedev
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Some improvements in Nil Rider before the Steam release of RogueViz [1]! Previously the game simply ended when you rode off the surface. Now, you can ride off to reach the layer below -- and because of how straight lines work in this geometry, you can drop directly below!
As explained in our video [2] without gravity objects follow helices, with radius smaller when the slope is closer to vertical. With gravity, the slope changes in time, so the projection of a freely falling unicycle is quite a funny curve (pink).
[1] https://store.steampowered.com/app/2271110/RogueViz_Collection/
[2] https://www.youtube.com/watch?v=FNX1rZotjjI#RogueViz #nilrider #NonEuclidean #NonEuclideanGeometry #mathart #gamedev
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Some improvements in Nil Rider before the Steam release of RogueViz [1]! Previously the game simply ended when you rode off the surface. Now, you can ride off to reach the layer below -- and because of how straight lines work in this geometry, you can drop directly below!
As explained in our video [2] without gravity objects follow helices, with radius smaller when the slope is closer to vertical. With gravity, the slope changes in time, so the projection of a freely falling unicycle is quite a funny curve (pink).
[1] https://store.steampowered.com/app/2271110/RogueViz_Collection/
[2] https://www.youtube.com/watch?v=FNX1rZotjjI#RogueViz #nilrider #NonEuclidean #NonEuclideanGeometry #mathart #gamedev
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Some social network analysis on Metroidvanias.
Data from https://www.reddit.com/r/metroidvania/comments/1dwqjp0/if_you_had_to_pick_5_of_the_best_metroidvanias/, two games are connected (with a weighted edge) when they appear in the same answer.
We arrange the games on the tiles, aiming to minimize the sum of (distance) * (weight). Hyperbolic geometry tends to be be good for this kind of visualization (closeness correlates to edge weight).
Tehora Rogue has run a community detection algorithm (using Gephi) on this network multiple times. This algorithm would find 4 to 6 communities in different runs, the 4 communities shown are based on aggregation of the results.
(There are "green" and "yellow" communities of sets of five games posted by "trolls" who have posted games not mentioned by anyone else, and the main genre splits into "blue" and "red" -- if you know these games, do you have any idea what the blue/red split could mean?In the second picture, the red / blue / green components (excluding trolls) are determined by how often the game appeared in the same community as Iconoclasts / Cookie Cutter / Castlevania: Harmony of Despair. These three games were chosen because they frequently belonged to different communities.
#metroidvania #mathart #socialnetworkanalysis #gamedesign #rogueviz #NonEuclideanGeometry #NonEuclidean #tessellation
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Our new video about the Thurston geometry we have not previously explained in our videos, "the universal cover of the 2x2 special linear group over reals". Why such a name? An exciting travel through spaces of motion, product, and twisted product geometries!
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Finding suitable embeddings for connectomes (spatially embedded complex networks that map neural connections in the brain) is crucial for analyzing and understanding cognitive processes. Recent studies have found two-dimensional hyperbolic embeddings superior to Euclidean embeddings in modeling connectomes across species, especially human connectomes. However, those studies had limitations: geometries other than Euclidean, hyperbolic, or spherical were not considered. Following William Thurston's suggestion that the networks of neurons in the brain could be successfully represented in Solv geometry, we study the goodness-of-fit of the embeddings for 21 connectome networks (8 species). To this end, we suggest an embedding algorithm based on Simulating Annealing that allows us to embed connectomes to Euclidean, Spherical, Hyperbolic, Solv, Nil, and product geometries. Our algorithm tends to find better embeddings than the state-of-the-art, even in the hyperbolic case. Our findings suggest that while three-dimensional hyperbolic embeddings yield the best results in many cases, Solv embeddings perform reasonably well.
Full video: https://www.youtube.com/watch?v=GQKaKF_yOL4 arXiv: http://arxiv.org/abs/2407.16077 with Tehora Rogue #NonEuclideanGeometry #connectome #RogueViz
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CW: high frequency sounds, hyperbolic geometry
Using hyperbolic geometry to create a weird musical instrument.
The drawing tool in HyperRogue lets us to draw on the hyperbolic plane; we combine this with the scrolling animation. This scrolling animation makes the pen move on the surface -- the further we are from the central horizontal line, the faster it moves (a property of hyperbolic geometry); it should of course make some scratching sound when it is drawing, and the frequency of this sound should be proportional to its speed. Also we draw on the Klein quartic to make the display more interesting.
#NonEuclidean #NonEuclideanGeometry #HyperRogue #RogueViz #mathart
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The pattern is broken somewhere in this animation. Can you find the offender?
Probably easier to find the offender in the second one. (Also, can you tell how this was done?)
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Two-point equidistant projection of the hyperbolic plane, but one point is in the center, and the other point is in the infinity, and changes its direction during this animation. The frame where horocycles are mapped to straight lines is insighftul. (Basically, a circle of radius 𝑟 around the center of ℍ² is mapped to a cirlce of radius 𝑟 around the center of 𝔼², and concentric horocycles are similarly mapped to straight lines; these two conditions determine where every point is mapped.) Based on an idea by bengineer8u.
By the way, our video "Portals to Non-Euclidean Geometries" https://youtu.be/yqUv2JO2BCs has just passed 1M views!
#NonEuclideanGeometry #rogueviz #youtube #mathart #HyperbolicGeometry #noneuclidean
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An animation of this game. (In the end, dead groups are removed for scoring purposes.)
Thanks to tres14159 on Twitter for the idea of the animation, and to @henryseg for the suggestion to make the stones larger. This is not a regular tiling, so some stones touch, but in some cases the distances between intersections are larger.
#noneuclidean #noneuclideangeometry #rogueviz #bringsurface #baduk #mathart -
A game of Go on a hyperbolic manifold, played in the HyperRogue discord server, ended like this.
#noneuclidean #noneuclideangeometry #rogueviz #bringsurface #baduk -
Our new video! We take you on a journey through a small game world and showcase the non-Euclidean transformations of its third dimension.
Full video on YouTube: https://youtu.be/Rhjv_PazzZE #noneuclidean #mathart #mathviz #NoneuclideanGeometry #rogueviz
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If they expand in the same 'z' direction, but with different rates instead, it looks more like a horosphere (compare the first visualization in this thread); this is why hexes in the visualization below are squished when we look at them orthogonally from far away. #mathart #noneuclidean #hyperrogue #rogueviz #mathviz #visualization