#rogueviz — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #rogueviz, aggregated by home.social.
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The catalog of tessellations in https://zenorogue.github.io/tes-catalog/ is updated!
It used an external image hosting service which is down now. So now, the images are generated on the fly! This also lets you change the settings (use different projections if you want to use "conformal egg" or conformal square or band etc., coloring schemes, change the size/detail level, etc.).
Most tessellations in the catalog by Marek Čtrnáct. There is also this new collection of tilings by Marek and Alessandro Longo: https://tiling-atlas.vercel.app/
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The catalog of tessellations in https://zenorogue.github.io/tes-catalog/ is updated!
It used an external image hosting service which is down now. So now, the images are generated on the fly! This also lets you change the settings (use different projections if you want to use "conformal egg" or conformal square or band etc., coloring schemes, change the size/detail level, etc.).
Most tessellations in the catalog by Marek Čtrnáct. There is also this new collection of tilings by Marek and Alessandro Longo: https://tiling-atlas.vercel.app/
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The catalog of tessellations in https://zenorogue.github.io/tes-catalog/ is updated!
It used an external image hosting service which is down now. So now, the images are generated on the fly! This also lets you change the settings (use different projections if you want to use "conformal egg" or conformal square or band etc., coloring schemes, change the size/detail level, etc.).
Most tessellations in the catalog by Marek Čtrnáct. There is also this new collection of tilings by Marek and Alessandro Longo: https://tiling-atlas.vercel.app/
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The catalog of tessellations in https://zenorogue.github.io/tes-catalog/ is updated!
It used an external image hosting service which is down now. So now, the images are generated on the fly! This also lets you change the settings (use different projections if you want to use "conformal egg" or conformal square or band etc., coloring schemes, change the size/detail level, etc.).
Most tessellations in the catalog by Marek Čtrnáct. There is also this new collection of tilings by Marek and Alessandro Longo: https://tiling-atlas.vercel.app/
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In some games (Terraria, Noita) the water flow is simulated, as in, if you create a hole in a water body, the water flows out through that hole. Unfortunately, these games are wrong about physics: connected surfaces do not balance to the same level. I do not know any games which do not have this issue.
Here is a simple simulation which does balance correctly. The @ is taken by the currents.
(On the right, it appears that there is more water after the simulation -- this is not a bug, this is because this is the "hyperbolic platformer" and the blocks are actually smaller below. Old video about the platformer: https://www.youtube.com/watch?v=0riQhP_oZlQ )
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In some games (Terraria, Noita) the water flow is simulated, as in, if you create a hole in a water body, the water flows out through that hole. Unfortunately, these games are wrong about physics: connected surfaces do not balance to the same level. I do not know any games which do not have this issue.
Here is a simple simulation which does balance correctly. The @ is taken by the currents.
(On the right, it appears that there is more water after the simulation -- this is not a bug, this is because this is the "hyperbolic platformer" and the blocks are actually smaller below. Old video about the platformer: https://www.youtube.com/watch?v=0riQhP_oZlQ )
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In some games (Terraria, Noita) the water flow is simulated, as in, if you create a hole in a water body, the water flows out through that hole. Unfortunately, these games are wrong about physics: connected surfaces do not balance to the same level. I do not know any games which do not have this issue.
Here is a simple simulation which does balance correctly. The @ is taken by the currents.
(On the right, it appears that there is more water after the simulation -- this is not a bug, this is because this is the "hyperbolic platformer" and the blocks are actually smaller below. Old video about the platformer: https://www.youtube.com/watch?v=0riQhP_oZlQ )
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In some games (Terraria, Noita) the water flow is simulated, as in, if you create a hole in a water body, the water flows out through that hole. Unfortunately, these games are wrong about physics: connected surfaces do not balance to the same level. I do not know any games which do not have this issue.
Here is a simple simulation which does balance correctly. The @ is taken by the currents.
(On the right, it appears that there is more water after the simulation -- this is not a bug, this is because this is the "hyperbolic platformer" and the blocks are actually smaller below. Old video about the platformer: https://www.youtube.com/watch?v=0riQhP_oZlQ )
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A solar eclipse in a wrapped world.
The moon radius is 2x smaller than Sun radius, but it is also 2x closer than Sun, so it covers the Sun exactly. Also there are actually 8 moons, so the periodic images of Sun are covered too.
The first image uses stereographic projection to achieve 210 degree field-of-vision, which looks cool, although maybe a bit cheating. The second one uses the usual linear perspective.
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A solar eclipse in a wrapped world.
The moon radius is 2x smaller than Sun radius, but it is also 2x closer than Sun, so it covers the Sun exactly. Also there are actually 8 moons, so the periodic images of Sun are covered too.
The first image uses stereographic projection to achieve 210 degree field-of-vision, which looks cool, although maybe a bit cheating. The second one uses the usual linear perspective.
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A solar eclipse in a wrapped world.
The moon radius is 2x smaller than Sun radius, but it is also 2x closer than Sun, so it covers the Sun exactly. Also there are actually 8 moons, so the periodic images of Sun are covered too.
The first image uses stereographic projection to achieve 210 degree field-of-vision, which looks cool, although maybe a bit cheating. The second one uses the usual linear perspective.
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A solar eclipse in a wrapped world.
The moon radius is 2x smaller than Sun radius, but it is also 2x closer than Sun, so it covers the Sun exactly. Also there are actually 8 moons, so the periodic images of Sun are covered too.
The first image uses stereographic projection to achieve 210 degree field-of-vision, which looks cool, although maybe a bit cheating. The second one uses the usual linear perspective.
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Our brain reconstructs the 3D scene based on the angles perceived by both eyes. So (under some natural assumptions) a human in hyperbolic space would perceive it as the Beltrami-Klein ellipsoid model -- their eyes would be at the foci of this ellipsoid!
Note that, in the picture in [2/3], for clarity, the distance between foci was much larger than the distance between the eyes of the Princess. Here is a picture that is more accurate to the size of HyperRogue characters. The cutting plane is more "flat" and the perceived shape of hyperbolic space is closer to a B-K ball than obvious ellipsoid.
(This was inspired by @theking's 2019 post https://www.reddit.com/r/Hyperrogue/comments/aq4i7k/euclidean_depth_perception_in_the_hyperbolic_plane/ abut what hyperbolic space looks like, and the "stretched B-K" result was originally proven by Magma in the HyperRogue discord -- however, Magma's proof only used continuity to show that the ellipsoid model is azimuthal in two points -- but not that they are actually foci.)
[3/3] #hyperrogue #vr #RogueViz #nonEuclidean #noneuclideanGeometry #mathart #geometry
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Our brain reconstructs the 3D scene based on the angles perceived by both eyes. So (under some natural assumptions) a human in hyperbolic space would perceive it as the Beltrami-Klein ellipsoid model -- their eyes would be at the foci of this ellipsoid!
Note that, in the picture in [2/3], for clarity, the distance between foci was much larger than the distance between the eyes of the Princess. Here is a picture that is more accurate to the size of HyperRogue characters. The cutting plane is more "flat" and the perceived shape of hyperbolic space is closer to a B-K ball than obvious ellipsoid.
(This was inspired by @theking's 2019 post https://www.reddit.com/r/Hyperrogue/comments/aq4i7k/euclidean_depth_perception_in_the_hyperbolic_plane/ abut what hyperbolic space looks like, and the "stretched B-K" result was originally proven by Magma in the HyperRogue discord -- however, Magma's proof only used continuity to show that the ellipsoid model is azimuthal in two points -- but not that they are actually foci.)
[3/3] #hyperrogue #vr #RogueViz #nonEuclidean #noneuclideanGeometry #mathart #geometry
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Our brain reconstructs the 3D scene based on the angles perceived by both eyes. So (under some natural assumptions) a human in hyperbolic space would perceive it as the Beltrami-Klein ellipsoid model -- their eyes would be at the foci of this ellipsoid!
Note that, in the picture in [2/3], for clarity, the distance between foci was much larger than the distance between the eyes of the Princess. Here is a picture that is more accurate to the size of HyperRogue characters. The cutting plane is more "flat" and the perceived shape of hyperbolic space is closer to a B-K ball than obvious ellipsoid.
(This was inspired by @theking's 2019 post https://www.reddit.com/r/Hyperrogue/comments/aq4i7k/euclidean_depth_perception_in_the_hyperbolic_plane/ abut what hyperbolic space looks like, and the "stretched B-K" result was originally proven by Magma in the HyperRogue discord -- however, Magma's proof only used continuity to show that the ellipsoid model is azimuthal in two points -- but not that they are actually foci.)
[3/3] #hyperrogue #vr #RogueViz #nonEuclidean #noneuclideanGeometry #mathart #geometry
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Our brain reconstructs the 3D scene based on the angles perceived by both eyes. So (under some natural assumptions) a human in hyperbolic space would perceive it as the Beltrami-Klein ellipsoid model -- their eyes would be at the foci of this ellipsoid!
Note that, in the picture in [2/3], for clarity, the distance between foci was much larger than the distance between the eyes of the Princess. Here is a picture that is more accurate to the size of HyperRogue characters. The cutting plane is more "flat" and the perceived shape of hyperbolic space is closer to a B-K ball than obvious ellipsoid.
(This was inspired by @theking's 2019 post https://www.reddit.com/r/Hyperrogue/comments/aq4i7k/euclidean_depth_perception_in_the_hyperbolic_plane/ abut what hyperbolic space looks like, and the "stretched B-K" result was originally proven by Magma in the HyperRogue discord -- however, Magma's proof only used continuity to show that the ellipsoid model is azimuthal in two points -- but not that they are actually foci.)
[3/3] #hyperrogue #vr #RogueViz #nonEuclidean #noneuclideanGeometry #mathart #geometry
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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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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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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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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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And here is the same visualization style applied to two other map projections.
Equirectangular keeps the scale constant on the equator and meridians. But the squares close to the poles are stretched.
Gall-Peters preserves the relative areas. The poles are even more stretched.
While the Mercator projection fails to preserve the relative sizes, it does map squares to (almost) squares, which made the Mercator visualization look very nice.
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And here is the same visualization style applied to two other map projections.
Equirectangular keeps the scale constant on the equator and meridians. But the squares close to the poles are stretched.
Gall-Peters preserves the relative areas. The poles are even more stretched.
While the Mercator projection fails to preserve the relative sizes, it does map squares to (almost) squares, which made the Mercator visualization look very nice.
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And here is the same visualization style applied to two other map projections.
Equirectangular keeps the scale constant on the equator and meridians. But the squares close to the poles are stretched.
Gall-Peters preserves the relative areas. The poles are even more stretched.
While the Mercator projection fails to preserve the relative sizes, it does map squares to (almost) squares, which made the Mercator visualization look very nice.
-
And here is the same visualization style applied to two other map projections.
Equirectangular keeps the scale constant on the equator and meridians. But the squares close to the poles are stretched.
Gall-Peters preserves the relative areas. The poles are even more stretched.
While the Mercator projection fails to preserve the relative sizes, it does map squares to (almost) squares, which made the Mercator visualization look very nice.
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A yet another visualization of the distortions of the Mercator projection.
An ASCII map using the Mercator projection is projected back on a sphere. In the map, all the characters are of the same size.
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A yet another visualization of the distortions of the Mercator projection.
An ASCII map using the Mercator projection is projected back on a sphere. In the map, all the characters are of the same size.
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A yet another visualization of the distortions of the Mercator projection.
An ASCII map using the Mercator projection is projected back on a sphere. In the map, all the characters are of the same size.
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A yet another visualization of the distortions of the Mercator projection.
An ASCII map using the Mercator projection is projected back on a sphere. In the map, all the characters are of the same size.
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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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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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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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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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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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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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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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A procedurally generated, non-human building. What creatures could live in buildings of this kind?
(There is a correct answer, but other answers are interesting too.)
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A procedurally generated, non-human building. What creatures could live in buildings of this kind?
(There is a correct answer, but other answers are interesting too.)
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A procedurally generated, non-human building. What creatures could live in buildings of this kind?
(There is a correct answer, but other answers are interesting too.)
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A procedurally generated, non-human building. What creatures could live in buildings of this kind?
(There is a correct answer, but other answers are interesting too.)
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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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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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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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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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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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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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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...)