I think you can make a skew monoportal. Look at your skew portals demonstration. Observe how the other side looks the same through both portals. Simply remove a piece of both portals so that their edges line up and put them together like you put together the regular monoportal.
The idea of a monoportal with the fact that portals come from one connected surface that seperates into two sides, makes me want to create a Moebius portal.
Ive been thinking about a non orientable 3d manifolds (not to be confused with the klein bottle which is a 2d surface) for a while and Im looking foreward to seeing one
this is beautiful you now realize that its your duty to develop a new puzzle game using these complex portals you invented, right? if you dont, no one else will, and they may be lost forever to obscurity.
"no one else will" ??? no someone else will for sure, what you talking about lol The fate of portals dont rest on this mans sholders, why you think he made thise videos in the first place? Because portal exist. Thaats the beauti of human lerning, we build one what those in the past lerned and discover more and more
I met a guy in Skövde, Sweden like... ten years ago... experimenting with a lot of this for a puzzle game he was making at the time. The idea was pretty unique and he used these portals as doors of connecting a series of seemingly identical rooms with various geometries. It looked like you were inside of a singular infinitely repeating prism connected by door ways on all sides, but by walking into a wall you'd find you were traversing non-linear portals. These typically were mirror dimensions and so on with wildly different transformations once inside. You could use the portals to scale, distort, and skew objects to solve perspective based puzzles. Going straight in one direction would eventually return you to the center of the complex with your original transformation. It was genuinely really clever, and I think he might have beat the OP to experimenting with some of these ideas.
Actually, a game already exists that does some of these things, it's called _Frames._ But it's still "sort of" a 1:1 correspondance between _pairs_ of frames, while this N-portal paradigm I don't think I've seen before...
Mathematitians and scientists: *try to understand properties of teleportation and movement in space for centruies* Portal players: *try to understand portal phenomena and paradoxes for years* Optozorax: There. I did it for you. And as a bonus, I made infinite more kinds of portals.
This feels like something that would happen if you combined SquishCraft with Patrick's Parabox and subtracted Sokoban. Logically straightforward, but only obvious _in hindsight._
squishcraft’s dev bcat112a actually made a puzzle game with a very similar line of thinking called portalsnake, in which you are surprisingly able to make every portal featured inside this video! you just have to use enough sets of 2-portals for the more complex portals, like 3 sets of 2-portals to create a 3-portal (it took me a moment to make sure that they were all possible, i was actually originally writing this comment saying that it would be interesting for them to add these portals shown in the video until i realized lol) theres also a ton more interesting and mind-warping features in the game, like the duplication portals seen in the beginning of the video. i definitely recommend you check it out if you liked squishcraft and you liked the concepts in this video. (i honestly like portalsnake a little more than squishcraft imo, both games are still amazing though)
@@cipeman3498 oh THAT'S the game I'm thinking of! I knew there was something with that aesthetic that had portals in it but I wasn't seeing any in screenshots of SquishCraft.
also anyone who hasn't heard of those games: go play Patrick's Parabox. if you're the kind of person to be reading comments below a video like this, you'll enjoy Patrick's Parabox. it has stellar difficulty pacing and is well polished.
If you dont get some kind of acknowledgement from Valve or even Gabe Newell himself, then I will be very disappointed. The mind-bending mathematics and graphics programming thats required to make this work and then being able to simplify it and explain it to an audience is simply incredible.
Like, each of these chapters could've been it's own video. Like I'm halfway starting to grasp one of em and he smashes the next one into my face. Amazing video
Portals are really a cool entry point to a lot of the concepts in 3D geometric topology. Thurston has a great video about knotted portals and their relation to 3D manifolds
@@moyo8960 I don't think William Thurston had a channel, but him talking about knotted portals is called "Knots to Narnia", that's probably what they're talking about
I like the fact that, the way we "construct" the complex portals in this video is exactly the way we learn science (math/phys/chem) at school. We start off with the most simple concept (two-part portal), prove its validity, then use that to build up more complex concept. As long as the math is still correct the new concept (new kind portals) is also valid. Also we have innovate portals, which means.. Portal 3 confirmed?
The three-way portal is just 3-pairs of normal portals.how would you visualize the portal entrance when there are just two portals placed? Aaandd.. the surface needed to place such kind of portal would be really inconvenient
5:10 "...even though it seemed like such a simple thing." Мой брат во Христе you just answered a question that most people couldn't even begin to philosophize about, let alone calculate the answer to.
3:32 So if a triple portal is functioning than same as 2 portals, the numbers of portals in a complex frame like at 5:17 could be deduced by counting the number of holes in the frame using topology. The number of portal would be the amount of holes + 1.
I'm not sure the reverse works, interestingly. The frame of the triple-portal is topologically equivalent to a "two-holed donut" but if we turn that into a frame we'd get something like two adjacent squares, which results in 2 portal pairs rather than a triple-portal. You can imagine taking the triple portal and slowly shrinking one of the three ends until it just becomes a dividing line between the halves of the remaining two. I've done some thinking, here's what I've been able to come up with. Far from anything rigorous, so corrections are welcome! Let's call a normal portal a "2-portal", a triple portal a "3-portal", and so on. If we have a frame with 1 hole (i.e. donut), we can only create a single 2-portal. With 2 holes (2-holed donut), we've just seen we can either have two 2-portals or one 3-portal. We can imagine pulling the middle section of the donut out to create the "3-branched frame" seen at 4:00 in the video. With 3 holes (3-holed donut) it gets more complicated. We can again have three 2-portals, as expected. We can also take either one of the middle sections and pull them out to obtain a 3-portal and a 2-portal. If we pull out both middle sections, we'd get a portal with a frame that looks a bit like "⟩-⟨". Thinking about it, this can split into 4 entrances: "\_/", "/‾\", "⟩", and "⟨". Therefore this is a 4-portal! Based on this, we know trivially that a frame of genus g (a g-holed donut) can definitely correspond to g 2-portals or a single g-portal. We also get less trivial combinations in between. I conjecture that whenever we "pull out a middle section" between an n-portal and a 2-portal, we get an (n+1)-portal in return. Similarly an n-portal and an m-portal together make an (n+m-1)-portal. If this is the case, then the possible portal combinations are given by all the _lists* of positive integers that sum to the genus g_ (where the degree of the portal is the integer + 1). For genus 3, for example, we can have 1 + 1 + 1 = 3 (three 2-portals) or 1 + 2 = 3 (a 2-portal and a 3-portal) or 3 = 3 (a 4-portal). Genus 4 should then have 1 + 1 + 1 + 1 = 4 (four 2-portals), 1 + 1 + 2 = 4 (three 2-portals, one 3-portal), 2 + 2 = 4 (two 3-portals), 1 + 3 = 4 (one 2-portal, one 4-portal), and 4 = 4 (a 5-portal). Thinking about the setup, this does seem to make sense! We have: "- - - -" or (1,1,1,1), "- - -⟨" or (1, 1, 2), "⟩- -⟨" or (2, 2), "- -¦-" or (1, 3), and ">¦-" or (5). (I did my best with ASCII representation. Spaces denote joined frames with a separation between them, so "- -" would look like a window with a single bar down the middle. The "¦" should be taken as two separate spokes, so "-¦-" is a 4-portal like "⟩-⟨" and ">¦-" is a 5-portal.) * Sidenote: the objects here aren't really "lists / tuples" or "sets", since we care about repetition but not the order of elements. Sets disregard both, while lists / tuples include both! Not sure if there's a name for this kind of object. edits: - formatting - added ASCII of the genus 4-cases
Dude while watching your last video I literally started thinking about a 3 portal portal and I got confused and went into a coma with the video playing on loop and then the notification noise for a new video popped up and I watched it and my thoughts were confirmed
I seriously think all the things you've presented in these videos is going to inspire so many game developers. So many of your discoveries were (as you put it) surprisingly not thought of or discussed before or discovered by accident, but after seeing that it works, it's just feels so intuitive (as intuitive as portals can be, at least) and it just feels right. It's a special thing when that happens.
I've watched your videos in Russian but my poor knowledge of the language got in the way of appreciating all of it. I'm glad that you made an English version.
I love this kind of stuff! I love portals that break geometry, non-euclidean geometry, time travel, timeline manipulation, multiverses, infinite chess, 5d chess, etc. Keep up the great work!
8:00 Please correct me if I'm wrong, but it seems like the fact that an object interferes with itself is not the true reason for why there's no tearing, in fact we can see in the clip shown just before that it still works even if we allow the object to intersect itself. Rather it seems to me that it's because the boundary is mapped onto itself, and tearing can only occur at the boundary
The three-way portal blew my mind. And all the other stuff that I didn't think was possible but clearly is, like a "scaling monoportal". Great videos, love them and your portal experiments.
12:05 those tilings are giving me a mild existential crisis. If you stand in one you see infinite recurring versions of yourself, and because of the finite speed of light they're all actually you at different points in time.
"The light here is not straight" is actually a very common misconception - the light is straight, the space is not. Think of a wormhole as an infinity portal, with many many linear portals stacked together to create what appears as a smooth curve! It's an example of a multiportal, just the limit of an infinite number of them to create a smooth surface.
@@optozorax_en ngl id love to write a game with physically accurate GR simulations but my programming is not there, just the theory. Let alone turning the theory into something I can write haha
A portal is a discrete version of a wormhole , in the same way a polyhedron is a discrete version of a sphere. A polyhedron has zero curvature almost everywhere, except for its vertices where there is "infinite curvature" at a single point. You can walk around a vertex in less than 360° and come back where you started. A space with a (pair of) portal has zero curvature almost everywhere, except for the edge of portal where you can go around it 720° and only then come back
8:58 with n-monoportals, what happens if we set the internal angle to something like 108 degrees instead of 120, so its a pentagon interior angle instead of hexagon, would it create a non-euclidean or hyperbolic area? 12:05 what if a monoportal is bent into a pentagon, does it create another hyperbolic geometry tiling? I would test in the demo but the n-monoportals are limited to integer slices and tilings to 3,4 or 6 sides
Sometimes you realize that your brain is not designed to function a certain way. Major respect to you, sir, for venturing into dimensions the rest of us are too basic to follow.
another interesting case may be to use the inside surface of a larger sphere to inscribe a portal on the outside of a tiny sphere or vice versa, So that reaching into the tiny sphere, makes you dive deeper into a dimension of space. I can imagine some pretty crazy system dynamics of space time fabrics if you managed to somehow apply some constraints towards the stability of each sphere size and how the distancing would work. I could imagine it could tie into the rate of change regarding the transformations from Linear portals to wormholes using distances from bubbles and scales as reference points.
This is the good stuff. I always think about monoportal, but I've never bothered with thinking about tripple portals. It's neat. Though for spherical portals: they're good for transposing two locations and then when you get rid of the portal; you are magically (but not magically) in a new location. This is actually how I imagine teleporting would work, it's dual temporary spherical portals.
Things get more interesting once the flat surface of one of the two connected portals has a curvature, morphing the exiting object. I've made once a small very crude demo in Source engine and the effects were quite funky.
You could probably also make things like pentagonal or heptagonal portal tilings, though they would probably have visible seams between the sides. You can also try 3D tilings like cubic or tetrahedral ones, or something of the sort Also I first saw this thumbnail and thought you managed to come up with knot portals or something, like ZenoTheRogue did. That would be interesting to see you explore
Re 10:09, I suspect that it would be possible to get different fractional displacements by putting an angle through the middle of the monoportal. Instead of constructing it with a 180° rotation, rotate it, for example, 120°. Like normal, the result is a portal that you can't move through the center of because you'll self-intersect. But offset it a third of its height, and it should work. My intuition is that, in general, this needs a 360°/n angle, and the denominator of the offset (in reduced form) must be exactly n.
I remember there's a game called Gateways which is like a 2D portal game, but it has multiple portal types including the scaling portal you mentioned. It has some great puzzles mixing multple different types of portals like that
I love how for the rotating monoportal you just casually say "cut it in the middle and rotate half the reflection in the 4th dimension" like it's something you do every day
This feels like it relates to algebraic topology from the little I know that subject, but I need to study it more. The portals act like homeomorphisms and how we create a bicontinuous map between regions.
There is a portal game on steam called "Frame: Portals on Steroids" that actually uses Monoportals as part of its puzzle design for many levels, it has both "mirror" and "non-mirror" monoportals aswell as scaling and rotating portals and gravity changing and just, it has everything
@@TabbyVee Frame also doesn't have skewed/sheared portals. I'm surprised optozorax calls them "not useful and interesting". At least from a game design perspective I'm sure that some interesting puzzles could be build based on that.
Great job Ilya! I admire your creativity and ability to bring these ideas to life. When you started talking about the portal mosaic, I wondered if it was possible to make an aperiodic mosaic from Penrose tiles? Or for that matter from the Aperiodic Monotile that was found in March 2023. It's interesting whether it's possible or not. 🦎 Отличная робота Илья! Восхищаюсь твоей креативностью и способностью воплощать эти идеи в жизнь. Когда ты начал говорить про мозаику из порталов, я подумал, а можно ли сделать апериодическую мозаику из плиток Пенроуза? Или, если уж на то пошло, из Апериодичной моноплитки, что нашли в марте 2023 года. Интересно в не зависимости от того возможно ли это, или нет. 🦎
With the Square, Hexagonal, and Triangular tilings, you could arrange the portals like any regular polygon to create regular tilings within the portals that can't normally be made in Euclidean space. Theoretically you could even bumping up the number of sides infinitely making a circle, but at that point it would very much not keep parallel lines parallel and may cause all sorts of weirdness with objects being warped as they try to enter a concave portal to exit another concave portal, basically like taking one of the hemisphere portals from early in the video and inverting it's geometry
isn't your "Triple Portal" solution identical to having three pairs of 2-portal systems? In your version where each is a pair of flat surfaces on one of the three portals, if instead you split those surfaces into their component flat parts, then each flat part is just one half of a 2-portal system with one of the halves from the other two original surface portals in the three-part system? I think it would be interesting to explore further and see if a triple-portal system that is "atomic" could exist -- that is to say, a system that could not be divided into smaller 2-portal constituent parts that are equivalent in functionality. Because of the way your triple-portal system works you could use the same principal to design an N-portal system where you effectively cut a circle into N-slices with the borders of each slice being another linked 2-portal system. So instead of having 120 degree slices for a triple portal system made of three 2-portal systems you could use 90 degree slices to make a quadruple portal system which is identical to four 2-portal systems.
*@optozorax* The support-portals, should be some other color or something, so they are visually shown to be "different" from "normal" portal, even if they are also "normal portals".
About the mirror part If you are what's stopping you from going through a monoportal And vampires can't be seen in mirrors This means a vampire can enter the mirror dimension
I used to create Monoportals with the help of the Immersive Portals Mod (for Minecraft!) It could be done simply by placing and entrance side-by-side with its respective exit. Just like you did!
what would a wormhole have to be to actually work? it cant be a portal between an exterior and interior surface of a sphere because that would be like having no portal at all. if the portal was between two exterior surfaces of a sphere then it could move you to a different location but there would be a problem. interior-exterior surface cancel out the curvature of the sphere but exterior-exterior surface must cause space on the other side of the sphere to have a curvature of 2 but if we want the portal to preserve the global curvature of space on the other side we need to somehow make the net curvature between the two portal surfaces to be 0. maybe if you have a gradient of hyperbolically curved space as you approach the portal surface that has a curvature of -1? that way both portal surfaces would have a curvature of zero at their surface? or alternatively, the surface could be a hyperbolic sphere with a curvature of -1 embedded in a space gradient of positive 1? that might look more like the typical wormhole depiction.
with tiled portals, i think you should be able to tile with p much any regular or non regular polygon, regardless of if it'd work in reality, to create some non-euclidean shennanigans like 5 sided "squares" and 720º squares. should be worth a shot
Its Three portals glued together really, isnt it? But one interesting thing i want to know is if you go through the middle, will you split when you cross the border of the other portals? and what happens if you stick one portal through in case it does split ?
is there actually a geometric explanation for portals tho? like one accepted by most mathematicians? we literally got one for knots, its called knot theory.
@@Thebenjiball0 the idea should be something "revolutionary", since the creator emphasizes so much on the fact that he alone discovered something incredible... but it just is a construction, that it alone is something amazing nonetheless, but the naming system ... is just wrong. Triple portal - 3 pairs of normal portal Monoportal - just two ends of a normal portal rotate 180 degrees I mean if you want to name those design, I think the name he gave are pretty cool, but... he isn't answering the question "is a 3-way portal possible?" not to the question "is a 1-way portal possibile?". A more logical answer to the 1-way portal is a portal that has a destination but not a return (that should be the real answer to a question like that) And a 3-way portal should have 3 destinations, really connecting three points in space. So probably the answer will always be no (being compatible with what a portal is) and he didn't discover anything new, except some really cool designs that are illusions of a real answer. I'm not saying it isn't interesting, but calling them "discoveries" is a bit overreacting to creating a cool design of something that already exists. Its not a discovery
@@begbaj uh ok. I agree with basically all of that I guess the triple portal is basically *the* way to do it. because of the split, it is technically just 3 basic pairs. there can't be a more "triple portal" than that. yeah it's not a "new discovery", but it is him discovering. I feel his one-sided portal also is probably the right way to do it. an entrance to a place without return is still basically the same as a normal portal, because it would still need a defined exit point. the exit point would be invisible though, and the object would have to grow into existence from there after entering, which is really weird.
Thinking about the spherical and hemispherical portal and more generalizations; there should be a distortion if both surfaces have the same curvature sign, or otherwise do not match. Idealized rigid objects would not be able to get thru; but if the object is a softbody (not necessarily limp, think about the stuff in BeamNG for example), with sufficient force they should be able to get thru warping portals, and depending on the material's properties and amount of warping, either recover on the other side or come out permanently deformed. And of course, light would get get distorted getting thru.
would be very interesting to see a physics engine integrated into this. Would also be cool if a way for the camera to go through the portals to their alternative universes where implemented. Both ideas are pretty advanced implementation wise but it's just a thought
Just came back after watching brainrot and I feel much better. I believe there are actual academic uses for brainrot if it is capable of cooling down the brain
You should make tiling's that aren't possible in real life, like a tiling that is only octagons. You could also add portals with an interior space, and see how that effects the view. I think portals with an interior space could be easily done by just making the portal go into a tube with another portal on the other end, but wormholes also possess an interior space, so maybe that tube could also be a looping cylindrical mono-portal.
I think you can make a skew monoportal. Look at your skew portals demonstration. Observe how the other side looks the same through both portals. Simply remove a piece of both portals so that their edges line up and put them together like you put together the regular monoportal.
That really works, you are genius!
upd: picture mathstodon.xyz/@optozorax/113766169963404170
This can also be considered as a regular monoportal in a skewed world.
@@optozorax_en can you show how an object wold be affected by a skewed monoportal?
@@optozorax_en can you put spamton into a portal to spread his form across the cosmos?
in english please
Missed opertunity to call the supporting portals "supportals"
Hahaha LOVE it
OMG, this is awesome, will use that name later!
Also using an animation that creates a portal between the letters that then move closer and join together
Combining words like that is called a portmanteau. Yes, that also starts with "port".
@MichaelDarrow-tr1mn because port means to move, like in airport and teleport
The idea of a monoportal with the fact that portals come from one connected surface that seperates into two sides, makes me want to create a Moebius portal.
I haven't put much tought to it but maybe it reduces down to a much simpler kind of monoportal idk
Next video will be about it
@@optozorax_en yooo sick !! can't wait !
Ive been thinking about a non orientable 3d manifolds (not to be confused with the klein bottle which is a 2d surface) for a while and Im looking foreward to seeing one
@@optozorax_en yeah, I remember how I watched your ru videos. Ah, how nice to see you show it all for another ones.
this is beautiful
you now realize that its your duty to develop a new puzzle game using these complex portals you invented, right? if you dont, no one else will, and they may be lost forever to obscurity.
"no one else will"
??? no someone else will for sure, what you talking about lol
The fate of portals dont rest on this mans sholders, why you think he made thise videos in the first place?
Because portal exist.
Thaats the beauti of human lerning, we build one what those in the past lerned and discover more and more
@@MouseGoat I really want to run a game of D&D that has these kind of non-euclidean shenanigans
I met a guy in Skövde, Sweden like... ten years ago... experimenting with a lot of this for a puzzle game he was making at the time.
The idea was pretty unique and he used these portals as doors of connecting a series of seemingly identical rooms with various geometries.
It looked like you were inside of a singular infinitely repeating prism connected by door ways on all sides, but by walking into a wall you'd find you were traversing non-linear portals. These typically were mirror dimensions and so on with wildly different transformations once inside.
You could use the portals to scale, distort, and skew objects to solve perspective based puzzles. Going straight in one direction would eventually return you to the center of the complex with your original transformation.
It was genuinely really clever, and I think he might have beat the OP to experimenting with some of these ideas.
Actually, a game already exists that does some of these things, it's called _Frames._ But it's still "sort of" a 1:1 correspondance between _pairs_ of frames, while this N-portal paradigm I don't think I've seen before...
portal 3
*halfway through the video* "now i'm thinking with portals
unlike you " *thinking with time machine* "
OH MY GOD the triple portal generalization can make such an interesting puzzle game! Aliensrock would play it probably
ALIENSROCK MENTIONED
portalsnake
Mathematitians and scientists: *try to understand properties of teleportation and movement in space for centruies*
Portal players: *try to understand portal phenomena and paradoxes for years*
Optozorax: There. I did it for you. And as a bonus, I made infinite more kinds of portals.
It's almost like simulation and models are better than analytical solutions and equations.
Equations are the end product not the means or the source.
Everyone, behold: The power of games.
@@monad_tcp reality sometimes doesn't like our imagination, but we can simulate our imagination, now here, more portals.
I believe minute physics did an explanation of portal in portal a long time ago as well
@woosix7735 yes and I also consider that video a good way to understand portals
This feels like something that would happen if you combined SquishCraft with Patrick's Parabox and subtracted Sokoban. Logically straightforward, but only obvious _in hindsight._
squishcraft’s dev bcat112a actually made a puzzle game with a very similar line of thinking called portalsnake, in which you are surprisingly able to make every portal featured inside this video! you just have to use enough sets of 2-portals for the more complex portals, like 3 sets of 2-portals to create a 3-portal (it took me a moment to make sure that they were all possible, i was actually originally writing this comment saying that it would be interesting for them to add these portals shown in the video until i realized lol)
theres also a ton more interesting and mind-warping features in the game, like the duplication portals seen in the beginning of the video. i definitely recommend you check it out if you liked squishcraft and you liked the concepts in this video. (i honestly like portalsnake a little more than squishcraft imo, both games are still amazing though)
@@cipeman3498 oh THAT'S the game I'm thinking of! I knew there was something with that aesthetic that had portals in it but I wasn't seeing any in screenshots of SquishCraft.
also anyone who hasn't heard of those games: go play Patrick's Parabox. if you're the kind of person to be reading comments below a video like this, you'll enjoy Patrick's Parabox. it has stellar difficulty pacing and is well polished.
If you dont get some kind of acknowledgement from Valve or even Gabe Newell himself, then I will be very disappointed.
The mind-bending mathematics and graphics programming thats required to make this work and then being able to simplify it and explain it to an audience is simply incredible.
Valve should give him an honorary doctorate xD
Like, each of these chapters could've been it's own video. Like I'm halfway starting to grasp one of em and he smashes the next one into my face. Amazing video
Portals are really a cool entry point to a lot of the concepts in 3D geometric topology. Thurston has a great video about knotted portals and their relation to 3D manifolds
Project manifold is a good example
Let's be honest...
Can you link said video? Can't find a channel under that name
@@moyo8960 th-cam.com/video/IKSrBt2kFD4/w-d-xo.html
@@moyo8960 I don't think William Thurston had a channel, but him talking about knotted portals is called "Knots to Narnia", that's probably what they're talking about
I like the fact that, the way we "construct" the complex portals in this video is exactly the way we learn science (math/phys/chem) at school. We start off with the most simple concept (two-part portal), prove its validity, then use that to build up more complex concept. As long as the math is still correct the new concept (new kind portals) is also valid.
Also we have innovate portals, which means.. Portal 3 confirmed?
New content update: 3rd portal added
Valve is gonna hire this one day and be the reason the 3 in Portal 3 exists
We will get GTA 6 before Portal 3
PLEASE YES!!!!
The three-way portal is just 3-pairs of normal portals.how would you visualize the portal entrance when there are just two portals placed? Aaandd.. the surface needed to place such kind of portal would be really inconvenient
This is why TH-cam is the best platform, there are thousands of creative and smart people honestly sharing their knowledge
support portals are genuinely such a genius idea! they open up so many possibilities
5:10 "...even though it seemed like such a simple thing." Мой брат во Христе you just answered a question that most people couldn't even begin to philosophize about, let alone calculate the answer to.
With the tilings, my immediate thought is: what would happen if you bent the monoportal into a regular pentagon?
This will be broken portal
non euclidian space
@Nikola_MHow would that even look like?
@@bamberghh1691imagine a space
then remove the Euclidean
@@Zyskr.. thanks man
"It's not magic - It's made up of ordinary portals!" I love the boldness of the statement. Great video!
Wait... so if the problem with a portal being the same size as itself is now solved, what happens if you move a small portal into a big one?
This is exactly my question as well
3:32 So if a triple portal is functioning than same as 2 portals, the numbers of portals in a complex frame like at 5:17 could be deduced by counting the number of holes in the frame using topology. The number of portal would be the amount of holes + 1.
I'm not sure the reverse works, interestingly. The frame of the triple-portal is topologically equivalent to a "two-holed donut" but if we turn that into a frame we'd get something like two adjacent squares, which results in 2 portal pairs rather than a triple-portal. You can imagine taking the triple portal and slowly shrinking one of the three ends until it just becomes a dividing line between the halves of the remaining two.
I've done some thinking, here's what I've been able to come up with. Far from anything rigorous, so corrections are welcome!
Let's call a normal portal a "2-portal", a triple portal a "3-portal", and so on.
If we have a frame with 1 hole (i.e. donut), we can only create a single 2-portal.
With 2 holes (2-holed donut), we've just seen we can either have two 2-portals or one 3-portal. We can imagine pulling the middle section of the donut out to create the "3-branched frame" seen at 4:00 in the video.
With 3 holes (3-holed donut) it gets more complicated. We can again have three 2-portals, as expected. We can also take either one of the middle sections and pull them out to obtain a 3-portal and a 2-portal. If we pull out both middle sections, we'd get a portal with a frame that looks a bit like "⟩-⟨". Thinking about it, this can split into 4 entrances: "\_/", "/‾\", "⟩", and "⟨". Therefore this is a 4-portal!
Based on this, we know trivially that a frame of genus g (a g-holed donut) can definitely correspond to g 2-portals or a single g-portal. We also get less trivial combinations in between.
I conjecture that whenever we "pull out a middle section" between an n-portal and a 2-portal, we get an (n+1)-portal in return. Similarly an n-portal and an m-portal together make an (n+m-1)-portal.
If this is the case, then the possible portal combinations are given by all the _lists* of positive integers that sum to the genus g_ (where the degree of the portal is the integer + 1).
For genus 3, for example, we can have 1 + 1 + 1 = 3 (three 2-portals) or 1 + 2 = 3 (a 2-portal and a 3-portal) or 3 = 3 (a 4-portal).
Genus 4 should then have 1 + 1 + 1 + 1 = 4 (four 2-portals), 1 + 1 + 2 = 4 (three 2-portals, one 3-portal), 2 + 2 = 4 (two 3-portals), 1 + 3 = 4 (one 2-portal, one 4-portal), and 4 = 4 (a 5-portal). Thinking about the setup, this does seem to make sense! We have:
"- - - -" or (1,1,1,1),
"- - -⟨" or (1, 1, 2),
"⟩- -⟨" or (2, 2),
"- -¦-" or (1, 3), and
">¦-" or (5).
(I did my best with ASCII representation. Spaces denote joined frames with a separation between them, so "- -" would look like a window with a single bar down the middle. The "¦" should be taken as two separate spokes, so "-¦-" is a 4-portal like "⟩-⟨" and ">¦-" is a 5-portal.)
* Sidenote: the objects here aren't really "lists / tuples" or "sets", since we care about repetition but not the order of elements. Sets disregard both, while lists / tuples include both! Not sure if there's a name for this kind of object.
edits:
- formatting
- added ASCII of the genus 4-cases
Dude while watching your last video I literally started thinking about a 3 portal portal and I got confused and went into a coma with the video playing on loop and then the notification noise for a new video popped up and I watched it and my thoughts were confirmed
I seriously think all the things you've presented in these videos is going to inspire so many game developers.
So many of your discoveries were (as you put it) surprisingly not thought of or discussed before or discovered by accident, but after seeing that it works, it's just feels so intuitive (as intuitive as portals can be, at least) and it just feels right. It's a special thing when that happens.
0:33 that visual is actually so cool
Cool video. And I agree with one of the commenters that you should make a puzzle game with these portals based on logic.
I've watched your videos in Russian but my poor knowledge of the language got in the way of appreciating all of it. I'm glad that you made an English version.
Absolutely amazing! I was expecting this was a much larger channel given the quality!
I love this kind of stuff! I love portals that break geometry, non-euclidean geometry, time travel, timeline manipulation, multiverses, infinite chess, 5d chess, etc.
Keep up the great work!
8:00 Please correct me if I'm wrong, but it seems like the fact that an object interferes with itself is not the true reason for why there's no tearing, in fact we can see in the clip shown just before that it still works even if we allow the object to intersect itself. Rather it seems to me that it's because the boundary is mapped onto itself, and tearing can only occur at the boundary
The three-way portal blew my mind. And all the other stuff that I didn't think was possible but clearly is, like a "scaling monoportal". Great videos, love them and your portal experiments.
По превьюшке подумал, что вижу что-то знакомое, а потом оказалось, что оригинал-то я уже и посмотрел :)
Удачи в покорении английского ютуба
Не помнишь название канала автора?
@@fellowdiman оптозоракс.
Я уж подумал что кто-то стырил видос и полез в комменты разборки устраивать, но нет
"Caroline, I have snorted a suitcase full of moon rocks, AND I'M STARTING TO FEEL THE EFFECTS!"
W H A T
pneumonia
@CatValentineOfficial "Cave Johnson, we're done here!"
i wonder if a knotted portal is possible with this like was demonstrated by Zeno Rogue in their video
next video will be about knotted portals
@@optozorax_en Holy shit I can't wait
12:05 those tilings are giving me a mild existential crisis. If you stand in one you see infinite recurring versions of yourself, and because of the finite speed of light they're all actually you at different points in time.
Every time you look in a mirror you are actually looking at a past version of yourself.
i watched your last video yesterday and i have not been able to stop thinking about portals since then
3:27 or "supportals", if you will
"The light here is not straight" is actually a very common misconception - the light is straight, the space is not. Think of a wormhole as an infinity portal, with many many linear portals stacked together to create what appears as a smooth curve!
It's an example of a multiportal, just the limit of an infinite number of them to create a smooth surface.
yeah, thanks, I need to understand wormholes better
@@optozorax_en ngl id love to write a game with physically accurate GR simulations but my programming is not there, just the theory. Let alone turning the theory into something I can write haha
Excellent video though!! I love this solution.
A portal is a discrete version of a wormhole , in the same way a polyhedron is a discrete version of a sphere. A polyhedron has zero curvature almost everywhere, except for its vertices where there is "infinite curvature" at a single point. You can walk around a vertex in less than 360° and come back where you started. A space with a (pair of) portal has zero curvature almost everywhere, except for the edge of portal where you can go around it 720° and only then come back
8:58 with n-monoportals, what happens if we set the internal angle to something like 108 degrees instead of 120, so its a pentagon interior angle instead of hexagon, would it create a non-euclidean or hyperbolic area?
12:05 what if a monoportal is bent into a pentagon, does it create another hyperbolic geometry tiling?
I would test in the demo but the n-monoportals are limited to integer slices and tilings to 3,4 or 6 sides
A portal with three parts? Not if Valve has any say in it.
and thus a legend was born, keep up the good work!
Amazing work! These are absolutely the best portal videos for math and programming nerds like us! 🙌🏻
Im so happy youre making more of these videos. The last one was phenomenal
i love this type of content!!!!!!!! this stuff is really interesting, keep up good work :D
DUDE awesome video! Soo trippy and cool effects! Imagine what you can do just with complex maths and shaders :D its so interesting
I cannot stress this enough: publish a mathematical article (too, keep the videos, of course, as long as you enjoy making them). This is amazing.
You are actually doing amazing work, I've never seen portals explored to such degrees. The monoportals especially blew my mind.
Get this guy an award for this amazing work!
I can't wait to see more!
I'm definitely going to try the program you made!
Really liked your video :3 portals are so cool
Sometimes you realize that your brain is not designed to function a certain way. Major respect to you, sir, for venturing into dimensions the rest of us are too basic to follow.
another interesting case may be to use the inside surface of a larger sphere to inscribe a portal on the outside of a tiny sphere or vice versa, So that reaching into the tiny sphere, makes you dive deeper into a dimension of space. I can imagine some pretty crazy system dynamics of space time fabrics if you managed to somehow apply some constraints towards the stability of each sphere size and how the distancing would work. I could imagine it could tie into the rate of change regarding the transformations from Linear portals to wormholes using distances from bubbles and scales as reference points.
This feels like an impending mathematical breakthrough.
At the start of the year?!?
How can we have it so good!!
This is the good stuff.
I always think about monoportal, but I've never bothered with thinking about tripple portals. It's neat.
Though for spherical portals: they're good for transposing two locations and then when you get rid of the portal; you are magically (but not magically) in a new location. This is actually how I imagine teleporting would work, it's dual temporary spherical portals.
Things get more interesting once the flat surface of one of the two connected portals has a curvature, morphing the exiting object. I've made once a small very crude demo in Source engine and the effects were quite funky.
You could probably also make things like pentagonal or heptagonal portal tilings, though they would probably have visible seams between the sides. You can also try 3D tilings like cubic or tetrahedral ones, or something of the sort
Also I first saw this thumbnail and thought you managed to come up with knot portals or something, like ZenoTheRogue did. That would be interesting to see you explore
These vids are so cool. Exactly the questions I’m curious about!❤
Re 10:09, I suspect that it would be possible to get different fractional displacements by putting an angle through the middle of the monoportal. Instead of constructing it with a 180° rotation, rotate it, for example, 120°. Like normal, the result is a portal that you can't move through the center of because you'll self-intersect. But offset it a third of its height, and it should work. My intuition is that, in general, this needs a 360°/n angle, and the denominator of the offset (in reduced form) must be exactly n.
I just checked that in my visual editor, and unfortunately that does not work
10:45 yay like I asked in the previous video 👍
Love the addition of skewing the portals
yesss!! another step to make the "3" world (made from numberlines, but instead of 2 directions its 3, so there are 3 signs every numberline has)
I remember there's a game called Gateways which is like a 2D portal game, but it has multiple portal types including the scaling portal you mentioned. It has some great puzzles mixing multple different types of portals like that
I can easily see this becoming an absolutly mind-bending game. there are SOO many cool things mentioned here.
I love how for the rotating monoportal you just casually say "cut it in the middle and rotate half the reflection in the 4th dimension" like it's something you do every day
This looks so cool! And thanks for providing demo
This broke my brain so much that the only thing I could think was, "All these squares make a circle. All these squares make a circle."
This feels like it relates to algebraic topology from the little I know that subject, but I need to study it more. The portals act like homeomorphisms and how we create a bicontinuous map between regions.
There is a portal game on steam called "Frame: Portals on Steroids" that actually uses Monoportals as part of its puzzle design for many levels, it has both "mirror" and "non-mirror" monoportals aswell as scaling and rotating portals and gravity changing and just, it has everything
It doesnt have any triple portals however, so as far as i know thats a brand new one that you've invented
author of that game also solved portal-in-portal
@@TabbyVee Frame also doesn't have skewed/sheared portals. I'm surprised optozorax calls them "not useful and interesting". At least from a game design perspective I'm sure that some interesting puzzles could be build based on that.
11:49 is what tusk act 5 would be like
Great job Ilya! I admire your creativity and ability to bring these ideas to life.
When you started talking about the portal mosaic, I wondered if it was possible to make an aperiodic mosaic from Penrose tiles?
Or for that matter from the Aperiodic Monotile that was found in March 2023.
It's interesting whether it's possible or not. 🦎
Отличная робота Илья! Восхищаюсь твоей креативностью и способностью воплощать эти идеи в жизнь.
Когда ты начал говорить про мозаику из порталов, я подумал, а можно ли сделать апериодическую мозаику из плиток Пенроуза?
Или, если уж на то пошло, из Апериодичной моноплитки, что нашли в марте 2023 года.
Интересно в не зависимости от того возможно ли это, или нет. 🦎
Welp now you got to make a portal 2 fan mod with 3 portals
You are doing fantastic work, this is all highly fascinating
NOW *YOU* are thinking with PORTALS!!! :D
🎶This was a triumph!... Huge success!🎶
Didn't expect a connection with crystallographic groups. I think this is enough content to define some axioms and write some formal maths about this.
I've been waiting for a portal expert for years, I have so many questions
With the Square, Hexagonal, and Triangular tilings, you could arrange the portals like any regular polygon to create regular tilings within the portals that can't normally be made in Euclidean space.
Theoretically you could even bumping up the number of sides infinitely making a circle, but at that point it would very much not keep parallel lines parallel and may cause all sorts of weirdness with objects being warped as they try to enter a concave portal to exit another concave portal, basically like taking one of the hemisphere portals from early in the video and inverting it's geometry
This dude is casually bending reality while we are doing nothing
isn't your "Triple Portal" solution identical to having three pairs of 2-portal systems? In your version where each is a pair of flat surfaces on one of the three portals, if instead you split those surfaces into their component flat parts, then each flat part is just one half of a 2-portal system with one of the halves from the other two original surface portals in the three-part system?
I think it would be interesting to explore further and see if a triple-portal system that is "atomic" could exist -- that is to say, a system that could not be divided into smaller 2-portal constituent parts that are equivalent in functionality.
Because of the way your triple-portal system works you could use the same principal to design an N-portal system where you effectively cut a circle into N-slices with the borders of each slice being another linked 2-portal system. So instead of having 120 degree slices for a triple portal system made of three 2-portal systems you could use 90 degree slices to make a quadruple portal system which is identical to four 2-portal systems.
I want to see the 3 bent portals assembled into a cube. What fun could be had with that.
*@optozorax*
The support-portals, should be some other color or something, so they are visually shown to be "different" from "normal" portal, even if they are also "normal portals".
Why do I feel like I've seen this video months ago? Great video!
Oh, it's because I saw it in the original language lmao
Wait, why is there no mention of that... I feel like I am being tricked into thinking this content is new.
Some of these portals reminds me of mechanical interactions in 'Frame: Portal on Steroids' but this is definitely more confusing.
About the mirror part
If you are what's stopping you from going through a monoportal
And vampires can't be seen in mirrors
This means a vampire can enter the mirror dimension
Alternatively this is because vampires are beings from the mirror dimension who killed their real life counterpart and took their place
3:39 Insane. And the portals were pretty impressive too
I checked this out already in github few days ago. never knew the lore was really deep
I love the insight of supporting portals.
Imagine falling through a Skew portal and then it closes. You're just permanently like that now
You just got italicized.
I used to create Monoportals with the help of the Immersive Portals Mod (for Minecraft!) It could be done simply by placing and entrance side-by-side with its respective exit.
Just like you did!
This is really cool! I hope the next video goes well
Now you're thinking with portals!
what would a wormhole have to be to actually work?
it cant be a portal between an exterior and interior surface of a sphere because that would be like having no portal at all.
if the portal was between two exterior surfaces of a sphere then it could move you to a different location but there would be a problem.
interior-exterior surface cancel out the curvature of the sphere but exterior-exterior surface must cause space on the other side of the sphere to have a curvature of 2
but if we want the portal to preserve the global curvature of space on the other side we need to somehow make the net curvature between the two portal surfaces to be 0.
maybe if you have a gradient of hyperbolically curved space as you approach the portal surface that has a curvature of -1? that way both portal surfaces would have a curvature of zero at their surface? or alternatively, the surface could be a hyperbolic sphere with a curvature of -1 embedded in a space gradient of positive 1? that might look more like the typical wormhole depiction.
with tiled portals, i think you should be able to tile with p much any regular or non regular polygon, regardless of if it'd work in reality, to create some non-euclidean shennanigans like 5 sided "squares" and 720º squares.
should be worth a shot
Love the frontier portal research happening here
With the tiling portals in the end, I was thinking it would be cool to see if they could be arranged as a non-repeating Penrose tiling.
Thank you youtube recommendations, this video is very epic
Its Three portals glued together really, isnt it? But one interesting thing i want to know is if you go through the middle, will you split when you cross the border of the other portals? and what happens if you stick one portal through in case it does split ?
thanks for making a distinction between wormholes and portals
is there actually a geometric explanation for portals tho? like one accepted by most mathematicians? we literally got one for knots, its called knot theory.
idk
That isn't a triple portal, it is just a few double portals glued together.
Exactly, even the monoportal is just a normal portal but with a different shape
That's the idea 😅
@@Thebenjiball0 the idea should be something "revolutionary", since the creator emphasizes so much on the fact that he alone discovered something incredible... but it just is a construction, that it alone is something amazing nonetheless, but the naming system ... is just wrong.
Triple portal - 3 pairs of normal portal
Monoportal - just two ends of a normal portal rotate 180 degrees
I mean if you want to name those design, I think the name he gave are pretty cool, but... he isn't answering the question "is a 3-way portal possible?" not to the question "is a 1-way portal possibile?".
A more logical answer to the 1-way portal is a portal that has a destination but not a return (that should be the real answer to a question like that)
And a 3-way portal should have 3 destinations, really connecting three points in space. So probably the answer will always be no (being compatible with what a portal is) and he didn't discover anything new, except some really cool designs that are illusions of a real answer.
I'm not saying it isn't interesting, but calling them "discoveries" is a bit overreacting to creating a cool design of something that already exists.
Its not a discovery
@@begbaj uh ok. I agree with basically all of that I guess
the triple portal is basically *the* way to do it. because of the split, it is technically just 3 basic pairs. there can't be a more "triple portal" than that. yeah it's not a "new discovery", but it is him discovering.
I feel his one-sided portal also is probably the right way to do it. an entrance to a place without return is still basically the same as a normal portal, because it would still need a defined exit point. the exit point would be invisible though, and the object would have to grow into existence from there after entering, which is really weird.
Thinking about the spherical and hemispherical portal and more generalizations; there should be a distortion if both surfaces have the same curvature sign, or otherwise do not match. Idealized rigid objects would not be able to get thru; but if the object is a softbody (not necessarily limp, think about the stuff in BeamNG for example), with sufficient force they should be able to get thru warping portals, and depending on the material's properties and amount of warping, either recover on the other side or come out permanently deformed. And of course, light would get get distorted getting thru.
would be very interesting to see a physics engine integrated into this. Would also be cool if a way for the camera to go through the portals to their alternative universes where implemented. Both ideas are pretty advanced implementation wise but it's just a thought
I feel like you are either rediscovering or straight up inventing a new branch of topology.
One interesting thing is that the time portal in portal reloaded actually acts as a monoportal, just with a delay.
A video has never hurt my brain so much.
Just came back after watching brainrot and I feel much better. I believe there are actual academic uses for brainrot if it is capable of cooling down the brain
Wait til you hear about 4d golf
You should make tiling's that aren't possible in real life, like a tiling that is only octagons. You could also add portals with an interior space, and see how that effects the view. I think portals with an interior space could be easily done by just making the portal go into a tube with another portal on the other end, but wormholes also possess an interior space, so maybe that tube could also be a looping cylindrical mono-portal.