Do you like what you see and want more of it in the future? Then, you may consider supporting my work on Patreon. It would help me a lot in producing more such videos for you. I really appreciate it! www.patreon.com/braintruffle
I have the dream of creating a game engine that could support a perfect (statistical) simulation of reality. Really love your approach to fluid dynamics!
Hands down the best produced mathematical content, by miles. The effort put into the animations are truly head and shoulders above anything else. Not to say there aren't plenty of amazing math channels already out there, but every time I watch one of your videos I am just stunned at the clarity and practicality of the explanations/animations. This topic feels far above what I should be able to understand mathematically, but the conjunct animations make it so that I can just manage to keep up. Can't wait for the next episode of this series!
The Material Coordinates method you outlined is just fascinating to me, how similar the idea is to one used in *video compression* of all things, the way one uses optical motion vectors to move regions of pixels around on the screen. And once that comes to mind, there's so many other things that video codecs do that then make total sense to backport to the original fluid simulation: resetting the material coordinate grid at regular intervals (similar to what I-Frames do for video); using a quadtree acceleration structure just like the macroblock structures used for P/B-frames. Heck, there might even be a way to leverage some of the video encode/decode acceleration features present on so many platforms these days to do part of the work, and get a _really_ performant simulation.
This video, and the previous ones, are masterpieces! Definitely in the running for the single best scientific/mathematical video series ever put on youtube! These videos leave graduate level courses in college in the dust (I know, I've taken them). My question is, how did you come to this level of understanding!? Was it just reading textbooks, working through the problems, etc.??
Thank you so much for your kind words! I'm really happy my work is seen as enjoyable and helpful. Throughout my studies, I often played with the problems at hand, trying to solve things on my own - intentionally postponing the thorough literature study to a later learning stage. This pushed me to think outside the box. One of the most valuable insights for me was realizing how similar lots of problems and solution approaches are once observed through the 'right' lens and, therefore, to keep looking for these lenses! That's what these videos are meant to promote: daring to change the perspective on things. There is so much fun stuff to explore along the journey, and with time the patterns will unveil.
@@braintruffle Thank you for your reply! I appreciate your perspective on problem solving lenses. I'm currently tackling some very complex thermal/heat transfer problems that are requiring me to search for these lenses. These videos definitely inspire me keep looking!
I wish I could describe how amazing these comments are, but it would take me so long to do it justice. Just please keep doing what you are doing - you are making the world a better place.
The "Unreal != Useless" text on your thumbnail is probably the best layman's explanation as to why the "spherical cow in the vacuum" exists that I have ever seen! I love it.
Came here looking for an explanation of lift (from aerodynamics) from first principles. Ended up watching the whole series so far :) Not sure how many would appreciate, but simulations comparing airfoils would tie nicely all concepts explained so far. Your content is amazing!
I don’t have enough comprehension of language to describe how awe inspiring your videos are. It shows the front-edge of what is possible at the intersection of mathematics, engineering, and story telling - that even us simple humans can begin to understand. Wow. Wow. Please never stop showing us what is on your mind. I, for one, am curious.
One small addition to your wonderful description of spatially-fixed and material-fixed coordinate systems (one I only know of because my grad school officemate studied it while working on his dissertation): The "unified" coordinate system. Here, the computation nodes move in the direction of flow but at a different (slower) speed than the flow. The speed of the nodes is something you choose yourself, and can be different at different points in space or time -- so you can try to encourage, e.g., the preservation of grid angles while still letting the grid deform into tight spaces or around corners.
Your videos are masterpieces ! You can explain such difficult topics with clarity and wonderful simulations. You deserve a lot bigger audience : your work is fantastic 😁
Wow. I've been looking for a new science channel, as I can't stand Sabine's channel any more. Your work is fabulous. The beauty of physics brought beauty to visualization, and clear descriptions of what we are seeing.
This is insane! I don't understand it but it's so fascinating. I just started my first class on differential equations and never found the modelling part of it interesting until now
Incredible video and great explanation! I love how you disect everything perfectly so that we can understand complex things easier! I subscribed a few months ago and it's great that you're continuing to make this S-tier content
Great man !! actually i just became a postgraduate student and hella interested in such type of simulations and complex fluids dynamics , i guess your work just ignited a spark within me to explore it further, THANK YOU very much !! keep doing the good work
This series sets a new bar of how to teach STEAM. I look forward to a world where all education has content this clear and well thought out. Amazing work!
Just to let you know. 11:55 is information dense to the 1000th degree. I will take time to parse it out, but it will probably take pause and start and 10 watches and ChatGPT discussions. I guess that’s fine as long as your aim is completeness of explanation instead of audience comprehension.
I wanted to touch on your statement around 36:30. This is actually also the reason why in fields like astronomy there are so many different groups building different simulations. Depending on the theory you are trying to simulate you build the simulator with the contrains given by the theory in mind and then try to do model robustness tests. The only thing that bothers me with this approach is that it feels a lot like enabling confirmation bias. You are building a sim that shows the effect you want it to show because of the theory you want to prove. What are your thoughts on this?
I don't think that's a coincidence. Notice how, as you climb the ladder, waves become fields, which become vectors, which generate particles, which make waves, and so on. This sounds a lot like real life systems. I wonder if entropy is just an inevitable data compression scheme; as the scale of a system goes up, it alternately behaves as particle, then wave, then field, then a particle again, all of which recursively affect each other in all dimensions simultaneously, and the line of time which we experience is simply the least energetically expensive way for that system to evolve. Imagine the stock market. It has particles (trade actions), waves (a big disruption propagates), and fields (prices). It can be analyzed fractally at any resolution, but The Uncertainty Principle still applies, to an extent.
l am very thankfull to you. In your videos when you complite some topics and ask question to all of us and then starting give us new thery or view pont is so awesome. it forces us to think and appricate all scientist with their hardwork. Maybe we do not understand you complitle but the main ideas you give helps us lelev up our understanding.
This video is so awesome I can even start to visually understand how black holes work. In fact, it basically explains a lot of things about the universe.
I really loved and appreciated this video. The explanations of Material derviatives where very insightful. And I'm about half way through the video!!! Excelent job!!
please consider making a video on how you're making these videos. i'm particularly interested in how you're animating formulae and what software you're using for combining formulae and video clips with simulaiton.
Brilliant visuals...! As a graduate student, studying fluid mechanics and using CFD, I am really curious what kind of tools you use for simulation and visualizations.. It is literally beautiful.
Just discovered your channel and I am hooked! This is so pleasant to watch :) Do you mind sharing what software tools you are using for the animations? I love the style, it really stands out. Looking forward to follow your journey and future videos :)
The visuals are absolutely stunning, you talk about it very casually yet I am in awe. How can I learn to do this on my own? I have a background in physics but no fluid dynamics yet...
funny that the part with the box of swirls is the most replayed, it's very pretty. I'd love to play around with that myself, just watching the swirls and chaotic flow.
right in the intro and later on when you have a wing profile flow, even though it looks pretty, it's actually behaving like a really bad wing surface due to flow separation and turbulence. in reality you never want turbulence to form around your wing, you want the flow to be as laminar as possible until it reaches the tip of the wing.
at 29:47. what do you mean by artificially scalling up the slower simulation velocites and the "playback speed" to "match" the flow speeds "visually" ?
Amazing video! BTW, i think about the part of infinitely fast compression waves could be better illustrated using a zoomed in visual which scrolls with the wave, that let's you see the flow speed equivalence more effectively.
I see in this a formal definition of magic. To find a perturbation or introductory states which are irreversible using the general laws derived by fluid mechanics - introductory states or perturbations that yield dramatically improbable results. These clearly exist, but are generally averaged out. But what if we can repeatably induce them by determining the math of them?
Hi, sorry for asking a question before watching the video in its entirety, but I've got a question about the "Trajectory Perspective" and "Spatially Fixed Perspective". I've studied some fluid dynamics in the past and encountered some different terminology. Are these perspectives also known as "Lagrangian" and "Eulerian", respectively? Thanks!
So why do we add the temperature stuff afterwards, instead of making the assumption that our density is 100% determined by the temperature? Wouldn't that also remove one equation?
Hello Braintruffle . Can you please suggest what you consider as the best fluid mechanics books (videos ) for a mathematician and a hydraulic engineer , and I need also books on the subject of Numerical Analysis ... thanks in advance
An admiring and inspiring video. Music, tone of voice of the narrator, Everything's perfect. The only problem is the accent of narrator. It is very hard to follow for me. Thank you.
May I ask what method you're actually using for the visualizations? Is it LBM + Blender, or something else? As a developer, I'd be really interested to learn how all of this is being simulated and visualised.
I am looking to learn CFD from scratch, I have done some basic projects like simulation of air through airfoil but want to have in-depth knowledge on the topic. Can anyone suggest me place to start?
Do you think it would be possible to compile your fluid simulation into a "simple" equation? SciPy has an iterative/machine-learning algorithm to simplify equations. It is terrible for simple stuff, but works well at approximating complex systems.
I have most definitely forgotten some important details but I think it might be possible to limit the small scale detail by making the continuous thing into discreet units like pixels or something? But then also treating it like a continuous thing in other ways? Like a field I guess
The probabilistic description of microscopic particles reminds me of the distinction between the ontic and epistemic models of the wave function. Some believe the wave function is real (ontic), and there are no hidden variables. Others believe the wave function is a description of our state of knowledge of the system (epistemic). Does your intuition lean one way or the other? Regarding Bell's theorem, a often neglected requirement of the theorem is statistical independence of measurements. With a deterministic universe, that assumption can be dropped, and local hidden variables are still allowed.
One approach to two-dimensional fluid dynamics uses vorticity in Brownian motion, as proposed by Alexandre Chorin. So we have a big system of differential equations and a random number generator. It is natural to ask what we can do for quantum mechanics. I have made a number of suggestions in various TH-cam videos on quantum theory.
Hi, I am not so familiar with differential equations. Why do you use sometimes "D" and sometimes the turned 6 (I think it's a lowercase delta?) and what is the difference between these expressions?
normal d is used in normal differential equations. Delta is used in partial differential equations. Big D is the material derivative and is dependent on how you look at things. In the Eulerian view in fluids its usually the expression he explains in 11:00
Здравствуйте. Благодарен за видео. У Вселенной есть цикличность во времени, которые разделяются по комбинациям взаимодействий и делятся на периоды; 1. Вселенная собранная в одну квант струну. 2. Вселенная из коротко живущих фрактал с переходом в хаос. 3. Вселенная из хаоса с переходом в долго живущие фракталы. 4. Вселенная из долго живущих фрактал с переходом в одну квант струну. При всех комбинациях, квант струна, может рваться но без отрыва при этом петлями складывается в мембраны образуя из них бутоны которые могут, от периода времени, сворачиваться ограничивая связи.
Awesome video series. But this video is a bit long. It requires dedication and time, and does not really work by watching it in multiple sessions. Yeah, so I recommend grabbing a snack for this.
Do you like what you see and want more of it in the future? Then, you may consider supporting my work on Patreon. It would help me a lot in producing more such videos for you. I really appreciate it! www.patreon.com/braintruffle
Any chance you’re looking for people to help grow the channel/help you with the workload? I’d be interested if so!
Yes! I need more similar videos
already have a video that proves this dc 0 point to ac Flux
@@jeremiecorkery9421 easy th-cam.com/video/nPVvlo2Hpjk/w-d-xo.html
I have the dream of creating a game engine that could support a perfect (statistical) simulation of reality. Really love your approach to fluid dynamics!
Fantastic video once again, I'm always stunned by the visuals, can't wait for the next one!
Thank you for taking the time to check out my latest video! I'm happy you like it and for your support!
I don't know how I've only just seen this video.. it's an absolute masterpiece!
The visuals in this video are unparalleled in effect. actually goated. wow
Hands down the best produced mathematical content, by miles. The effort put into the animations are truly head and shoulders above anything else. Not to say there aren't plenty of amazing math channels already out there, but every time I watch one of your videos I am just stunned at the clarity and practicality of the explanations/animations.
This topic feels far above what I should be able to understand mathematically, but the conjunct animations make it so that I can just manage to keep up. Can't wait for the next episode of this series!
The Material Coordinates method you outlined is just fascinating to me, how similar the idea is to one used in *video compression* of all things, the way one uses optical motion vectors to move regions of pixels around on the screen. And once that comes to mind, there's so many other things that video codecs do that then make total sense to backport to the original fluid simulation: resetting the material coordinate grid at regular intervals (similar to what I-Frames do for video); using a quadtree acceleration structure just like the macroblock structures used for P/B-frames.
Heck, there might even be a way to leverage some of the video encode/decode acceleration features present on so many platforms these days to do part of the work, and get a _really_ performant simulation.
This video, and the previous ones, are masterpieces! Definitely in the running for the single best scientific/mathematical video series ever put on youtube! These videos leave graduate level courses in college in the dust (I know, I've taken them). My question is, how did you come to this level of understanding!? Was it just reading textbooks, working through the problems, etc.??
Thank you so much for your kind words! I'm really happy my work is seen as enjoyable and helpful. Throughout my studies, I often played with the problems at hand, trying to solve things on my own - intentionally postponing the thorough literature study to a later learning stage. This pushed me to think outside the box. One of the most valuable insights for me was realizing how similar lots of problems and solution approaches are once observed through the 'right' lens and, therefore, to keep looking for these lenses! That's what these videos are meant to promote: daring to change the perspective on things. There is so much fun stuff to explore along the journey, and with time the patterns will unveil.
@@braintruffle Thank you for your reply! I appreciate your perspective on problem solving lenses. I'm currently tackling some very complex thermal/heat transfer problems that are requiring me to search for these lenses. These videos definitely inspire me keep looking!
I wish I could describe how amazing these comments are, but it would take me so long to do it justice. Just please keep doing what you are doing - you are making the world a better place.
The "Unreal != Useless" text on your thumbnail is probably the best layman's explanation as to why the "spherical cow in the vacuum" exists that I have ever seen! I love it.
Bro this is series is so fucking good! Please dont stop!
Came here looking for an explanation of lift (from aerodynamics) from first principles. Ended up watching the whole series so far :) Not sure how many would appreciate, but simulations comparing airfoils would tie nicely all concepts explained so far. Your content is amazing!
The quallity of the animations for the video is absolutely amazing! Thank you, that is so much better than anything in this area.
I don’t have enough comprehension of language to describe how awe inspiring your videos are. It shows the front-edge of what is possible at the intersection of mathematics, engineering, and story telling - that even us simple humans can begin to understand. Wow. Wow. Please never stop showing us what is on your mind. I, for one, am curious.
This is the most amazing video series I'm much too dumb to understand.
One small addition to your wonderful description of spatially-fixed and material-fixed coordinate systems (one I only know of because my grad school officemate studied it while working on his dissertation): The "unified" coordinate system. Here, the computation nodes move in the direction of flow but at a different (slower) speed than the flow. The speed of the nodes is something you choose yourself, and can be different at different points in space or time -- so you can try to encourage, e.g., the preservation of grid angles while still letting the grid deform into tight spaces or around corners.
Your videos are masterpieces ! You can explain such difficult topics with clarity and wonderful simulations.
You deserve a lot bigger audience : your work is fantastic 😁
I appreciate you for putting this up on TH-cam.
Man this is way underrated than it should be!!!🤯🤯
Wow. I've been looking for a new science channel, as I can't stand Sabine's channel any more. Your work is fabulous. The beauty of physics brought beauty to visualization, and clear descriptions of what we are seeing.
Haven't watched it yet but liked anyway cuz I know it's gonna be amazing!
I've been looking forward to your next video!
Awesome quality! Worth the wait
I'm just speechless how clear and with such a deep insight this topic gets explained. And on top of all of this those beautiful animations. Chapeau!
This is insane! I don't understand it but it's so fascinating. I just started my first class on differential equations and never found the modelling part of it interesting until now
By far the most in depth videos I’ve ever seen on, well, anything. This series is simply incredible!
Incredible video and great explanation!
I love how you disect everything perfectly so that we can understand complex things easier!
I subscribed a few months ago and it's great that you're continuing to make this S-tier content
baltarfajinkankonk satan 🤣 hahahaha
th-cam.com/video/nPVvlo2Hpjk/w-d-xo.html
infinit potential but hole
Great man !! actually i just became a postgraduate student and hella interested in such type of simulations and complex fluids dynamics , i guess your work just ignited a spark within me to explore it further, THANK YOU very much !! keep doing the good work
This series sets a new bar of how to teach STEAM. I look forward to a world where all education has content this clear and well thought out. Amazing work!
Just to let you know.
11:55 is information dense to the 1000th degree.
I will take time to parse it out, but it will probably take pause and start and 10 watches and ChatGPT discussions.
I guess that’s fine as long as your aim is completeness of explanation instead of audience comprehension.
My favorite series on youtube. Thank you.
I could fall asleep to this.
That's not criticism. It's a compliment.
Beautiful
I wanted to touch on your statement around 36:30. This is actually also the reason why in fields like astronomy there are so many different groups building different simulations. Depending on the theory you are trying to simulate you build the simulator with the contrains given by the theory in mind and then try to do model robustness tests. The only thing that bothers me with this approach is that it feels a lot like enabling confirmation bias. You are building a sim that shows the effect you want it to show because of the theory you want to prove. What are your thoughts on this?
This channel present fascinating content but with rate of 17.55 second /day
This grid-bending effect at 0:00 reminded me of how, according to GR, spacetime is deformed due to gravity
I don't think that's a coincidence. Notice how, as you climb the ladder, waves become fields, which become vectors, which generate particles, which make waves, and so on. This sounds a lot like real life systems. I wonder if entropy is just an inevitable data compression scheme; as the scale of a system goes up, it alternately behaves as particle, then wave, then field, then a particle again, all of which recursively affect each other in all dimensions simultaneously, and the line of time which we experience is simply the least energetically expensive way for that system to evolve. Imagine the stock market. It has particles (trade actions), waves (a big disruption propagates), and fields (prices). It can be analyzed fractally at any resolution, but The Uncertainty Principle still applies, to an extent.
@@starrmont4981I think you are correct.
l am very thankfull to you. In your videos when you complite some topics and ask question to all of us and then starting give us new thery or view pont is so awesome. it forces us to think and appricate all scientist with their hardwork. Maybe we do not understand you complitle but the main ideas you give helps us lelev up our understanding.
This is super high quality series.
This video is so awesome I can even start to visually understand how black holes work. In fact, it basically explains a lot of things about the universe.
Absolutely stunning. Bravo! 🎉
I really loved and appreciated this video. The explanations of Material derviatives where very insightful. And I'm about half way through the video!!! Excelent job!!
What an educational masterpiece! Thank you very much! Hope you will improve more
please consider making a video on how you're making these videos. i'm particularly interested in how you're animating formulae and what software you're using for combining formulae and video clips with simulaiton.
best youtube channel ever
Your videos are sooooooo Good. Can't wait for the Discretization video
Brilliant visuals...! As a graduate student, studying fluid mechanics and using CFD, I am really curious what kind of tools you use for simulation and visualizations.. It is literally beautiful.
The whole series has been AMAZING. The narrative, visuals and quality of production is top notch, thank you for gifting us this work
Fantastic simulations. What rendering software do use for plotting the dynamics data? Blender?
If u post stuff like that even once per 2 months , i ll never unsub
the levels of approximation and regimes of validity dsicussed at the end were helpfu in understanding some of my own simulation work
Just discovered your channel and I am hooked! This is so pleasant to watch :) Do you mind sharing what software tools you are using for the animations? I love the style, it really stands out.
Looking forward to follow your journey and future videos :)
Noooo, you cooked that little guy at 37:57 😢
Amazing video btw
Edit: 39:48 looks refreshing. I love the little details
The visuals are absolutely stunning, you talk about it very casually yet I am in awe. How can I learn to do this on my own? I have a background in physics but no fluid dynamics yet...
th-cam.com/video/nPVvlo2Hpjk/w-d-xo.html right here
How can I pay to support your content? We need more content like this, this is pure quality, thank you for bringing this wonderful content for free
funny that the part with the box of swirls is the most replayed, it's very pretty. I'd love to play around with that myself, just watching the swirls and chaotic flow.
right in the intro and later on when you have a wing profile flow, even though it looks pretty, it's actually behaving like a really bad wing surface due to flow separation and turbulence. in reality you never want turbulence to form around your wing, you want the flow to be as laminar as possible until it reaches the tip of the wing.
Awesome video! Thank you!
Really amazing visuals. You could probably do a whole series teaching people data viz!
at 29:47. what do you mean by artificially scalling up the slower simulation velocites and the "playback speed" to "match" the flow speeds "visually" ?
Making a note to come back and watch later ;)
gdamn man your visualisations are beautiful
sehr gut gemacht!
Really superb video!
well done~ mind blown!
I really like the visuals used in this video. May I ask what software you used to create these animations?
Thank you for another amazing and informative video :)
What does the “e” variable represent at 25:57 ?
Simply lovely work
Amazing video! BTW, i think about the part of infinitely fast compression waves could be better illustrated using a zoomed in visual which scrolls with the wave, that let's you see the flow speed equivalence more effectively.
Thanks ! Have a nice day !
What software do you use for the 3-D rendering and/or simulations?
It’s an excellent video. It’s good to use computers with it. It seems like Mandelbrot and Julia sets and predicted dependable weather. Thankyou
Which software do you use sir ? Blender ?
I think he is using Unity. I could be wrong. He doesn't mention anywhere from I can tell.
Can you simulate electrical currents as long-range-interacting pressure waves travelling through the conductor?
I see in this a formal definition of magic.
To find a perturbation or introductory states which are irreversible using the general laws derived by fluid mechanics - introductory states or perturbations that yield dramatically improbable results.
These clearly exist, but are generally averaged out. But what if we can repeatably induce them by determining the math of them?
Hi, sorry for asking a question before watching the video in its entirety, but I've got a question about the "Trajectory Perspective" and "Spatially Fixed Perspective". I've studied some fluid dynamics in the past and encountered some different terminology. Are these perspectives also known as "Lagrangian" and "Eulerian", respectively? Thanks!
So why do we add the temperature stuff afterwards, instead of making the assumption that our density is 100% determined by the temperature? Wouldn't that also remove one equation?
right here th-cam.com/video/nPVvlo2Hpjk/w-d-xo.html
Hello Braintruffle .
Can you please suggest what you consider as the best fluid mechanics books (videos ) for a mathematician and a hydraulic engineer , and I need also books on the subject of Numerical Analysis ... thanks in advance
Damn this channel is so cool!
this too th-cam.com/video/nPVvlo2Hpjk/w-d-xo.html
An admiring and inspiring video. Music, tone of voice of the narrator, Everything's perfect. The only problem is the accent of narrator. It is very hard to follow for me. Thank you.
May I ask what method you're actually using for the visualizations? Is it LBM + Blender, or something else? As a developer, I'd be really interested to learn how all of this is being simulated and visualised.
I am looking to learn CFD from scratch, I have done some basic projects like simulation of air through airfoil but want to have in-depth knowledge on the topic. Can anyone suggest me place to start?
Do you think it would be possible to compile your fluid simulation into a "simple" equation? SciPy has an iterative/machine-learning algorithm to simplify equations. It is terrible for simple stuff, but works well at approximating complex systems.
I have most definitely forgotten some important details but I think it might be possible to limit the small scale detail by making the continuous thing into discreet units like pixels or something? But then also treating it like a continuous thing in other ways? Like a field I guess
The probabilistic description of microscopic particles reminds me of the distinction between the ontic and epistemic models of the wave function. Some believe the wave function is real (ontic), and there are no hidden variables. Others believe the wave function is a description of our state of knowledge of the system (epistemic).
Does your intuition lean one way or the other?
Regarding Bell's theorem, a often neglected requirement of the theorem is statistical independence of measurements. With a deterministic universe, that assumption can be dropped, and local hidden variables are still allowed.
One approach to two-dimensional fluid dynamics uses vorticity in Brownian motion, as proposed by Alexandre Chorin. So we have a big system of differential equations and a random number generator. It is natural to ask what we can do for quantum mechanics. I have made a number of suggestions in various TH-cam videos on quantum theory.
Hi, I am not so familiar with differential equations. Why do you use sometimes "D" and sometimes the turned 6 (I think it's a lowercase delta?) and what is the difference between these expressions?
normal d is used in normal differential equations. Delta is used in partial differential equations. Big D is the material derivative and is dependent on how you look at things. In the Eulerian view in fluids its usually the expression he explains in 11:00
@@schadenfreude7812 Thanks for the explaination ^^
Do you have the code published on github?
i love conciseness
what is the program language ??
Amazing
Subscribe to the channel by going through the comment section itself. Yet to watch the video.
Amazing!
21:07 so cute!!!!!!!
So far I managed to grasp every aspeckt in the videos, but on this one I got lost
So many air galaxies formed.
Здравствуйте. Благодарен за видео.
У Вселенной есть цикличность во времени, которые разделяются по комбинациям взаимодействий и делятся на периоды; 1. Вселенная собранная в одну квант струну. 2. Вселенная из коротко живущих фрактал с переходом в хаос. 3. Вселенная из хаоса с переходом в долго живущие фракталы. 4. Вселенная из долго живущих фрактал с переходом в одну квант струну.
При всех комбинациях, квант струна, может рваться но без отрыва при этом петлями складывается в мембраны образуя из них бутоны которые могут, от периода времени, сворачиваться ограничивая связи.
thank you 👍👍👍
Excelente!!!
Brilliant
awesome.
Heavy Duty ! 👍
9 ways to solve the same problem!? Whoa
Awesome video series. But this video is a bit long. It requires dedication and time, and does not really work by watching it in multiple sessions. Yeah, so I recommend grabbing a snack for this.