Visualizing the varying angles progression as a fractal evolving over time is such a creative way to view chaos theory that I haven't seen anywhere else before. And it looks so beautiful.
How on earth does this only have 1.000 views? Everything from the editing, to his voice, to the way things are demonstrated and explained is so well done
full disclosure: As I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
¡Great animacion! Video need more detail. • ¿Pèndulums in grid all have equal length? • Range x and y axis is -π; π • ¿What is start velocity? • ¿How select color? • Range x and y for last grid is 0; 2π Should compare equal level geography: • Butterfly in Brasil; tornado in US or • Butterfly in Amazonas; tornado in Texas
2:05 there's obviously something wrong with this simulation. Look at the pendulums at the bottom right corner. It's spinning around faster and faster, which means the mechanical energy involved is increasing over time. Now, if I were to guess it's rounding errors which is unavoidable, but there are some simple error smoothing you can add: for every frame, after you calculate the angular velocity/angles of the next frame, first calculate the total energy invovled with that, and then normalize it back to the value you started with, then have the normalized result be fed into the next frame. You'll still get slightly off results, but it won't be quite this drastic.
Woah amazing. That's the typical misunderstanding, or rather misuse of fractals shown right here. A fractal typically isn't self familiar. The reason we focus on those is because they're beautiful and easily produced but a fractal usually is way more chaotic, like the one shown here. It's awesome man, great vid
Beautiful representation :) I have always wondered whether the double pendulum would retain any sort of continuity after having heard of chaos theory. But hey, it did (somehow)! and that is a nice looking turbulence.
@@calculator_gaming As I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
Thank you so much 🙏🏻 something in particular that stood for you? I created this mostly by coding it myself in Javascript utilising the p5js library. I would recommend checking out “The Coding Train” for full tutorials on how to make these kind of visuals :🙏✨✨🙆♂️
@@nicogsplayground I find the probability heat map overtime especially inspiring. Its almost like blending together spatial-temporal dimensions into a new realm of its own.
Great video. Sub'd. I intellectually love this sort of thing most deeply of all. It's a category error to say "...how chaos theory shapes our world." Chaos Theory involves our attempt to model chaotic phenomena. It's not the phenomena itself, which is what shapes our world. That statement conflates the map with the territory.
Thank you so much Clark 🙏🏻 But doesn’t our attempt to model the phenomenon shape our world too? Take The three body problem, this shapes our understanding of the world and therefore shapes our world no? 🙆♂️ (my apologies if I understood the Q wrong) But apart from the error anything in particular that you loved?🙆♂️✨
Thank you so much 🙏🏻 I did not know the term photoelasticity, had to google it, but you are 100% right, looks a lot like these holographic reflections!
Converted the angles, which we mapped on the grid to colors, rgb values. (01:57) But you are right that I should've probably put more emphasise on that!
@@nicogsplayground Makes sense. Since this looks like a continuous map and angles need to jump back to 0 if they go past 2π, you would need to map the sine or dot product or something like that to RGB space. Do you know the exact details?
I've seen this fractal on Sam Maksimovich's channel before, but less well explained. This is a beautiful way to depict how that fractal is formed, my only criticism is the video transcript feels verbose without adding much, like it's been generated with chatgpt. It also doesn't help that the voice is AI generated.
Thank you so much 🙏🏻 I don’t see it as criticism, but as valuable feedback! I used AI to help with the writing of my intro and outro otherwise only spelling was corrected as English is my third language. Thanks for pointing that out! As I hate recording my voice I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over and the pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅 Anything in particular that stood out for you on how I explained it? Thanks in advance for the feedback! 🙏🙆♂️
Motions in chaotic behavor is based on nonlinearity of the mechnical systems. However, chaos is not a random motion. As you have seen, the motion can be described with a specific nested structure, which is called fractal.
@@nicogsplayground Thanks for your answer. Nothing is random, therefore chaos doesn't exist. In fact, I can't even grasp what chaos would be, or how even hypothetically could exist...
@@ConnoisseurOfExistence that’s why it’s called Chaos Theory. The idea isn’t that something behaves randomly, one can predict it’s behaviour given the initial conditions. But when we try to determine the initial conditions based on it’s behaviour, it get’s pretty hard because of the “chaos”.
@@nicogsplayground Maybe we can't even determine its exact behavior (future state, position and momentum) from the initial conditions, without actually letting it play out. They call it computational irreducibility. Many complex systems are like that. Beautiful video, by the way. I shared it in many places. I love fractals!
😳 triple angles, 3D-version of the fractal. But how to calculate the color in this case. For 2 angles I assume sin(a,b) and 0=red, 1=violet. Is there stereoscopic variant 🤔
@@Evan---- Thanks!!! They often take a lot of time. Keyframing and tweaking curves so the speed and motion fits the whole composition and story line, can take hours for maybe 0.8 seconds of motion. Knowing that it doesn't go unnoticed by others really makes my day, appreciate it!
Would this be considered a fractal? I thought fractals require self-similarity... Wouldn't this be a subset of samples of the phase space of the system evolving as you scroll forward through time? Sorry if this is a dumb question.
@@HarishBabuM Coded in Javascript using the p5js library 🙆♂️ Will share the github online version soon probably ✨anything in particular that stood out for you?
@@nicogsplaygroundIn my opinion your videos are perfect. If you want more views to begin sharing your content, I would try to get promoted by similar youtubers. I saw that some of popular youtubers actually promoted small creators.
I used several audio tracks from several libraries I bought over the years, some are from premium beat, others from ezco and others like that. Not a specific artist or full song
All of the simulations where created using Javascript & the p5js library. Then I put everything together in Premiere Pro & animated the B-roll + some of the explanations. For example the grid was simulated in JS but I animated the x-axis & y-axis transition in After Effects :))
They are saying that "Chaos theory suggests that minuscule changes in initial conditions can lead to massive differences later on" But that is WRONG. The particular part that is wrong is the "minuscule changes". The changes are not "minuscule", they are *INFINITESIMAL* and that is where chaos arises. We have a function, a real - DETERMINISTIC - function, that perfectly describes from the initial conditions that we gave to the computer of the experiment... But in order for that function to be calculated we need INFINITE amount of time... Because the function's graph is a fractal... And thus, *INFINITESIMAL* changes can create non-infinitesimal differences later on. Thus, we can never fully create a perfect model for our experiment, because the information that we need to know is infinite.
@@-_Nuke_- Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution and is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. Sources: Kellert, Stephen H. (1993). In the Wake of Chaos: Unpredictable Order in Dynamical Systems. University of Chicago Press. p. 32. ISBN 978-0-226-42976-2. Bishop, Robert (2017), "Chaos", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2017 ed.), Metaphysics Research Lab, Stanford University Werndl, Charlotte (2009). "What are the New Implications of Chaos for Unpredictability?". The British Journal for the Philosophy of Science. 60 (1): 195-220. arXiv:1310.1576. doi:10.1093/bjps/axn053. S2CID 354849.
@@nicogsplayground I agree! My nitpicking part is that these differences in initial conditions don't need to be small, because the word "small" is still a huge word in the world of chaos. Even an infinitesimally small difference will be enough for the whole thing to derail into chaos. I just made this comment to really emphasize the sheer infinity in the nature of chaos.
As much as i love the visuals, sound, and explanation (it was very well made), please credit Sam Maksimovich for his first original take on this concept (th-cam.com/video/n7JK4Ht8k8M/w-d-xo.html). It is so clearly tied to his video on it, even using the same concept and even color mapping.
@@ray-pu8vt To be completely honest, I came by a paper with the same name written by Jeremy S. Heyl more than 16 years ago. The next and basically only source I worked with was a blog post by Jason on the softologyblog While working on the visualisation someone on reddit replied with a code snippet, with a very neat implementation for the colors coming from Nikolai Mikuszeit, published in 2015, which on its turn was based on the colors from a book: Symmetry in Chaos: A search for Pattern in Mathematics, Art, and Nature, by Micheal Field and Martin Golubitsky. As I used different measurements I tweaked it so the colors would match. It is only after coding the project, putting it together in a video & finishing it all together that I discovered the TH-cam video by Sam which is awesome! Although I do not mind giving credit where credit is due, but I don’t see how this should be the case here. I explained a mathematical phenomena, from a different perspective, and from a different input angle with Chaos Theory. Nor was Sam the first discovering the concept, nor the usage of the colors. But regardless, being the first to discover of a mathematical concept, is different from being the first to create something, in which credit would certainly be appropriate. In this case I don’t see how it would be appropriate nor fair to credit Sam. (And this is nothing against Sam or anyone else, love his video, and I will add this to the description + all the resources I did use to come to my visualisation, not because I think credit is due, but rather so that others can see another way of explaining the concept)
@@nicogsplayground Im terribly sorry for taking such a one sided perspective on your video. I now realize that i was wrong and that you had no real intention to directly copy Sam's video. Thanks for clarifying!
@@ray-pu8vt That is 100% okey! In a world of social media we can let the one sided POV’s get the best of us, although we are aware another side of a story could exist. I respect your time & energy you put in defending someone’s work btw + The fact that you are aware of the other side now & decided to apologise is a something so rare in a comment section of a TH-cam video, that I’m honestly so grateful for the reasonable & very mature comment. I appreciate you
Motions in chaotic behavor is based on nonlinearity of the mechnical systems. However, chaos is not a random motion. As you have seen, the motion can be described with a specific nested structure, which is called fractal. around 02:52, the edges, every pixel represents a pendulum that had less than 0.001 deg in difference, but the vast amount of different colors shows the chaos that emerges from smaal initial differences. Many other chaotic systems look symmetrical btw 🙆♂
Appreciate it! When simulating a double pendulum the mass of the two balls and the length of the legs connecting them stay constant and won’t change over time, that’s what I meant with “constant variables”. Meanwhile the position of the balls or the angles made by the legs are variables that change. I Should’ve said that indeed, thanks for the feedback!! 🙏🙏
English is not my first, nor my second language. With dutch & frensh being my motherlanguages, some of the sentence structures might sound strange, except from some suggestions by NotionAI for better words & grammar, the script is written by le me. 🙆♂️ first time someone called my writing non-human, but I’ll take the compliment as “out of this world” 😅❤️
Unless you where talking about the voice over, that’s actually a mistake 💀 As I hate recording my voice (accent, english yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
I agree! As mentioned before: I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
![⭐ฮิตในTikTok!! ( มะมะมะหมูเด้ง MooDeng ) Ver. แดนซ์ ReMix BY [ ดีเจกิต รีมิกซ์ ]](http://i.ytimg.com/vi/4noyAoMa7bQ/mqdefault.jpg)
Breaking computers by asking questions too hard for them is one of my favorite things to do.
the divide by 0 is still the one and original
Visualizing the varying angles progression as a fractal evolving over time is such a creative way to view chaos theory that I haven't seen anywhere else before. And it looks so beautiful.
Thank you so much 🙏🏻
How on earth does this only have 1.000 views? Everything from the editing, to his voice, to the way things are demonstrated and explained is so well done
Thank you so much 🙏🏻 Appreciate it!
full disclosure: As I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
¡Great animacion! Video need more detail.
• ¿Pèndulums in grid all have equal length?
• Range x and y axis is -π; π
• ¿What is start velocity?
• ¿How select color?
• Range x and y for last grid is 0; 2π
Should compare equal level geography:
• Butterfly in Brasil; tornado in US
or
• Butterfly in Amazonas; tornado in Texas
Probably posted from Mars 😂
The voice is AI dude lol
2:05 there's obviously something wrong with this simulation. Look at the pendulums at the bottom right corner. It's spinning around faster and faster, which means the mechanical energy involved is increasing over time.
Now, if I were to guess it's rounding errors which is unavoidable, but there are some simple error smoothing you can add: for every frame, after you calculate the angular velocity/angles of the next frame, first calculate the total energy invovled with that, and then normalize it back to the value you started with, then have the normalized result be fed into the next frame. You'll still get slightly off results, but it won't be quite this drastic.
Who agrees this guy is criminally underrated:
like beggar
Woah amazing. That's the typical misunderstanding, or rather misuse of fractals shown right here. A fractal typically isn't self familiar. The reason we focus on those is because they're beautiful and easily produced but a fractal usually is way more chaotic, like the one shown here. It's awesome man, great vid
Some clips from this video could be dropped right into an Apple keynote and no one would bat an eye.
That’s a huge compliment! Thank you so much 🙏🏻
(if anyone at Apple would be reading this: email me oxxo)
I love the narration style, it brings back so many memories.
Bro's David Attenborough
Superb video, very nicely explained ! I would have loved to see a zoom into the fractal !
Thank you so much 🙏🏻 might create some extra visual content next week, i’ll keep you posted 🙆♂️
Beautiful representation :)
I have always wondered whether the double pendulum would retain any sort of continuity after having heard of chaos theory.
But hey, it did (somehow)! and that is a nice looking turbulence.
Thank you so much 🙏🏻 appreciate it!
Add a third dimension for the percentage of the length the joint is at and take different planar sections of it to see what's happening
It's like splitting hairs when the differences accumulate to the point the conditions part ways and become no longer similar
Very trippy. Will add it to my list of things to watch if I ever try mushrooms.
I can't tell if this is an AI generated voice or a real voice becuase it never changes in tone (thats a compliment)
@@calculator_gaming As I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
Very well made video!!! Super interesting. I'd love to see a tutorial of how to visualize things like this on computer.
Thank you so much 🙏🏻 something in particular that stood for you?
I created this mostly by coding it myself in Javascript utilising the p5js library. I would recommend checking out “The Coding Train” for full tutorials on how to make these kind of visuals :🙏✨✨🙆♂️
@@nicogsplayground I find the probability heat map overtime especially inspiring. Its almost like blending together spatial-temporal dimensions into a new realm of its own.
Guys, the new David Attenborough just dropped!
Wow really great video - didn´t know these kinds of fractals - loving it! 👍
Thank you so much Tobias 🙏🏻 Anything in particular that stood out for you?
Time to update my milkdrop plugin. Superb visuals here.
At least 20y since I’ve heard of Milkdrop waw haha! & Thank you so much 🙏🏻 anything in particular that you liked? 🙆♂️
2:07
I love how the corners can become a seizure trigger
I don't know how else to describe it, this is not a negative comment
Great video. Sub'd. I intellectually love this sort of thing most deeply of all.
It's a category error to say "...how chaos theory shapes our world." Chaos Theory involves our attempt to model chaotic phenomena. It's not the phenomena itself, which is what shapes our world. That statement conflates the map with the territory.
Thank you so much Clark 🙏🏻
But doesn’t our attempt to model the phenomenon shape our world too? Take The three body problem, this shapes our understanding of the world and therefore shapes our world no? 🙆♂️ (my apologies if I understood the Q wrong)
But apart from the error anything in particular that you loved?🙆♂️✨
Its beautifully smooth
Could the unchanging center bit give us information on which initial conditions give us the longest duration of predictable outcomes?
Wonderful! Thanks for making this!
Thanks Jeffrey! Appreciate it!
Bro what the fuck. What a masterpiece
Ayeeee appreciate it a lot! 😂🙆♂️🙏
This has only 18k views.
Outrageous.
@@bean751-n2y I would even say: deplorable
Wow, this is cool. Looks very much like photoelasticity.
Thank you so much 🙏🏻 I did not know the term photoelasticity, had to google it, but you are 100% right, looks a lot like these holographic reflections!
Sneak peek at Pendulum’s next album cover
this is so good, it deserves a place in the yt trends ngl
Thank you so much broo 🙏🏻
The production on this video is SO! high! 💪
Appreciate it! Something specific that you liked? 🙏
@@nicogsplayground Specifically, all of it :D
Underrated animation
@@progamer69243 I appreciate the compliment Mario! Was there a scene or specific animation that you liked in particular? Thanks again 🙏🙏🙏
I need like all of those visuals as a gif or something
Awesome video! I think you didn't explain an important detail though, what do the colors represent?
Converted the angles, which we mapped on the grid to colors, rgb values. (01:57) But you are right that I should've probably put more emphasise on that!
@@nicogsplayground Makes sense. Since this looks like a continuous map and angles need to jump back to 0 if they go past 2π, you would need to map the sine or dot product or something like that to RGB space. Do you know the exact details?
@@Miaumiau3333have to double check but I think:
R: 255/2 + 255/2 * Sin(angle 1) * cos(angle 2)
G: 255/2 + 255/2 * Sin(angle 1) * sin(angle 2)
B: 255/2 + 255/2 * cos(angle 1)
@@nicogsplayground This looks good, thanks Nicog!
For anyone wondering:
Blue = Pendulum at lowest
Red = Pendulum at highest
Darker = Low Velocity
Brighter = High Velocity
I've seen this fractal on Sam Maksimovich's channel before, but less well explained. This is a beautiful way to depict how that fractal is formed, my only criticism is the video transcript feels verbose without adding much, like it's been generated with chatgpt. It also doesn't help that the voice is AI generated.
Thank you so much 🙏🏻 I don’t see it as criticism, but as valuable feedback! I used AI to help with the writing of my intro and outro otherwise only spelling was corrected as English is my third language. Thanks for pointing that out! As I hate recording my voice I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over and the pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
Anything in particular that stood out for you on how I explained it?
Thanks in advance for the feedback! 🙏🙆♂️
What is chaos? All I've ever seen are different states of order.
Motions in chaotic behavor is based on nonlinearity of the mechnical systems. However, chaos is not a random motion. As you have seen, the motion can be described with a specific nested structure, which is called fractal.
@@nicogsplayground Thanks for your answer. Nothing is random, therefore chaos doesn't exist. In fact, I can't even grasp what chaos would be, or how even hypothetically could exist...
@@ConnoisseurOfExistence that’s why it’s called Chaos Theory. The idea isn’t that something behaves randomly, one can predict it’s behaviour given the initial conditions. But when we try to determine the initial conditions based on it’s behaviour, it get’s pretty hard because of the “chaos”.
@@nicogsplayground Maybe we can't even determine its exact behavior (future state, position and momentum) from the initial conditions, without actually letting it play out. They call it computational irreducibility. Many complex systems are like that. Beautiful video, by the way. I shared it in many places. I love fractals!
@ConnoisseurOfExistence Plenty of things are random. Statistics and Thermodynamics rely on randomness existing to be accurate sciences.
Beautiful
Why does this channel only have 422 subscribers?
Asking myself that question every single day 🥹✨🙆♂️
Everybody gangsta until triple pendulum
I was already sweating now tbh
😳 triple angles, 3D-version of the fractal. But how to calculate the color in this case. For 2 angles I assume sin(a,b) and 0=red, 1=violet. Is there stereoscopic variant 🤔
Awesome
Thank you so much Evan 🙏🏻 Something in particular that you enjoyed? Can always use the feedback
@@nicogsplayground animations are quality
@@Evan---- Thanks!!! They often take a lot of time. Keyframing and tweaking curves so the speed and motion fits the whole composition and story line, can take hours for maybe 0.8 seconds of motion. Knowing that it doesn't go unnoticed by others really makes my day, appreciate it!
what hidden gem did I just stumble into?
Ten out of ten.
@@LivingBreathingRedFlag 🫡 Thank you so much, was there anything specific that stood out for you (or any feedback)?
Would this be considered a fractal? I thought fractals require self-similarity... Wouldn't this be a subset of samples of the phase space of the system evolving as you scroll forward through time? Sorry if this is a dumb question.
No such thing as dumb questions, I had to google it to be sure, but Self similiarity includes Multifractal scaling
what determines the color of the pendulum in this simulation?
The only variables that evolve over time: the angles made by the legs of the pendulum, hence why I mapped it on a grid 😅🙆♂️
This is so coooool
Beauty
Bro just updated chaos theory.
I got my lasagna dude! 😎
Waoh! Can you run the simulation longer?
@@adrienledoux357 will upload some extra content, with some zoom in’s etc next week 🙆♂️ will keep you posted ✨
@@nicogsplayground what's the softwares used?
@@HarishBabuM Coded in Javascript using the p5js library 🙆♂️ Will share the github online version soon probably ✨anything in particular that stood out for you?
perfect video everyone watch this.
Appreciate it IceMan! Anything specific that you liked?
holy shit this is sick
This video is better than all the ones I've seen so far.
Thank you so much 🙏🏻 Anything specific that it made it better than all the other ones? Feedback is much appreciated!!!
@@nicogsplaygroundIn my opinion your videos are perfect. If you want more views to begin sharing your content, I would try to get promoted by similar youtubers. I saw that some of popular youtubers actually promoted small creators.
@@nicogsplaygroundoh, and a lot of tags
May i ask where thou got the music from
I used several audio tracks from several libraries I bought over the years, some are from premium beat, others from ezco and others like that. Not a specific artist or full song
How did you animated this? o:
All of the simulations where created using Javascript & the p5js library. Then I put everything together in Premiere Pro & animated the B-roll + some of the explanations. For example the grid was simulated in JS but I animated the x-axis & y-axis transition in After Effects :))
@@nicogsplayground you are f#cking talented bro
@@nachoalk ayeee appreciate it!!!!
It’s 3am and I’m somewhere here
3am vibez guaranteed
Your channel rocks. Subscribed. This is so useful of a visualization of the notorious double pendulum!
Thank you so much Chase 🙏🏻 Glad you find it useful!!!! Makes my day
bros narrating a nature documentary 💀💀💀
They are saying that "Chaos theory suggests that minuscule changes in initial conditions can lead to massive differences later on"
But that is WRONG.
The particular part that is wrong is the "minuscule changes". The changes are not "minuscule", they are *INFINITESIMAL* and that is where chaos arises.
We have a function, a real - DETERMINISTIC - function, that perfectly describes from the initial conditions that we gave to the computer of the experiment... But in order for that function to be calculated we need INFINITE amount of time... Because the function's graph is a fractal... And thus, *INFINITESIMAL* changes can create non-infinitesimal differences later on. Thus, we can never fully create a perfect model for our experiment, because the information that we need to know is infinite.
@@-_Nuke_- Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution and is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos.
Sources:
Kellert, Stephen H. (1993). In the Wake of Chaos: Unpredictable Order in Dynamical Systems. University of Chicago Press. p. 32. ISBN 978-0-226-42976-2.
Bishop, Robert (2017), "Chaos", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2017 ed.), Metaphysics Research Lab, Stanford University
Werndl, Charlotte (2009). "What are the New Implications of Chaos for Unpredictability?". The British Journal for the Philosophy of Science. 60 (1): 195-220. arXiv:1310.1576. doi:10.1093/bjps/axn053. S2CID 354849.
@@nicogsplayground I agree! My nitpicking part is that these differences in initial conditions don't need to be small, because the word "small" is still a huge word in the world of chaos. Even an infinitesimally small difference will be enough for the whole thing to derail into chaos.
I just made this comment to really emphasize the sheer infinity in the nature of chaos.
Blud thinks he is an artist (is one f*cking genius ) ❤
Almost looks like the outside of a Julia set at
I did not notice that, but now that you say so….
Orrrrrrr the Julia set looks like the inside of the Double Pendulum Fractal
Absurd, what have you used to create this?
Thank you so much 🙏🏻 Using Javascript & the p5js library for all the simulations 🙆♂️🙆♂️
Is this actually a fractal? From my naive understanding, it doesn't seem to be a fractal
Can you do it with n-pendulum?
@@adrienledoux357 In theory yes, but then we should have an n-axis grid, which wouldn’t create anything interesting I guess haha
Even 3D glasses wouldn't be enough for that. You'd need nD glasses, not to mention a biology that could make sense of it.
it looks like starglow from after effects
The plugin? Never used it tbh, what part of it’s functionality has a similar look? 👀 Could be interesting for future video’s 🙆♂️🙆♂️
As much as i love the visuals, sound, and explanation (it was very well made), please credit Sam Maksimovich for his first original take on this concept (th-cam.com/video/n7JK4Ht8k8M/w-d-xo.html). It is so clearly tied to his video on it, even using the same concept and even color mapping.
@@ray-pu8vt To be completely honest, I came by a paper with the same name written by Jeremy S. Heyl more than 16 years ago.
The next and basically only source I worked with was a blog post by Jason on the softologyblog
While working on the visualisation someone on reddit replied with a code snippet, with a very neat implementation for the colors coming from Nikolai Mikuszeit, published in 2015, which on its turn was based on the colors from a book: Symmetry in Chaos: A search for Pattern in Mathematics, Art, and Nature, by Micheal Field and Martin Golubitsky. As I used different measurements I tweaked it so the colors would match.
It is only after coding the project, putting it together in a video & finishing it all together that I discovered the TH-cam video by Sam which is awesome!
Although I do not mind giving credit where credit is due, but I don’t see how this should be the case here. I explained a mathematical phenomena, from a different perspective, and from a different input angle with Chaos Theory.
Nor was Sam the first discovering the concept, nor the usage of the colors. But regardless, being the first to discover of a mathematical concept, is different from being the first to create something, in which credit would certainly be appropriate.
In this case I don’t see how it would be appropriate nor fair to credit Sam.
(And this is nothing against Sam or anyone else, love his video, and I will add this to the description + all the resources I did use to come to my visualisation, not because I think credit is due, but rather so that others can see another way of explaining the concept)
@@nicogsplayground Im terribly sorry for taking such a one sided perspective on your video. I now realize that i was wrong and that you had no real intention to directly copy Sam's video. Thanks for clarifying!
@@ray-pu8vt That is 100% okey! In a world of social media we can let the one sided POV’s get the best of us, although we are aware another side of a story could exist. I respect your time & energy you put in defending someone’s work btw + The fact that you are aware of the other side now & decided to apologise is a something so rare in a comment section of a TH-cam video, that I’m honestly so grateful for the reasonable & very mature comment. I appreciate you
how do you even convert angels into points?
😕😕😕😕😕😕😕😕😕😕😕😕
(x,y) = (theta1, theta2) = (first angle, second angle)
its*
bro that graphics card probably got cooked 😭😭😭
@@xoxoheartz 😂 the power of GPU va CPU 💪
I’d love to see this fractal projected onto a torus
I see symmetrical pattern, not chaos
Motions in chaotic behavor is based on nonlinearity of the mechnical systems. However, chaos is not a random motion. As you have seen, the motion can be described with a specific nested structure, which is called fractal.
around 02:52, the edges, every pixel represents a pendulum that had less than 0.001 deg in difference, but the vast amount of different colors shows the chaos that emerges from smaal initial differences. Many other chaotic systems look symmetrical btw 🙆♂
lol i thought you were a tts
Nice video but chatgpt ahh script
"length and mass are constant variables" doesn't make much sense but the video was good
Appreciate it! When simulating a double pendulum the mass of the two balls and the length of the legs connecting them stay constant and won’t change over time, that’s what I meant with “constant variables”. Meanwhile the position of the balls or the angles made by the legs are variables that change. I Should’ve said that indeed, thanks for the feedback!! 🙏🙏
I wonder how much AI you used in the video making process. The wording of some sentences sounds kind of... non human.
English is not my first, nor my second language. With dutch & frensh being my motherlanguages, some of the sentence structures might sound strange, except from some suggestions by NotionAI for better words & grammar, the script is written by le me. 🙆♂️ first time someone called my writing non-human, but I’ll take the compliment as “out of this world” 😅❤️
Unless you where talking about the voice over, that’s actually a mistake 💀 As I hate recording my voice (accent, english yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅
Don't like the AI voice, feels soulless and uninteresting to listen for more than a few seconds.
I agree! As mentioned before: I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅