Chaos Theory: the language of (in)stability
ฝัง
- เผยแพร่เมื่อ 10 พ.ค. 2024
- The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system evolves in the real world. This video aims to tell the story of chaos step by step, from simple non-chaotic systems, to different types of attractors, to fractal spaces and the language of unpredictability.
Timestamps:
00:00 - Intro
02:17 - Dynamical Systems
04:11 - Attractors
06:28 - Lorenz Attractor: Strange
08:54 - Lorenz Attractor: Chaotic
Music by:
Karl Casey @ White Bat Audio
• 80s Horror Cinematic T...
• Cyberpunk Dark Synthwa...
/ @whitebataudio
LAKEY INSPIRED
/ lakeyinspired
/ @lakeyinspired
Lucas Tie
• Video
/ @offline8244
References
Chaos: The Mathematics Behind the Butterfly Effect - James Manning
www.colby.edu/mathstats/wp-co...
YFX1520 Nonlinear Dynamics Lecture 9 - Dmitri Kartofelev
www.ioc.ee/~dima/YFX1520/Lect...
Attractors: Nonstrange to Chaotic - Robert L. V. Taylor
evoq-eval.siam.org/Portals/0/P... - วิทยาศาสตร์และเทคโนโลยี
![[TH]FFWS SEA Spring 2024 Knockout Stage - Day 16](http://i.ytimg.com/vi/jpvPyp7LESA/mqdefault.jpg)
That transition to master oogway was so smooth, I'm still shocked
He has an Oogway with words.
the fact that this was top comment put me on edge like the whole video until the transition
The video was so well made and well explained, and had no self promotion at all, I was predicting it would have some “please like and subscribe”, I didn’t predict that transition at all
Me too
I fainted.
As a graduate student in Mathematics with speciality in (infinite dimensional) dynamical systems and differential equations, I must admit this has to be one of the most beautiful videos on the internet about this topic!
Appreciate that!
So when you go on a date, how exactly do you tell them you’re a genius? Just say what you’re studying? Or maybe save that fo when you need to confuse them really quickly.. Haha. Talk about setting the bar high…
@@GS-hv9rd Most intelligent people are humble so he most likely doesn't make a big deal about it, he simply tells them.
@@QuincySterloidDoogan truly intelligent people know they aren't truly intelligent so he'd most likely just not say anything ab being a genius (he definitely is tho)
th-cam.com/video/uzJXeluCKMs/w-d-xo.html
You are CRIMINALLY underrated my guy. You explain everything clearly and keep me interested all throughout. The animations are stellar and you make everything feel intuitive.
Edit: he just quoted master oogway, we need more people like you
Thank you, I appreciate it!
jellyfish logo, very creotive!
@@itsjustleo3371 It's Jeremy from Creosphere
Yeah, I have seen similar videos by Veritasium and 3Blue1Brown, and this is on par or better. I would like to study this field more academically once I have reached a sufficient level of education :)
YO WTF CREO JELLYFISH
I like how we are the og fans of this channel xD
treu
true*
Me 2 feels good
True that
Hey guys how does it feel to be able to witness it all from the beginning? 😅
How do you do research for your videos? You've covered so many different topics in different fields more in depth than most popular science channels do. It's impressive.
I google the topic with filetype:pdf at the end
@@Gonkee so research papers mainly?
@@SYBIOTE Research papers are sometimes very dense. However, you can find many tutorials and introductions online.
For instance, he nicely summarized a part of what you would get in a course in nonlinear analysis.
There is a huge market for research paper to infotainment conversion.
If anyone, like me, was confused by the apparent intersection at 7:45, remember that the curve is actually in 3D. The x and y values might be the same but the z value will be different.
Also it is the del vector, that doesn't match up, if it were to match the the initial position for next step would be the same, making a loop.
"Do you still think there's nothing to chaos theory?"
- Half Life Scientist
This is such high quality work!
Thank you very much for your effort, it is really appreciated!
I feel like this is one of those videos that you would only watch at 3 a.m. and I love it.
What a quality of production. I'm amazed this needs more recognition
The best video on chaos theory I've seen, and I've seen a lot! Clear and simple yet not trivial. Perfect balance between maths, graphics and explanations. Congrats 👍
Simply put, that was by far the best introductory video on chaos theory I have seen out of 10s of videos I have watched. Truly wonderful!
I can't believe you used my favourite quote in a video about my favourite topic! You deserve more man! Keep up the good work!!
Absolutely beautiful. Thank you for your decision to start to make videos. Your videos are radiance of millions of stars in the sky of youtube!
This is some high quality stuff! Definitely proud to be one of your early fans ;)
Bro this video is absolutely an incredible job! Love the details, the simplicity, the smooth logic, and the visual presentation. You should definitely keep this up cuz bro video like yours makes me wanna learn more and learn harder and you cannot refuse anyone who wants to learn.
I was just stuck on a chapter of a book about this exact subject, perfect timing!
Doing mechanical engineering modelling, I so wish you were my math teacher this semester. You basically covered more topics in 13 minutes, which our prof failed to make us understand and learn in 13x6x45minutes.
This is just beautiful, something that is worth to learn, study but it was not taught too well.
where does the 6 come from? I would have expected 13x3*45
11:04 that was so interesting, and extremely new for me, I've never seen such a calculation and it was so helpful! Definitely worth a sub, keep up the great work dude!
the quality of your videos is insane, underrated af
Nice, thank you for this. I was looking for a reminder of the Lorenz's Attractor. This is very clear, I have been thinking on this for over fifty years AND I learned something from this presentation. Thank you again. The problem I'm looking at is the measuring of the measuring of REAL's
Just found you and loving all of these. Please don’t stop having as much of the math and code in the vids as possible!
I’ve been learning Nonlinear Systems, which also introduced phase plane, equilibrium types and Lyapunov stability.
Your video is awesome. I found the contents familiar and intelligible. I’m now expecting to learn more about chaos.
NEW VIDEO WOOOOOOOOO
So, I discovered your channel when you had just dropped the Music and Sound Synthesis video and I have to say, you are incredibly underrated, as other commenters have also pointed out. For 17K subs, the level of visuals and detailed explanations without making it super complex is a very tough task and it seems like you have perfected it witt only 5 videos lol.
Amazing channel, keep uploading and some day you will blow up. Trust me. The only TH-camr I can think of with a similar video style would be Zach Star(aka MajorPrep) but your visuals have a higher detail and quality to it.
I have really no criticism except at some parts it felt like you were going a little bit too fast but to be honest, great work, keep doing this and please don't stop putting memes in your videos just make sure to not do too much of it ( That Master Oogway quote at the end was brilliant ).
I am sure you will blow up soon so don't forget me ;).
That was smooth...really smooth! I don't think that I have come across any video till date that explains chaos in simpler terms.
that ending was amazing, especially with the music
usually i put videos like this on 1.5 because of my brain dead attention span, but you managed to keep me interested, good job!
These videos are GOLD. Thank you!
Amazing video! You're gonna blow up in no time!
This video explained this concept so well. Thanks a lot man :)
This man comes once every few months and pops up in my subscriptions tab, and I just have to immediately drop everything and take a peek.
great video, thanks man. I've been wondering about this stuff for a while
You know what's also a gift? Your channel!
Awesome as always 👍👍
Your quality is unbelievable, massively underrated. You should expand to doing contents on other things such as mysteries , strange events , frauds , unsolved cases, explaining complex things(quantum computers, blackholes etc..). You've got the soothing voice and editing skills , perfect match for an educational channel. After Lemmino and ColdFusion , I add Inspecto to my list.
Wow, I am amazed! Thanks for this gem.
Great video! The transitions between different sections remind me of Lemmino
That's exactly what I was going for :)
Really good introduction, good luck on the channel my guy
superbly presented in an unbelievably concise manner! Thanks!
Very few channels get a subscribe, on the first video I watch of them, and even fewer get a bell, good job my dude =)
damn bro that was the coolest thing this week !
How did you animate the slope field at 2:08? My guess is manim but I'd be curious to see if there are other options.
Chaos theory is very interesting
Wow I have not been paying attention to the number of views on these videos
your channel is criminally underrated
This is my new favorite channel
This is an amazing video. Thank you.
How amazing is that! Thank you very much.
Everytime you post a video it feels like christmas
This is god damn incredible. Quality Quality video and channel.
This is so cool! Awesome and very well explained video
Beautifully done video. Attractive visually, well described, and... in some ways most important, the pause for thought between statements. *subscribed* :)
Damn. This was awesome. Your explanation on this topic was so simple and elegant. Thank you. This topic one of the most interesting I think because I believe that this is how nature and evolution works. It's genius how it's possible to use the language of mathematics to describe it but it still is impossible to predict nature.
Amazing content. Love your programming videos and general sense for graphical presentation
Such a beautiful explanation !!
This is awesome, please keep doing it.🥇
“There are no accidents” - Master Oogway
"World is full of accidents and chaos"
- who cares(name)
@@anhbayar11 happy little accidents
Thank You for this.
Very high quality video, I have no complaints
Edit: also love the music choice, I am a big fan of synthwave
thanks for the amazing content mate :)
How on earth you are not +1 million subscribers? Your content is wonderful !
This is why I subbed!
High quality shit man keep it up you’ll be big one day
This is why I still have an internet connection my dude!!
thank you for the amazing perspective!!
EDIT: Why aren't you having a discord server already?!
An amazing video--excellent presentation
Unpredictable ending - great way to give an example of the Chaos Theory using the actual punchline
Good job, earned my sub!
Plain,simple,powerful. Congrags
Such a high quality video!
Fantastic video! Great job.
This video is so great! 💪
LOVE THE CONTENT
What software do you use to make these BEAUTIFUL animations?
He could be using manim, the software developed by 3blue1brown: github.com/3b1b/manim
In his video about epidemiology - th-cam.com/video/xsmV6Oi1k7o/w-d-xo.html
He answered someone - "I'm writing my own graphics library with Java as I make these videos, which uses LWJGL and NanoVG."
Edit: Thanks @LimitedWard, I was actually searching for this!
It isn't difficult. For the dual Lorenz animation around 8:00 I wrote a program and you can get it free here:
www.fractal-animation.net/progz/filez.html
.
He said on his video that he uses a program coded by himself
Quickest sub in a while
My man you blow my mind every video please keep doing you buddy 👍👍👍
nice summary of Chaos. Thank you
Glad to be here before this channel blows up.
Beautiful video.
The return of the legend
This is beautiful
Loved it, Good explaination
❤❤❤
the music for the transition slides was dope!
I'm flabbergasted how this video is so informative and visually sophisticated... the outro really made me question my worth and aim in life though. thanks man!!!
Just interacting for algorithm points to you!
brilliant video. thank you
Best math channel on TH-cam hands down
That's purely excellent
Awesome!
This is an excellent video
It is nice as far as the subject matter. Thx.
Great video dude:)
Broh, you really had this great explicite explanition! Really comprehensive! Excuse to my very chaotic spelling and what not.
Really well presented video! Also I had no idea that lambda stood for something. I always thought it was some arbitrarily assigned coefficient. There's definitely always something new to learn
Wtf i finished this video expecting it to have at least 50k views. U deserve better 😭
wtf sameee 😭
Thank you, this was a wonderful lesson
Wow I liked this video very much, it is very easy to follow
Awesome Quote!
Watching this well structured and informative video in 2024. You did a really great job. Thank you for your knowledge shared and your time!
I like the way you present stuff, also, ending made me giggle.
imagine there is this kind of a user-friendly public website/resources where it has a great amount of tutorial about physics featuring the pros and cons with a very direct fat information and data.
Excellent video
Great ending point!