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Chaos Theory: the language of (in)stability 

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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
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Gao-DHIyj0Q.html&ab_channel=WhiteBatAudio
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-2gsn1HrDtdI.html&ab_channel=WhiteBatAudio
ru-vid.com/show-UC_6hQy4elsyHhCOskZo0U5g
LAKEY INSPIRED
soundcloud.com/lakeyinspired
ru-vid.com/show-UCOmy8wuTpC95lefU5d1dt2Q
Lucas Tie
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-K5F2wz-Rig8.html&ab_channel=LucasTie
ru-vid.com/show-UCFIK0Vk54HNOOZ1HD79wiyA
References
Chaos: The Mathematics Behind the Butterfly Effect - James Manning
www.colby.edu/mathstats/wp-content/uploads/sites/81/2017/08/2017-Manning-Thesis.pdf
YFX1520 Nonlinear Dynamics Lecture 9 - Dmitri Kartofelev
www.ioc.ee/~dima/YFX1520/LectureNotes_9.pdf
Attractors: Nonstrange to Chaotic - Robert L. V. Taylor
evoq-eval.siam.org/Portals/0/Publications/SIURO/Vol4/Attractors_Nonstrange_to_Chaotic.pdf?ver=2018-04-06-103239-977

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18 май 2021

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Комментарии : 495   
@LucasMalandrino
@LucasMalandrino 3 года назад
That transition to master oogway was so smooth, I'm still shocked
@abhijithcpreej
@abhijithcpreej 2 года назад
He has an Oogway with words.
@joezcool
@joezcool 2 года назад
the fact that this was top comment put me on edge like the whole video until the transition
@RodrigoTakehara
@RodrigoTakehara 2 года назад
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
@fjames208
@fjames208 2 года назад
Me too
@Thisisnotmyrealname8
@Thisisnotmyrealname8 2 года назад
I fainted.
@bramlentjes
@bramlentjes 3 года назад
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!
@Gonkee
@Gonkee 3 года назад
Appreciate that!
@GS-hv9rd
@GS-hv9rd Год назад
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…
@GMOsterloidDoogan
@GMOsterloidDoogan Год назад
@@GS-hv9rd Most intelligent people are humble so he most likely doesn't make a big deal about it, he simply tells them.
@tg_kaneki4371
@tg_kaneki4371 Год назад
@@GMOsterloidDoogan 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)
@andrewacornwell8678
@andrewacornwell8678 Год назад
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-uzJXeluCKMs.html
@nix3l_
@nix3l_ 3 года назад
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
@Gonkee
@Gonkee 3 года назад
Thank you, I appreciate it!
@itsjustleo3371
@itsjustleo3371 2 года назад
jellyfish logo, very creotive!
@natew4724
@natew4724 2 года назад
@@itsjustleo3371 It's Jeremy from Creosphere
@eccentricity23
@eccentricity23 2 года назад
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 :)
@duccline
@duccline 2 года назад
YO WTF CREO JELLYFISH
@legalnut9950
@legalnut9950 3 года назад
I like how we are the og fans of this channel xD
@krishna2803
@krishna2803 3 года назад
treu
@krishna2803
@krishna2803 3 года назад
true*
@dionysianapollomarx
@dionysianapollomarx 2 года назад
Me 2 feels good
@12333333333435454646
@12333333333435454646 2 года назад
True that
@tomaszmuza1957
@tomaszmuza1957 2 года назад
Hey guys how does it feel to be able to witness it all from the beginning? 😅
@teehee2589
@teehee2589 2 года назад
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.
@valaysalve2388
@valaysalve2388 2 года назад
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.
@darioisakovic7802
@darioisakovic7802 2 года назад
"Do you still think there's nothing to chaos theory?" - Half Life Scientist
@FunkyJeff22
@FunkyJeff22 3 года назад
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.
@Gonkee
@Gonkee 3 года назад
I google the topic with filetype:pdf at the end
@SYBIOTE
@SYBIOTE 3 года назад
@@Gonkee so research papers mainly?
@davidherrera4837
@davidherrera4837 2 года назад
@@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.
@abraruralam3534
@abraruralam3534 7 месяцев назад
There is a huge market for research paper to infotainment conversion.
@nicolasgiaconia8051
@nicolasgiaconia8051 3 года назад
This is such high quality work! Thank you very much for your effort, it is really appreciated!
@doommarine4239
@doommarine4239 2 года назад
I feel like this is one of those videos that you would only watch at 3 a.m. and I love it.
@mohamedlotfi982
@mohamedlotfi982 2 года назад
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!
@nonamenofamily405
@nonamenofamily405 2 года назад
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 👍
@tomaszmuza1957
@tomaszmuza1957 2 года назад
What a quality of production. I'm amazed this needs more recognition
@saikatmajumder3284
@saikatmajumder3284 2 года назад
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!!
@CrosSeaX
@CrosSeaX 2 года назад
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.
@TheGamingHungary
@TheGamingHungary 3 года назад
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.
@brianriely8107
@brianriely8107 2 года назад
where does the 6 come from? I would have expected 13x3*45
@vaheakli4551
@vaheakli4551 2 года назад
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!
@henryg7474
@henryg7474 3 года назад
I was just stuck on a chapter of a book about this exact subject, perfect timing!
@carly09et
@carly09et 2 года назад
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
@alexfan3279
@alexfan3279 2 года назад
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.
@priyadarshimukherjee9571
@priyadarshimukherjee9571 2 года назад
That was smooth...really smooth! I don't think that I have come across any video till date that explains chaos in simpler terms.
@bonkybonk_ow2793
@bonkybonk_ow2793 2 года назад
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!
@Scrawlerism
@Scrawlerism 2 года назад
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!
@inon4037
@inon4037 3 года назад
NEW VIDEO WOOOOOOOOO
@Chadderbox
@Chadderbox 2 года назад
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.
@kofiekue7386
@kofiekue7386 2 года назад
the quality of your videos is insane, underrated af
@erichopp244
@erichopp244 3 года назад
This is some high quality stuff! Definitely proud to be one of your early fans ;)
@CreaniKun
@CreaniKun 2 года назад
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!
@juliankandlhofer7553
@juliankandlhofer7553 3 года назад
You know what's also a gift? Your channel! Awesome as always 👍👍
@LorddirtGaming
@LorddirtGaming 2 года назад
that ending was amazing, especially with the music
@Julian-tf8nj
@Julian-tf8nj Год назад
superbly presented in an unbelievably concise manner! Thanks!
@nyscersul42
@nyscersul42 2 года назад
Beautifully done video. Attractive visually, well described, and... in some ways most important, the pause for thought between statements. *subscribed* :)
@alchemist2048
@alchemist2048 2 года назад
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.
@chemaguerra1635
@chemaguerra1635 2 года назад
These videos are GOLD. Thank you!
@baaaaaaaaaaaaaaaaaaaaaaam
@baaaaaaaaaaaaaaaaaaaaaaam 2 года назад
Wow I have not been paying attention to the number of views on these videos your channel is criminally underrated
@Himanshu-wg3ib
@Himanshu-wg3ib 2 года назад
This video explained this concept so well. Thanks a lot man :)
@hortonzkog609
@hortonzkog609 2 года назад
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.
@mecidgaliba2854
@mecidgaliba2854 3 года назад
Wow, I am amazed! Thanks for this gem.
@solphe
@solphe 2 года назад
Unpredictable ending - great way to give an example of the Chaos Theory using the actual punchline
@gehteuchnichtsan7911
@gehteuchnichtsan7911 2 года назад
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.
@MarcosLourencoAntonio
@MarcosLourencoAntonio 2 года назад
How amazing is that! Thank you very much.
@nejcbezget47
@nejcbezget47 2 года назад
Great video! The transitions between different sections remind me of Lemmino
@Gonkee
@Gonkee 2 года назад
That's exactly what I was going for :)
@no-bk4zx
@no-bk4zx 3 года назад
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 RU-vidr 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 ;).
@christosgalanis5984
@christosgalanis5984 Месяц назад
Watching this well structured and informative video in 2024. You did a really great job. Thank you for your knowledge shared and your time!
@jocker6271
@jocker6271 2 года назад
Very high quality video, I have no complaints Edit: also love the music choice, I am a big fan of synthwave
@salmon4402
@salmon4402 3 года назад
Very few channels get a subscribe, on the first video I watch of them, and even fewer get a bell, good job my dude =)
@marco4570
@marco4570 2 года назад
Amazing content. Love your programming videos and general sense for graphical presentation
@irmakakyldz1382
@irmakakyldz1382 Год назад
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!!!
@Baahaz
@Baahaz 2 года назад
This is an amazing video. Thank you.
@EggoTree
@EggoTree 2 года назад
great video, thanks man. I've been wondering about this stuff for a while
@abdelrahmansalah8602
@abdelrahmansalah8602 2 года назад
How on earth you are not +1 million subscribers? Your content is wonderful !
@niels.m
@niels.m 2 года назад
Amazing video! You're gonna blow up in no time!
@miguelgomezsierra5662
@miguelgomezsierra5662 2 года назад
This is my new favorite channel
@BLAISEDAHL96
@BLAISEDAHL96 2 года назад
Thank You for this.
@ericornelasmath
@ericornelasmath 2 года назад
This is god damn incredible. Quality Quality video and channel.
@dylanpainterisexistential
@dylanpainterisexistential 2 года назад
This is so cool! Awesome and very well explained video
@arthsojitra53
@arthsojitra53 2 года назад
Such a beautiful explanation !!
@ujjwalpandey1571
@ujjwalpandey1571 2 года назад
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?!
@eapenninan4950
@eapenninan4950 2 года назад
Plain,simple,powerful. Congrags
@brianriely8107
@brianriely8107 2 года назад
An amazing video--excellent presentation
@truffleshuffle314
@truffleshuffle314 2 года назад
Really good introduction, good luck on the channel my guy
@sheltondany8209
@sheltondany8209 2 года назад
damn bro that was the coolest thing this week !
@omidpakbin
@omidpakbin 4 месяца назад
Fantastic video! Great job.
@drxyd
@drxyd 11 месяцев назад
Beautiful video.
@tupacalypse88
@tupacalypse88 9 месяцев назад
My man you blow my mind every video please keep doing you buddy 👍👍👍
@hortonzkog609
@hortonzkog609 2 года назад
Broh, you really had this great explicite explanition! Really comprehensive! Excuse to my very chaotic spelling and what not.
@Angel-vc3bw
@Angel-vc3bw 3 года назад
Everytime you post a video it feels like christmas
@dundee2858
@dundee2858 2 года назад
Best math channel on RU-vid hands down
@iainmackenzieUK
@iainmackenzieUK 2 года назад
nice summary of Chaos. Thank you
@mpbiggame1010
@mpbiggame1010 Год назад
brilliant video. thank you
@willrandall4012
@willrandall4012 Год назад
Such a high quality video!
@christopherwalsh3101
@christopherwalsh3101 2 года назад
the music for the transition slides was dope!
@carlosmelochupas1189
@carlosmelochupas1189 2 года назад
This is awesome, please keep doing it.🥇
@fredward3410
@fredward3410 Год назад
I really want to believe that you made this entire video for the sole purpose of that ending
@lukedigiovanna9544
@lukedigiovanna9544 3 года назад
Wtf i finished this video expecting it to have at least 50k views. U deserve better 😭
@aka1782
@aka1782 3 года назад
wtf sameee 😭
@valaysalve2388
@valaysalve2388 2 года назад
The return of the legend
@brendawilliams8062
@brendawilliams8062 2 года назад
It is nice as far as the subject matter. Thx.
@tcreate.s
@tcreate.s 2 года назад
Awesome Quote!
@CHIKIPLEITOS
@CHIKIPLEITOS Год назад
LOVE THE CONTENT
@ConnoisseurOfExistence
@ConnoisseurOfExistence 2 года назад
Awesome!
@SAAARC
@SAAARC 2 года назад
Excellent video
@ChocolateMilkCultLeader
@ChocolateMilkCultLeader Год назад
This is beautiful
@krishna2803
@krishna2803 3 года назад
thanks for the amazing content mate :)
@HU5541N
@HU5541N Год назад
Loved it, Good explaination ❤❤❤
@lamarnash2439
@lamarnash2439 Год назад
Thank you, this was a wonderful lesson
@okay2037
@okay2037 2 года назад
High quality shit man keep it up you’ll be big one day
@donovanholm
@donovanholm 3 года назад
This is why I subbed!
@lachlancooke
@lachlancooke 3 года назад
“There are no accidents” - Master Oogway
@anhbayar11
@anhbayar11 2 года назад
"World is full of accidents and chaos" - who cares(name)
@shakisyaboi991
@shakisyaboi991 2 года назад
@@anhbayar11 happy little accidents
@elsorino
@elsorino Год назад
beautiful video
@loirenhuh
@loirenhuh Год назад
You make such as art of teachings
@psibarpsi
@psibarpsi 2 года назад
Glad to be here before this channel blows up.
@ZephirFX
@ZephirFX 3 года назад
That's purely excellent
@marcobrunacci6221
@marcobrunacci6221 2 года назад
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
@AICoffeeBreak
@AICoffeeBreak 2 года назад
This video is so great! 💪
@kjaanishji2595
@kjaanishji2595 Год назад
Great ending point!
@elimain1261
@elimain1261 2 года назад
This is an excellent video
@azvka
@azvka Год назад
Top notch
@Brazil-loves-you
@Brazil-loves-you 2 года назад
Wow I liked this video very much, it is very easy to follow
@rodie3602
@rodie3602 Год назад
So interesting!
@MrAman47
@MrAman47 2 года назад
I like the way you present stuff, also, ending made me giggle.
@CheshireArt_
@CheshireArt_ Год назад
Some high level stuff right here. My brain stopped analyzing by 9 mins........