This equation will change how you see the world (the logistic map)

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  • ๊ฒŒ์‹œ์ผ 2024. 03. 28.
  • The logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: www.fasthosts.co.uk/veritasium Code for interactives is available below...
    Animations, coding, interactives in this video by Jonny Hyman ๐Ÿ™Œ
    Try the code yourself: github.com/jonnyhyman/Chaos
    References:
    James Gleick, Chaos
    Steven Strogatz, Nonlinear Dynamics and Chaos
    May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976). doi.org/10.1038/261459a0
    Robert Shaw, The Dripping Faucet as a Model Chaotic System
    archive.org/details/ShawRober...
    Crevier DW, Meister M. Synchronous period-doubling in flicker vision of salamander and man.
    J Neurophysiol. 1998 Apr;79(4):1869-78.
    Bing Jia, Huaguang Gu, Li Li, Xiaoyan Zhao. Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns Cogn Neurodyn (2012) 6:89-106 DOI 10.1007/s11571-011-9184-7
    A Garfinkel, ML Spano, WL Ditto, JN Weiss. Controlling cardiac chaos
    Science 28 Aug 1992: Vol. 257, Issue 5074, pp. 1230-1235 DOI: 10.1126/science.1519060
    R. M. May, D. M. G. Wishart, J. Bray and R. L. Smith Chaos and the Dynamics of Biological Populations
    Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 413, No. 1844, Dynamical Chaos (Sep. 8, 1987), pp. 27-44
    Chialvo, D., Gilmour Jr, R. & Jalife, J. Low dimensional chaos in cardiac tissue. Nature 343, 653-657 (1990). doi.org/10.1038/343653a0
    Xujun Ye, Kenshi Sakai. A new modified resource budget model for nonlinear dynamics in citrus production. Chaos, Solitons and Fractals 87 (2016) 51-60
    Libchaber, A. & Laroche, C. & Fauve, Stephan. (1982). Period doubling cascade in mercury, a quantitative measurement. dx.doi.org/10.1051/jphyslet:01.... 43. 10.1051/jphyslet:01982004307021100.
    Special thanks to Patreon Supporters:
    Alfred Wallace, Arjun Chakroborty, Bryan Baker, DALE HORNE, Donal Botkin, halyoav, James Knight, Jasper Xin, Joar Wandborg, Lee Redden, Lyvann Ferrusca, Michael Krugman, Pindex, Ron Neal, Sam Lutfi, Tige Thorman, Vincent
    Special thanks to:
    Henry Reich for feedback on earlier versions of this video
    Raquel Nuno for enduring many earlier iterations (including parts she filmed that were replaced)
    Dianna Cowern for title suggestions and saying earlier versions weren't good
    Heather Zinn Brooks for feedback on an earlier version.
    Music from:
    epidemicsound.com "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4"
    ve42.co/Artlist "Busy World" "Children of Mystery"

๋Œ“๊ธ€ • 26K

  • @AustenAlexander
    @AustenAlexander 4 ๋…„ ์ „ +55770

    Me: struggles with elementary algebra
    Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram
    Me: go on

    • @nickreed7277
      @nickreed7277 4 ๋…„ ์ „ +1434

      Damn dude. your elementary had algebra? i didnt get to that till highschool

    • @Matt_10203
      @Matt_10203 4 ๋…„ ์ „ +477

      @@nickreed7277 or he means that it is elementary level algebra, not in relation to schooling, just that he struggles to understand the basics of algebra

    • @melvinedlund6316
      @melvinedlund6316 4 ๋…„ ์ „ +363

      Bro I dont even know what algebra means

    • @JoeyLovesTrains
      @JoeyLovesTrains 4 ๋…„ ์ „ +48

      Lol I got algebra in 8th grade in Middle school
      But my class was the only one, everyone else had pre-Algebra

    • @luppa79
      @luppa79 4 ๋…„ ์ „ +86

      Verisatrium :)

  • @veritasium
    @veritasium  4 ๋…„ ์ „ +1489

    Feedback from UCLA A/Prof Heather Zinn Brooks:
    "At first, it seems totally crazy that increasing r would lead to cycles... if it's describing population growth, why would a bigger r cause a drop in some years? In fact, the magic is in the (1-x_n) factor of the equation, which models a carrying capacity. The idea is that populations are typically resource-limited, so growth can only be supported up to a certain point. Once you think about that, it makes sense that huge growth rates could result in "boom and bust" cycles in the population, because the population would grow faster than their resources would support."

    • @shetty98
      @shetty98 4 ๋…„ ์ „ +7

      1:30 @m in ๐Ÿ‡ฎ๐Ÿ‡ณ

    • @NatePrawdzik
      @NatePrawdzik 4 ๋…„ ์ „ +28

      I imagine increasing rabbits also increases wolves, so that probably factors in as well.

    • @timezone5259
      @timezone5259 4 ๋…„ ์ „ +1

      Yes

    • @gordonrichardson2972
      @gordonrichardson2972 4 ๋…„ ์ „ +11

      This topic came up when I was studying applied mathematics around 1980: en.wikipedia.org/wiki/Lotka-Volterra_equations

    • @11quinnjet75
      @11quinnjet75 4 ๋…„ ์ „ +22

      Can this be applied to the expanding universe? because it has a growth rate and if I remember right scientists think that that rate has changed?

  • @user-qx5cn1si1q
    @user-qx5cn1si1q ๋…„ ์ „ +2415

    Things like these actually make our world more magical than any science fiction

    • @glowerworm
      @glowerworm ๋…„ ์ „ +80

      We're living in a simulation and the 4.669 number just happened to be one of the global variable definitions.

    • @ihatemicrosoftsobadly3188
      @ihatemicrosoftsobadly3188 ๋…„ ์ „ +80

      @@glowerworm Dear matrix guys don't use global variables it's bad practice

    • @glowerworm
      @glowerworm ๋…„ ์ „ +65

      @@ihatemicrosoftsobadly3188 lmao, maybe it's destiny that every programmer, no matter how powerful, will write bad code.

    • @ihatemicrosoftsobadly3188
      @ihatemicrosoftsobadly3188 ๋…„ ์ „ +2

      @@glowerworm so true ... ;)

    • @justpassingbyy
      @justpassingbyy ๋…„ ์ „ +9

      @@glowerworm Shoulda been 4.2069 imo

  • @brucefoote540
    @brucefoote540 ๋…„ ์ „ +1107

    Your 3 dimensional animation of the rotating Mandelbrot Set graph conveys so very much information and complexity. Amazing!

    • @ingridfong-daley5899
      @ingridfong-daley5899 4 ๊ฐœ์›” ์ „ +1

      YES! Thank you for such well-constructed visualisations. They really are like compact little gold mines of information. :)

    • @3orM00Rrecharacters
      @3orM00Rrecharacters 4 ๊ฐœ์›” ์ „ +2

      Iโ€™m an artist and took screenshots of the set graph and logical equation as inspiration. Data really is beautiful.

    • @ingridfong-daley5899
      @ingridfong-daley5899 4 ๊ฐœ์›” ์ „

      OMG i took screenshots as well :)
      Agreed--data IS lovely.@@3orM00Rrecharacters

    • @HiManLOL
      @HiManLOL 3 ๊ฐœ์›” ์ „

      people out there proving existance of god with Mandelbrot fractal

    • @convolutionality
      @convolutionality 3 ๊ฐœ์›” ์ „

      its so pretty my inspiration too

  • @CuteC3
    @CuteC3 3 ๋…„ ์ „ +4181

    So basically like when the bass drops, the tempo keeps doubling until it just goes into complete madness.

    • @Cher007
      @Cher007 3 ๋…„ ์ „ +80

      The 101 of Speedcore and Splittercore ๐Ÿ˜‚

    • @sethreardon8805
      @sethreardon8805 3 ๋…„ ์ „ +442

      Something tells me that you might have said the smartest thing in these comments. Music is vibration, vibration is periodic. This equation probably can be found in music somewhere...

    • @TheMaxwellee
      @TheMaxwellee 3 ๋…„ ์ „ +82

      I hope a nerdy DJ builds his set this way

    • @StormEngineer
      @StormEngineer 3 ๋…„ ์ „ +58

      I almost spit my coffee. Well done.

    • @RCFrizz
      @RCFrizz 3 ๋…„ ์ „ +59

      @@StormEngineer Imma go brew some coffee so I can almost spit it!

  • @entropy_7827
    @entropy_7827 3 ๋…„ ์ „ +8325

    Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.

    • @FunTheMentalist
      @FunTheMentalist 3 ๋…„ ์ „ +459

      when he rotated the Mandelbrotset on the z axis, i felt that

    • @kumarsaieshrane9692
      @kumarsaieshrane9692 3 ๋…„ ์ „ +18

      ๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚

    • @masterpsk
      @masterpsk 3 ๋…„ ์ „ +121

      I did the "Keanu whoa" follow by a long "Duuuude!"

    • @gangsta6730
      @gangsta6730 3 ๋…„ ์ „ +64

      I was like "hol up-"

    • @eusebiorozco
      @eusebiorozco 3 ๋…„ ์ „ +8

      Hahahahaha

  • @maegodragon
    @maegodragon ๋…„ ์ „ +545

    Only got to 5 mins and 18secs and already getting Heart Flutter! This video animations, graphing bifurcations, and the questions you pose prior to clear explanation is absolutely AWESOME! Thanks for the Thrills!

    • @marco-salfi
      @marco-salfi ๋…„ ์ „

      You a rabbit by any chance

    • @hugojj101
      @hugojj101 ๋…„ ์ „ +8

      You're heart chaotically fibrillated, you maybe dying haha. Nah that's mad though. If you're heart did actually double beat, that was literally an example of the video. So strange, and even stranger that complex numbers that exist on a plane we can't see are linked to all our hearts and the rest. One day we'll understand maybe. hah

  • @zanityedpo1398
    @zanityedpo1398 9 ๊ฐœ์›” ์ „ +139

    When I was young, I always paid attention to my leaky faucets. I would mess with the flow since we were already wasting water, and I noticed this happening. Warms my heart to see it explained ๐Ÿ’œ

    • @strayspark1967
      @strayspark1967 7 ๊ฐœ์›” ์ „ +6

      i've had a similar experience, now explained 30 years later......strange world we live in, everything makes sense, eventually

    • @dmajorvgm8735
      @dmajorvgm8735 3 ๊ฐœ์›” ์ „ +1

      The video didnโ€™t really explain the behaviour though, it just made an observation/comparison to the mathematics they were talking about. Iโ€™d be interested in a more in depth video that actually explains why we see this behaviour so often

    • @nu1x
      @nu1x 18 ์ผ ์ „

      @@dmajorvgm8735 Well, noone knows WHY, people just noticed where it matches the algorithm.
      And why may be, I strongly suspect, some extremely fundamental basis on which the whole reality has existence, hence why this video is quite startling.

  • @tanvisharma6903
    @tanvisharma6903 3 ๋…„ ์ „ +14728

    Once the video reaches a certain rate of complexity, our brain starts to understand only periodic parts of it. Until it's all chaos and you throw your phone away.

  • @garfieldturismo
    @garfieldturismo 4 ๋…„ ์ „ +7713

    Everyone here were gangsta till he turned the Mandelbrot-set 3D

    • @cfneal1459
      @cfneal1459 4 ๋…„ ์ „ +28

      Explain?
      Please.

    • @doctorquantum3364
      @doctorquantum3364 4 ๋…„ ์ „ +67

      @@cfneal1459 r/woosh

    • @jinx5349
      @jinx5349 4 ๋…„ ์ „ +560

      @@doctorquantum3364 you can't woosh someone for wanting an explanation.. ๐Ÿ™„

    • @rohangaikwad255
      @rohangaikwad255 4 ๋…„ ์ „ +6

      Hahaha

    • @maxlank539
      @maxlank539 4 ๋…„ ์ „ +7

      I'm dead ๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚

  • @joekelley5121
    @joekelley5121 ๋…„ ์ „ +284

    I've had courses in Algebra, Calculus and Trigonometry, but never really had these concepts connected to actual real-world phenomena, so it always felt very... mechanical, very transactional. If they incorporated these concepts into the teaching, I believe it would make it much more relatable during the process.

    • @mikeinjapan2004
      @mikeinjapan2004 4 ๊ฐœ์›” ์ „ +5

      Good point. But there are people who can actually connect those things naturally. I think this is also a skill on its own - we don't need to be thought because we see those patterns interacting each other and what have presented seems to be trivial...

    • @stiefjac5082
      @stiefjac5082 3 ๊ฐœ์›” ์ „ +3

      100% i always thought that we would have leaps and bounds of breakthroughs in understanding the entire structure of the universe if we taught students in school basic math... and then showed them crazy concepts like these in the hopes that one of the billions of people on the earth will see them and go "huh that reminds me of x, what if we apply it here?" rather than pushing them through advanced mathematics to get degrees
      not only that but if you look up slow motion explosions on youtube and look closely the inital explosion looks like the mandelbrot set, and you can see that as it expands there are little bits of contraction in every single explosion if you take it frame by frame
      i watched this video when it came out 3 years ago and i've been obsessed with the concept ever since

    • @ADUAquascaping
      @ADUAquascaping 3 ๊ฐœ์›” ์ „ +2

      โ€‹@@mikeinjapan2004You probably notice all of the 25+ functions within plasma/flame ๐Ÿ˜ฎ๐Ÿ˜‚

    • @va941
      @va941 3 ๊ฐœ์›” ์ „ +1

      Guess you never did psychedelics while in school then๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚

    • @piercelane7757
      @piercelane7757 2 ๊ฐœ์›” ์ „

      A lot of this video is centered in something you might find in a numerical analysis class. I just took one in college and we went over a lot of this kinda stuff.

  • @madeeb04
    @madeeb04 ๋…„ ์ „ +34

    The fact that โ€œchaos theoryโ€ is a real thing absolutely blows my mind. Even pure chaos can be mathematically modeled. Incredible.

  • @DanielSmania
    @DanielSmania 3 ๋…„ ์ „ +4523

    I am a mathematician, and I do study phenomena associated with the Feigenbaum constant. You did justice to the topic! Excellent video!

    • @mackhomie6
      @mackhomie6 3 ๋…„ ์ „ +44

      i want this guy on my team after a nuclear holocaust. me and a bunch of mathematicians.

    • @MoorganHart
      @MoorganHart 3 ๋…„ ์ „ +23

      Yeah, another well done video. I am left wondering the relevance of the Mandelbrot Set though. I'm not a mathematician, and I've never heard of it before. I'll do a web search, but would have liked to hear about where the equation came from within the video.

    • @Polarwhisper6
      @Polarwhisper6 3 ๋…„ ์ „ +5

      I think you meant: "I am 'A' mathematician"

    • @christianmathison5892
      @christianmathison5892 3 ๋…„ ์ „ +105

      @@Polarwhisper6 he didnt claim to be an english major

    • @Sergiuss555
      @Sergiuss555 3 ๋…„ ์ „ +19

      @@christianmathison5892 to be fair there could be girls among those mathematicians.

  • @ColorwaveCraftsCo
    @ColorwaveCraftsCo 3 ๋…„ ์ „ +2511

    The Mandelbrot Set in 3D is probably one of the coolest things I've ever seen

    • @erteple2647
      @erteple2647 3 ๋…„ ์ „ +70

      looks like a deformed pringle

    • @benhsuan4817
      @benhsuan4817 3 ๋…„ ์ „ +41

      That and the "shadow" of a 4-dimensional cube passing through 3 dimensional space are the coolest mathematical animations I've seen. Matt parker shows it at the end of his talk at the Royal Institute if you're interested.

    • @mizomint4197
      @mizomint4197 3 ๋…„ ์ „ +9

      But... Humans can't see in 3D... So... Have you really seen it?

    • @bestawdomx6835
      @bestawdomx6835 3 ๋…„ ์ „

      @@erteple2647 there is infinite?

    • @steveskeletonne-7394
      @steveskeletonne-7394 3 ๋…„ ์ „ +4

      krplus.net/bidio/abloioaWqIjbcno
      This is essentially just a bunch of 3D fractals.

  • @falcxne
    @falcxne ๋…„ ์ „ +74

    For anyone wanting to study the math of this, I recommend Steven Strogatz - Nonlinear Dynamics and Chaos. That was the textbook I used in undergrad.

    • @simrans3675
      @simrans3675 ๋…„ ์ „ +5

      So, basically, 'Chaos' is a misnomer now. There is clear method and math to the madness. Are we really living in a simulation :-)? Sometimes, it fascinates me to see all the advancements made in math, science. probability. stats etc with a simple thesis to put some structure/framework to quantify the world around us. It has helped us explain a few phenomenons, create products, even predict stock prices, human behavior (looking at patterns and trends etc) but the other part of me is conflicted - for life and its energies cant be modeled. It's too fascinating to be modeled out and the vastness of the universe and my spiritual beliefs are a complete anti-thesis to my scientific side. Heck, even science is ever changing - now, we are discovering qubits - particles that carry both -ve and +ve charges, which has deep implication to our view of physics and the world around us!
      While amazing, how much can humans really 'figure out' vs realizing there is something more to life that what even our more prolific attempts at math/AI/ML will ever get us to.. Or, perhaps, there isnt a higher power :-)?

  • @BanditMatt
    @BanditMatt ๋…„ ์ „ +213

    Currently writing a report on chaotic behaviours and bifurcations, remembered this video existed and im so grateful now

  • @feynstein1004
    @feynstein1004 4 ๋…„ ์ „ +3830

    Numberphile: Makes video about the Feigenbaum constant
    Veritasium: Makes video about the Feigenbaum constant but includes the z-axis

    • @unathimatu
      @unathimatu 4 ๋…„ ์ „ +334

      it was a bifurcation

    • @BinyaminTsadikBenMalka
      @BinyaminTsadikBenMalka 4 ๋…„ ์ „ +60

      @@unathimatu lol, perfect response dude!

    • @BasiC7786
      @BasiC7786 4 ๋…„ ์ „ +246

      and then there's 3blue1brown telling you what PI has to do with all of this

    • @cezarcatalin1406
      @cezarcatalin1406 4 ๋…„ ์ „ +81

      Feigenbaum constant: Works for all recurrences that come from functions with a single hump.
      A mathematician: Well, we have to demonstrate that
      A computer scientist: Give me the Summit supercomputer for a few days to find a counterexample

    • @larrysal8866
      @larrysal8866 4 ๋…„ ์ „ +9

      _mind blow_

  • @youmaybebusy
    @youmaybebusy 4 ๋…„ ์ „ +17735

    "Oh cool, the Mandelbrot-Set. I have seen that before."
    *turns Mandelbrot-Set in 3D*
    "What the ...?! That's illegal!"

    • @DrIridium
      @DrIridium 4 ๋…„ ์ „ +167

      haha same

    • @scurvofpcp
      @scurvofpcp 4 ๋…„ ์ „ +106

      I know, right

    • @IRuinEvrything
      @IRuinEvrything 4 ๋…„ ์ „ +55

      relatable

    • @smoothe14
      @smoothe14 4 ๋…„ ์ „ +519

      This is getting out of hand, now thereโ€™s two of them... wait four of them. Hold up. Eight of them... wtf a chaotic number set of them??!? This really is getting out of hand. Oh wait no just two of them.

    • @Uberkist
      @Uberkist 4 ๋…„ ์ „ +66

      mandelbulbs are gunna blow you away bro

  • @jeff_tj
    @jeff_tj ๋…„ ์ „ +31

    That book is amazing - and you have done it justice. That 3d graph was awesome!

  • @Peace2051
    @Peace2051 9 ๊ฐœ์›” ์ „ +11

    Thank you for making some fundamental mysteries of math/nature at least approachable if not fully understandable to the general public. Great job!

  • @Chord_
    @Chord_ 2 ๋…„ ์ „ +4496

    "I'm so excited about chaos" -man one month into 2020

    • @maumau9466
      @maumau9466 2 ๋…„ ์ „ +30

      Lmao๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚

    • @norpriest521
      @norpriest521 2 ๋…„ ์ „ +1

      @@maumau9466
      What that means

    • @starryepidemic2532
      @starryepidemic2532 2 ๋…„ ์ „ +18

      @@norpriest521 it means laughing my ..... Off and no im not gonna fill in the blanks

    • @koborkutya7338
      @koborkutya7338 2 ๋…„ ์ „ +12

      Well, it just tells us someone is messing with the parameters big time.

    • @MrSleepyweezul
      @MrSleepyweezul 2 ๋…„ ์ „ +10

      When things are chaotic, you focus on chaos. And when you focus long and hard enough, even chaos can make sense.

  • @roshnirana2098
    @roshnirana2098 4 ๋…„ ์ „ +1770

    2019:- so this is aerogel
    2020:- let's throw a little chaos at children and each other

    • @AngelOrtiz-wt7xt
      @AngelOrtiz-wt7xt 4 ๋…„ ์ „

      Roshni Rana aqq msm

    • @zperdek
      @zperdek 4 ๋…„ ์ „ +2

      Chaos is magic.

    • @PavR376
      @PavR376 4 ๋…„ ์ „

      Hey we have the same last name, first time I've meet one online

    • @user-pj8mt2kd4v
      @user-pj8mt2kd4v 3 ๋…„ ์ „

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  • @Sagitarria
    @Sagitarria ๋…„ ์ „ +24

    You really did a good job with this one. This is something thatโ€™s been fascinating to me for a long time, and there was even a point a few years ago when I was trying to explain to my mathematical friends, the connections between the logistic map and the Mandelbrot set and they didnโ€™t believe me! This stuff seems so fundamental, but it doesnโ€™t seem like itโ€™s tot as a unifying principle when it could be. Itโ€™s just nice to see somebody acknowledge all of these different pieces of the puzzle so thank you and thank you for making some thing I can .2.

  • @jaianupamvarun8722
    @jaianupamvarun8722 ๋…„ ์ „ +15

    I truly am humbled by the way you present such a complicated topic in such a simple way that even i who isn't a fan of mathematics got interested immediately ๐Ÿ˜ƒโค๏ธ๐Ÿ’•

  • @edstervedster
    @edstervedster 4 ๋…„ ์ „ +718

    6:40 When the animation showed the Mandelbrot set being related to the bifurcation diagram my mind was blown...

    • @elee9056
      @elee9056 4 ๋…„ ์ „ +34

      edstervedster I WANT THAT MODEL AS A CHANDELIER. SO. BAD.

    • @carloshogar2
      @carloshogar2 4 ๋…„ ์ „ +13

      Same here. I am fascinated by fractals and never knew this relationship

    • @airpolygon2714
      @airpolygon2714 4 ๋…„ ์ „ +3

      @@elee9056 you should make that idea a reality! I'd buy two

    • @rianby64
      @rianby64 4 ๋…„ ์ „

      The same happened to me! not sure if really they're related... must rewind and check it again.

    • @Cloud7050
      @Cloud7050 4 ๋…„ ์ „

      Crowdsourceeee

  • @BAgodmode
    @BAgodmode 2 ๋…„ ์ „ +2747

    When you turned the Mandelbrot on itโ€™s side to show the bifurcation, Iโ€™ll be honest, it blew my mind.

    • @jingalls9142
      @jingalls9142 2 ๋…„ ์ „ +68

      That one made me stand up an pace frantically for awhile....mind blown..

    • @shadeop6773
      @shadeop6773 2 ๋…„ ์ „ +22

      @@jingalls9142 same..... It blew my mind.

    • @asparagii
      @asparagii 2 ๋…„ ์ „ +15

      yeah that was awesome

    • @carriersignal
      @carriersignal 2 ๋…„ ์ „ +45

      Same here. Had to stop it and sit back in my chair. Perhaps this is well known, but this is the first time I have ever heard of it.

    • @r0flcats
      @r0flcats 2 ๋…„ ์ „ +8

      Its now my wallpaper!!! That image its insane

  • @magic.marmot
    @magic.marmot ๋…„ ์ „ +12

    I've been studying emergent behavior since the 80's, when I first read Conway's Game of Life.
    Back then, it was treated as a nuisance, irrelevant, and annoying.
    I love watching the break into oscillation as your R-value changes .That's the same behavior as a damped spring, or feedback in an audio system.
    The transition to chaos between states makes a lot of sense.
    I love the visualization of the Mandelbrot set, that gave me the perfect starting point to understand it in another dimension. Wonderful.

  • @rianschoeman559
    @rianschoeman559 ๋…„ ์ „ +25

    James Gleick's book is really good. Once in a post office que I observed someone putting a fan on a scale. The reading bifurcated. I asked her to set the fan to a higher speed. The reading bifurcated again between four readings. I was blown away.

  • @JohnSmith-gs4zv
    @JohnSmith-gs4zv 4 ๋…„ ์ „ +446

    13:57 "What _really_ *IS* a faucet?" - Vsauce music starts

    • @impanthering
      @impanthering 4 ๋…„ ์ „

      ok John Smith

    • @calix451
      @calix451 4 ๋…„ ์ „ +10

      I miss him

    • @geekjokes8458
      @geekjokes8458 4 ๋…„ ์ „ +7

      But his video would actually *start* liake that
      And finish by talking about *UNIVERSALITY*

    • @DrSpooglemon
      @DrSpooglemon 4 ๋…„ ์ „ +11

      "This is water dripping from a faucet.
      OR is it?!"

    • @ricardopieper11
      @ricardopieper11 4 ๋…„ ์ „ +1

      I read the first 3 words of your comment in michael's voice before acknowledging the word "vsauce" in it

  • @warrenchinn4114
    @warrenchinn4114 3 ๋…„ ์ „ +1887

    Magnificent. I am a 53 year old professional entomologist and this is utterly pertinent to invertebrate population biology. You state you are 37 years old in this presentation and I feel very humbled. Thank you for restoring my confidence in a world that seems bent on science denial, superficiality and facebook banality. Please keep up these exceptional presentations of important and complex concepts in nature, top marks !

    • @warrenchinn4114
      @warrenchinn4114 3 ๋…„ ์ „ +84

      @@shyamkarthikeya4769 That was my point ... :)

    • @supteg2.495
      @supteg2.495 3 ๋…„ ์ „ +24

      @@warrenchinn4114 again a smart man..

    • @genericusername4206
      @genericusername4206 3 ๋…„ ์ „ +3

      Warren Chinn true

    • @bfern053
      @bfern053 3 ๋…„ ์ „ +35

      @@shyamkarthikeya4769 delete this

    • @DickEnchilada
      @DickEnchilada 3 ๋…„ ์ „ +5

      I learned about this constant (and the equation) when I was taking a System dynamics course 2 years ago. Absolutely loved that course. Stay learning dude!

  • @nsfa19
    @nsfa19 ์ผ ์ „

    This has got me really interested and fascinated as well. Congrats on such high quality top-notch videos! Thank you very much!

  • @penguinswithpencils2333
    @penguinswithpencils2333 3 ๊ฐœ์›” ์ „

    I ran across this video about a month into my discrete dynamical systems course. It has been super helpful to have something that gave me some intuition surrounding these patterns before I encountered them formally in class. Sharing it with my professor now :)

  • @briancherry8088
    @briancherry8088 4 ๋…„ ์ „ +687

    8:43 - Boom. Mind blown. We've been missing the 3rd dimension of the Mandelbrot set this whole time.

    • @mikeciul8599
      @mikeciul8599 4 ๋…„ ์ „ +78

      Actually, I think there might be a 4th dimension, because for some complex values of c, the equation could converge to complex numbers.

    • @DemonSwrd
      @DemonSwrd 4 ๋…„ ์ „ +12

      now imagine the 4th dimension.

    • @briancherry8088
      @briancherry8088 4 ๋…„ ์ „ +9

      @@DemonSwrd - no. The world will explode.

    • @hammerth1421
      @hammerth1421 4 ๋…„ ์ „ +12

      โ€‹@@mikeciul8599 It is the real part of the complex value returned from the complex logistic map. If the result was also complex the Mandelbrot set would be 4D.

    • @brando3342
      @brando3342 4 ๋…„ ์ „ +3

      @@DemonSwrd We can't imagine that. That's like asking someone to imagine a one dimensional point. Yes, some cosmologists want to say that was what the singularity was at the beginning of the universe, but think about it, it doesn't make sense.

  • @blobishlybelfer2717
    @blobishlybelfer2717 3 ๋…„ ์ „ +1611

    thanks for showing me that as a child i had absolutely no chance of predicting when a water drop will drop.

    • @K3zz21
      @K3zz21 3 ๋…„ ์ „ +37

      "when a water will drop" a SINGLE water

    • @who-ow5ix
      @who-ow5ix 3 ๋…„ ์ „ +5

      ๐Ÿ˜‚๐Ÿ˜‚

    • @plaverbach
      @plaverbach 3 ๋…„ ์ „ +4

      @@K3zz21 When the water would drop?

    • @zacharyhall7466
      @zacharyhall7466 3 ๋…„ ์ „ +6

      Chaos theory?

    • @haydenbellis3047
      @haydenbellis3047 3 ๋…„ ์ „ +1

      .Turn to United Brethren Church. Using the Lords name in vain is a sin and so is cursing upon your enemies. And so is saying anything hateful, premarital sex and lust are all sins..โฐ

  • @KM-co5mx
    @KM-co5mx ๋…„ ์ „ +4

    We need more videos like this! โญ๏ธ

  • @nfc14g
    @nfc14g ๋…„ ์ „ +7

    Feels like when you are using exponential equations your inputs are very important and deserve a lot of explaining why you chose it, regardless of real value or best estimate value

  • @jemert96
    @jemert96 2 ๋…„ ์ „ +3876

    *_rotates the Mandelbrot plot_*
    Everyone: "wait what's he doing"
    Me: "he's beginning to believe"

  • @DreamLoud05
    @DreamLoud05 4 ๋…„ ์ „ +370

    THat was definitely one of the shortest 18 minute video I have ever watched on youtube. Very fascinating

    • @FnaticKiller
      @FnaticKiller 4 ๋…„ ์ „ +2

      Now that is a compliment.

    • @IRL.johnny
      @IRL.johnny 4 ๋…„ ์ „ +4

      this is frighteningly true... I watch it at 1x while my wife brushed her teeth... how's that possible?

    • @diabl2master
      @diabl2master 4 ๋…„ ์ „ +3

      wtf, I did not realise that was 18 minutes, I was totally enthralled

    • @pdutube
      @pdutube 4 ๋…„ ์ „ +1

      If you observe a subject watching this video at a specific fraction of the speed of light, you could see it at 18 minutes no matter what the subject's playback speed was.

    • @liqwiz
      @liqwiz 4 ๋…„ ์ „ +1

      I felt Exactly the same. Only by reading your comment I realised "wait... That was almost 20 minutes?"

  • @shamsamir1698
    @shamsamir1698 ๋…„ ์ „

    One of the most beautiful videos on youtube! keep getting back to it every time.

  • @preranaprasaddeshmukhbe20b34
    @preranaprasaddeshmukhbe20b34 4 ๊ฐœ์›” ์ „ +1

    This is one of the most amazing video I had seen on KRplus till now

  • @ShiftK
    @ShiftK 3 ๋…„ ์ „ +2177

    **slightly opens kitchen faucet*
    Me: I'm somewhat of a scientist myself

  • @TehmasKhan
    @TehmasKhan 4 ๋…„ ์ „ +383

    You know the video is good when itโ€™s 18:39 minutes long and you still didnโ€™t want it to end

    • @za012345678998765432
      @za012345678998765432 4 ๋…„ ์ „ +12

      I didn't even notice until you pointed it out, thought it was like 9 minutes

    • @MartinBuzon
      @MartinBuzon 4 ๋…„ ์ „ +2

      @@za012345678998765432 I was going to say 9 too. Damn witchcraft.

    • @za012345678998765432
      @za012345678998765432 4 ๋…„ ์ „ +4

      @@MartinBuzon Next thing you know Derek comes here and tells us that this equation can explain that as well and it was all planned from the start XDD

    • @setsugennoao3137
      @setsugennoao3137 4 ๋…„ ์ „

      @@za012345678998765432 same

    • @KillaahMusik
      @KillaahMusik 4 ๋…„ ์ „ +5

      It felt like 4,669 minutes

  • @iamlubos
    @iamlubos ๋…„ ์ „ +4

    Great video! It's also a really good subject for a take-home final exam in a scientific computing class I am teaching this semester.

  • @harshildobariya6773
    @harshildobariya6773 9 ๊ฐœ์›” ์ „

    One of the most mind-bending concept I have came across. I love your channel, it is one of the best.

  • @MrTigershark11
    @MrTigershark11 4 ๋…„ ์ „ +301

    6:37 One of the best plot twist I've seen in my entire life

  • @TheMsksk
    @TheMsksk 4 ๋…„ ์ „ +2236

    "How did I get to be 37 years old without hearing about the Feigenbaum constant", thank you for lowering that bound to at least a 24 year old. Your videos always leave me inspired!

    • @SergioEduP
      @SergioEduP 4 ๋…„ ์ „ +53

      It lowered it for an 18 year old too =P maybe there are even younger people watching, and if there aren't we could share the video to them

    • @incription
      @incription 4 ๋…„ ์ „ +26

      @@SergioEduP 17, beat that

    • @arvintis2293
      @arvintis2293 4 ๋…„ ์ „ +14

      InCrIpTiOn 16.

    • @incription
      @incription 4 ๋…„ ์ „ +11

      @@arvintis2293 I think krish beat both of us

    • @tomifiju
      @tomifiju 4 ๋…„ ์ „ +6

      @Krish Kalra yet here I am during meiozis I

  • @mihalykort84
    @mihalykort84 ๋…„ ์ „ +5

    I went to the "Chaos Conference" at Sydney in (I think?) 87, met some pretty incredible physicists and mathematicians, and even got a couple of Autographs :) but mostly felt just awed that this was an interesting thing, and that I knew somehow it also was kind of important. B Mandelbrots lecture was lovely, but some of the different maths topics (from geometry obviously, but Prime number theory, Analytic and Discrete maths and biological mathematics. For me it was a memorable experience. So I get you, and I wish you more power to your arm, because yeah there's something compellingly beautiful and yet still mysterious. Good on you for your work, long may you continue and thanks!

  • @amanuka291
    @amanuka291 ๋…„ ์ „

    I can't even describe how amazed I am. Thank you for this video! It was a huge help with my studies and such an entertaintment!

  • @andriypredmyrskyy7791
    @andriypredmyrskyy7791 4 ๋…„ ์ „ +362

    As a control systems engineer, I've seen this behaviour before in several systems when control goes awry.
    Now that I know there might be something I can do about it, this opens up all sorts of possibilities to new control methods. I'm freaking out a little bit.

    • @Rotem_S
      @Rotem_S 4 ๋…„ ์ „ +23

      Actually the first physical chaos measured was an engineer using a simple circuit with a transistor and a harmonic input, where he sometimes saw one period, sometimes two, and sometimes all of them

    • @austinwessels
      @austinwessels 4 ๋…„ ์ „ +7

      I was thinking about controls too for most of the video!

    • @revenevan11
      @revenevan11 4 ๋…„ ์ „ +11

      Wow, you could control something back from the edge of chaos or even from already started chaotic behavior (like an airplane already entering an aerodynamic stall) using the methods that those scientists used on the rabbit hearts! I hope you're looking into that paper right now lol.

    • @brocktechnology
      @brocktechnology 4 ๋…„ ์ „ +6

      I'm no engineer, but I'm right there with you. I was hit by the realization that this little bit of math is the reason PID is so difficult to do well.

    • @revenevan11
      @revenevan11 4 ๋…„ ์ „ +8

      @@brocktechnology I'm super excited for the possibilities of better control algorithms by using something analogous to the research in restabilizing heartbeats, the implications are awesome for aerospace engineering.

  • @sidsixpoint7
    @sidsixpoint7 3 ๋…„ ์ „ +2357

    Jokes on you, this didn't change the way I see the world because I'm dumb.

    • @HerGatiox
      @HerGatiox 3 ๋…„ ์ „ +67

      at least you see that. You know that you don't know anything. congrats

    • @gabeharrison7683
      @gabeharrison7683 3 ๋…„ ์ „ +83

      @@HerGatiox a bit condescending

    • @poyo5512
      @poyo5512 3 ๋…„ ์ „ +5

      Lmao

    • @aaroncruz9181
      @aaroncruz9181 3 ๋…„ ์ „ +3

      You see math without numbers

    • @BenDover-vh9rs
      @BenDover-vh9rs 3 ๋…„ ์ „ +1

      @Majin Buu then how tf does he know that?

  • @Khpr666
    @Khpr666 ๋…„ ์ „

    Bro! I love you! Thank you! Your work is increasing the growth rate of knowledge.

  • @potat8089
    @potat8089 ๋…„ ์ „ +1

    I remember watching this video when I was about 14 years old and being fascinated by this, but my understanding kinda dropped off when the Mandelbrot Set came into the video (I knew nothing about it).
    Rewatching this video at age 16, I can really appreciate it so much more, now that I understand it.
    Thank you for introducing me to the Logistic Map!

  • @bradleyewoodworth
    @bradleyewoodworth 3 ๋…„ ์ „ +261

    Out of all of the KRplus channels that I don't understand, this one is my favorite.

    • @zaphodsbluecar9518
      @zaphodsbluecar9518 3 ๋…„ ์ „ +1

      ROTFL - Nice work Brad! :-)

    • @AzTech71
      @AzTech71 3 ๋…„ ์ „ +1

      Lol

    • @Streamwalker1000
      @Streamwalker1000 3 ๋…„ ์ „ +1

      LOL ! I'm with you on that.

    • @simphiwenxumalo4387
      @simphiwenxumalo4387 3 ๋…„ ์ „ +1

      @@Streamwalker1000 LOL me too

    • @johnmartin9451
      @johnmartin9451 3 ๋…„ ์ „

      I'm sure you understand more than you thought, otherwise you wouldn't be drawn in. It's about patterns and randomness and how the two shall not meet.

  • @farhan132_
    @farhan132_ 4 ๋…„ ์ „ +1970

    The more I learn, the more I realize I don't really know anything!

    • @mdestwo
      @mdestwo 4 ๋…„ ์ „ +143

      Ah, so you really have been paying attention! That seems to be one of the more important lessons to learn in life. So, hereโ€™s to you, me, and everyone else realizing we know less and less each year! ๐Ÿ˜€

    • @farhan132_
      @farhan132_ 4 ๋…„ ์ „ +25

      @@mdestwo Well said!

    • @glaucovillasboas8212
      @glaucovillasboas8212 4 ๋…„ ์ „ +59

      That's for sure. I always think I'm smart, but a year later I always remember how stupid and dumb I was, and it keeps repeating

    • @avikdas4055
      @avikdas4055 4 ๋…„ ์ „ +32

      Exactly man. But now I'm 100% convinced that I know absolutely nothing.

    • @Kraflyn
      @Kraflyn 4 ๋…„ ์ „ +13

      welcome to the club! :D

  • @IIronyy
    @IIronyy ๋…„ ์ „

    Dude I have absolutely no idea of anything I just heard but I still listened all the way through it takes a very talented type of person to intrigue his audience that much.

  • @jfidel3943
    @jfidel3943 ๋…„ ์ „ +2

    I love James Gleick's Chaos book. It's such an amazing book and I always learn something new from it.

  • @sloanehowell6166
    @sloanehowell6166 3 ๋…„ ์ „ +1419

    โ€œWhen this baby rotates on the z-axis, youโ€™re gonna see some serious sh*t.โ€ - Dr. Emmett Brown

    • @davememelandcanada6722
      @davememelandcanada6722 3 ๋…„ ์ „ +11

      We don't talk about the Doc, since he f**ked up the timeline for 2020.

    • @chop-daresistance7514
      @chop-daresistance7514 3 ๋…„ ์ „ +5

      Wow doc.. that's heavy

    • @chop-daresistance7514
      @chop-daresistance7514 3 ๋…„ ์ „ +8

      @@davememelandcanada6722 I don't think that was doc.. I think that was biff when he stole the DeLorean

    • @anasaamir5595
      @anasaamir5595 3 ๋…„ ์ „

      wht is z asix

    • @Leosayshi
      @Leosayshi 3 ๋…„ ์ „ +4

      @@anasaamir5595 If I had to guess itโ€™s probably another axis like the y and x axis except itโ€™s used for 3D shapes.

  • @belgianbushrc7934
    @belgianbushrc7934 3 ๋…„ ์ „ +2712

    I am intelligent enough to find this interesting but not quite smart enough to fully understand... Great video!

    • @eletinalex
      @eletinalex 3 ๋…„ ์ „ +46

      covid-19=
      this is control over the rabbit population

    • @naturelovingfroggy6348
      @naturelovingfroggy6348 3 ๋…„ ์ „ +21

      Well said, me too x

    • @shadowpresident4203
      @shadowpresident4203 3 ๋…„ ์ „ +114

      That's probably the ideal situation. If a tutor were to customize a lesson for you specifically, they'd probably aim for a difficulty level you'd find interesting, and a lecture that you could mostly follow. You'd also be very slightly outside your comfort zone, to give you room to "grow into" the lesson. It would also be a bit challenging and would leave you with a few questions to mull over, thereby slightly increasing the chance of watching another video, or of reading a book or article on a similar topic. Your comment would probably be music to the ears of a lot of educators.

    • @eletinalex
      @eletinalex 3 ๋…„ ์ „ +3

      @@shadowpresident4203 thx

    • @comet1954
      @comet1954 3 ๋…„ ์ „ +6

      I feel your pain! I truly do....

  • @VisualJoey
    @VisualJoey 11 ๊ฐœ์›” ์ „ +3

    You definitely did this topic justice in my personal experience! Thank you (โ€ฆ)
    And this is just one topic where you do justice. I donโ€™t practice maths nor more of the topics you have covered. At least, in a professional or study kind of way that is. However, I have found your explanations to be inspiring and fascinating. You really hit a spot of interest of which I have always had an interest for but never got my head to understand due to the complexity. Itโ€™s a gift to be able to watch your videos and get a grasp of understanding. Even though sometimes the grasp barely touches the surface.

  • @matgeezer2094
    @matgeezer2094 ๋…„ ์ „

    Again, did not expect to be blown away but am utterly. Superb video, bringing quite a 'dry' subject alive.

  • @locotx215
    @locotx215 4 ๋…„ ์ „ +218

    6:41 - "The Plot Twist" figuratively and literally

  • @CHLOCHLOLP
    @CHLOCHLOLP 3 ๋…„ ์ „ +617

    if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.

    • @CHLOCHLOLP
      @CHLOCHLOLP 3 ๋…„ ์ „ +21

      @chcpr1 i think its more that no one in power cares to invest in school systems to make them better, but I dont think they are shitty on purpose, just due to neglect. Why would rich government officials care about public schools when are their kids are privately educated anyways, you know?

    • @Eden894HisBiome
      @Eden894HisBiome 3 ๋…„ ์ „ +1

      Yeah sadly they donโ€™t teach you anything your not tested for. Unless they a good teacher.

    • @kaffeetasse9455
      @kaffeetasse9455 3 ๋…„ ์ „ +4

      One of my teachers actually showed us the mandelbrot set and told us about chaos teory. :D

    • @chrisbarber7291
      @chrisbarber7291 3 ๋…„ ์ „ +2

      Um, they do teach this.

    • @sirxobsidian408
      @sirxobsidian408 3 ๋…„ ์ „ +10

      Unfortunately, this simply isn't true. I'm a high school math teacher, and I've shown this kind of thing to my students on numerous occasions, and the response is pretty much always the same; disinterest. If it's not on a test, they see it as an excuse to take a nap, zone out, or work on other classes' assignments.

  • @pudayshankar1036
    @pudayshankar1036 ๋…„ ์ „

    Your videos never failed to make me think about what is the purpose of this universe.. why is it there and how it works so perfectly without anyone controlling it..

  • @namakoro_osu
    @namakoro_osu ๋…„ ์ „

    since the start of the pandemic i have come back to this video time and time again and it was the first video i watched of yours and every time i rewatched it i under stand just a little more thank you for making many complicated topics over the years bite size and understandable

  • @PietchRhum
    @PietchRhum 4 ๋…„ ์ „ +198

    I feel so dumb! I have a PhD in Ecological Modelling, I have used this equation - and more complex version of it - to model population dynamic multiple time and I didn't knew of this Feigenbaum constant!!! I had teaching on Chaos and none of my professor mentioned it! Well, thanks Veritasium for teaching us new things!

    • @KarasuInaiga
      @KarasuInaiga 4 ๋…„ ์ „ +13

      P. V. I read that as โ€œExecutive Meddlingโ€.

    • @metanumia
      @metanumia 4 ๋…„ ์ „

      @@KarasuInaiga ๐Ÿคฃ

    • @spencerquirk6917
      @spencerquirk6917 4 ๋…„ ์ „

      @@KarasuInaiga ๐Ÿคฃ๐Ÿคฃ๐Ÿคฃ

    • @BrandonRx2
      @BrandonRx2 4 ๋…„ ์ „

      Huh

    • @ansh6370
      @ansh6370 4 ๋…„ ์ „ +7

      Bruh I'm just an eight grader. Tomorrow's my maths test and I'm supposed to learn mensuration and algebra but I'm here trying to figure out what this video even is about after watching it for the 7th time.

  • @Max_Jacoby
    @Max_Jacoby 4 ๋…„ ์ „ +716

    - What is the answer to the Ultimate Question of Life, the Universe, and Everything?
    - 4.669

    • @jcornman24
      @jcornman24 4 ๋…„ ์ „ +35

      Nice

    • @mmmmmark9751
      @mmmmmark9751 4 ๋…„ ์ „ +23

      It's 42......of course we really don't know what the question is.....(ps. it is 6x9.....which is why it's all fuk dup)....thanks Douglas

    • @contessa420
      @contessa420 4 ๋…„ ์ „ +2

      Nice reference

    • @BinyaminTsadikBenMalka
      @BinyaminTsadikBenMalka 4 ๋…„ ์ „ +7

      It's 3 Pi /2

    • @RagavPuli
      @RagavPuli 4 ๋…„ ์ „ +5

      @@BinyaminTsadikBenMalka 1.5xฯ€

  • @lintonatlas8933
    @lintonatlas8933 10 ๊ฐœ์›” ์ „ +1

    Outstanding explanation of chaos theory. I especially liked the unifying of the madelbrot set diagram and the doubling diagram, I don't recall seeing that before.

  • @rainthevaporeon7852
    @rainthevaporeon7852 ๋…„ ์ „ +1

    I've not shown any interest in mathematics (or physics for that matter) for a long while, and this somehow sparked up my interest in it again, thanks. Really fascinating stuffs

  • @liondeluxe3834
    @liondeluxe3834 2 ๋…„ ์ „ +572

    This video made me obsessed. I didnโ€™t sleep last night. This morning I went to my core editor and made a Mandelbrotโ€™s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.

    • @aion2177
      @aion2177 2 ๋…„ ์ „ +9

      github link please?

    • @jamesfield5415
      @jamesfield5415 2 ๋…„ ์ „ +3

      I got obsessed too itโ€™s mesmerising

    • @NovaWarrior77
      @NovaWarrior77 2 ๋…„ ์ „ +2

      please let us know. I for one for sure want to see it.

    • @goutamboppana961
      @goutamboppana961 2 ๋…„ ์ „ +6

      the beauty come when u keep zooming it

    • @CrackedCandy
      @CrackedCandy 2 ๋…„ ์ „ +6

      Oh my, my heart is beating faster now, so, where can I see this art?

  • @lc7ineo
    @lc7ineo 4 ๋…„ ์ „ +1585

    I found this incredibly fascinating... but understood incredibly little.

    • @jakewatson1160
      @jakewatson1160 4 ๋…„ ์ „ +19

      I was interested in it but i will always hate math cuz ths made me fall asleep lol

    • @panpsalt6757
      @panpsalt6757 4 ๋…„ ์ „ +10

      I understood more than I want, but still less

    • @thechappist
      @thechappist 4 ๋…„ ์ „

      Yup! Make me want to go learn some math!

    • @thechappist
      @thechappist 4 ๋…„ ์ „ +2

      I had to write some things down to look up definitions! But interesting

    • @unbiasedhuman1659
      @unbiasedhuman1659 4 ๋…„ ์ „ +5

      Fibonacci equation.

  • @rajeswaranparameswaran6611
    @rajeswaranparameswaran6611 10 ๊ฐœ์›” ์ „

    Amazing quality of presentation!
    Besides being a scientist with msrcellius 'teaching' skills, you are a classic cameraman too!
    Grateful.

  • @vishalrander9805
    @vishalrander9805 ๋…„ ์ „

    Very much obliged to watch your videos. Thank you for making the complex to simple .

  • @g0g0duck20
    @g0g0duck20 4 ๋…„ ์ „ +2161

    Me: Watches video because I think I'm smart
    My brain: Hold on there buckaroo

    • @paratame105
      @paratame105 4 ๋…„ ์ „ +40

      I feel attacked

    • @AverageAlien
      @AverageAlien 4 ๋…„ ์ „ +90

      Don't worry we're all retarded here. Welcome to the club.

    • @Dontlagmebro
      @Dontlagmebro 4 ๋…„ ์ „ +15

      Well how do you think (we) get smart?

    • @trevsanna
      @trevsanna 4 ๋…„ ์ „ +10

      LOL....You can actually apply the equation to your comment to see how funny your comment actually is! :)

    • @rznleagueoflol4545
      @rznleagueoflol4545 4 ๋…„ ์ „ +4

      Trevor Baylis no u cant

  • @smithisnotoriginal9454
    @smithisnotoriginal9454 4 ๋…„ ์ „ +192

    13:56 What really is a faucet? Hey, VSauce! Michael here

    • @pi17
      @pi17 4 ๋…„ ์ „ +7

      Somehow this relation never ceases to intrigue me

    • @o_o............
      @o_o............ 4 ๋…„ ์ „ +1

      I actually didn't know what a faucet is...

  • @mikedavies5551
    @mikedavies5551 3 ๊ฐœ์›” ์ „

    Brilliant especially the final part about different functions. That is new to me. Thanks.

  • @TechnoShamanism
    @TechnoShamanism 10 ์ผ ์ „

    This is the best channel on youtube! โค

  • @vincenzkoop43
    @vincenzkoop43 3 ๋…„ ์ „ +762

    6:43 most underrated placement of the term โ€šplot twistโ€˜

  • @avrenna
    @avrenna 4 ๋…„ ์ „ +750

    When the Mandelbrot set rotates: whooaaaahhhhh

    • @xiaoxiaoxiao686
      @xiaoxiaoxiao686 4 ๋…„ ์ „ +1

      5erif meme echoes in my head...

    • @Adam_Bosscoe
      @Adam_Bosscoe 4 ๋…„ ์ „ +1

      Right!?!?!!

    • @valentinbernard8126
      @valentinbernard8126 3 ๋…„ ์ „ +1

      Yeh that was spectacular

    • @trickytreyperfected1482
      @trickytreyperfected1482 3 ๋…„ ์ „ +1

      "You're not supposed to do that!"

    • @aurelia8028
      @aurelia8028 3 ๋…„ ์ „ +3

      I swear to god, my mind was blown away by that! I had only ever seen the Mandelbrot Set as that 2 dimensional boundary thing, so seeing that it was actually a 3D-thing was insane

  • @priyankapandit383
    @priyankapandit383 ๋…„ ์ „ +19

    The best place learn new and fascinating things I am student in just class 8th and these things are super fascinating for me keep up the job sir and please make new videos like this

    • @saurabhjarodia335
      @saurabhjarodia335 ๋…„ ์ „ +3

      If u really are in class 8th and watching these videos u must be special. Do u feel u different from others in anyway? I would suggest understanding urself coz now I am struggling and even I don't know what is going on with me except a few things. Its just chaos in my mind and no one is helping me. And I don't even know what to do with my life but I know I definitely know a lot of stuff with others don't and is actually important. But what this society expects of me is something different. Idk what I just said ...just don't believe anyone....NO ONE. I can't explain everything here but yea ....... Would u be intrested if I talk to u somewhere?

    • @estherjoanna8835
      @estherjoanna8835 ๋…„ ์ „ +7

      @@saurabhjarodia335 u alright bro?

    • @StratophonicDubstep
      @StratophonicDubstep ๋…„ ์ „ +1

      @@estherjoanna8835 fr lmao

    • @NotNiloc
      @NotNiloc ๋…„ ์ „ +1

      @@saurabhjarodia335 Go to the therapist

    • @anju_reddy
      @anju_reddy ๋…„ ์ „

      @@saurabhjarodia335 are you having existential crisis bro

  • @rudyardkipling4569
    @rudyardkipling4569 ๋…„ ์ „ +1

    Excellent video. The ubiquitous emergence of the Feigenbaum constant is just disturbingly, weirdly beautiful.

  • @slaughterround643
    @slaughterround643 4 ๋…„ ์ „ +1388

    Veritasium: "Students can have a little chaos, as a treat."

  • @t-riz7630
    @t-riz7630 4 ๋…„ ์ „ +1661

    Me: cannot do basic calculus
    *sees title of video*
    KRplus just gets me.

    • @BudEnzo
      @BudEnzo 4 ๋…„ ์ „ +26

      I taught myself basic calculus from videos on KRplus. Both Khan Acad and 3blue1brown really helped. I was able to skip Math 251 (Calc 1) at my college and move straight to Calc 2 after a 4-year break between studying BASIC algebra in high school and returning to college.

    • @tishafeed8085
      @tishafeed8085 4 ๋…„ ์ „ +2

      @@BudEnzo wait what, you studied basic algebra in high school?

    • @BudEnzo
      @BudEnzo 4 ๋…„ ์ „ +2

      @@tishafeed8085 I guess lol. My school called it pre-calculus so basically it was algebra+trig.

    • @tishafeed8085
      @tishafeed8085 4 ๋…„ ์ „ +1

      @@BudEnzo what years/classes? in my highschool (9th-11th year) we did trig+calculus

    • @tishafeed8085
      @tishafeed8085 4 ๋…„ ์ „ +3

      @gamecube.enthusiast - - i did, but the fundamentals were studied in years 5-9, then it was trigonometry and calculus. Actually, i just realised it depends on what you call 'highschool'

  • @DavidMauas
    @DavidMauas ๋…„ ์ „

    This is really mind-blowing, I absolutely love it!

  • @Elletanvilla
    @Elletanvilla ๋…„ ์ „

    Thank you so much for this video!!! I canโ€™t understand it fully but my God it still moved me to tears

  • @RPS2443
    @RPS2443 4 ๋…„ ์ „ +442

    "The mandelbrot set is numbers that don't blow up"
    Mind blows up.
    Seriously the best explanation ever. Then he shows it in 3d. Learned more in 20 minutes than in the last 20 years.

  • @harterza
    @harterza 3 ๋…„ ์ „ +2367

    Today I learned that โ€œAnsโ€ means โ€œanswerโ€ on the Google calculator

  • @Devisidev
    @Devisidev ๋…„ ์ „

    You were 37 when you learned about it, I'm 17. Youre doing good, you're teaching as I agree we all should be. This is incredibly fascinating.

  • @nottechytutorials
    @nottechytutorials ๋…„ ์ „ +4

    Something that can be regularly chaotic sounds like such a normal yet fascinating part of life.

  • @keving1085
    @keving1085 4 ๋…„ ์ „ +127

    Fastest 18 minutes of my life. I think I actually found what I want to be when I want to grow up. A mathematician

    • @muttersoehnchen100
      @muttersoehnchen100 4 ๋…„ ์ „ +13

      Kevin Guanoluisa canโ€™t recommend

    • @luisfelipe5589
      @luisfelipe5589 4 ๋…„ ์ „ +1

      Ha
      Ha
      Ha

    • @manamritsingh969
      @manamritsingh969 4 ๋…„ ์ „ +12

      Do it ๐Ÿ‘ Maths is the supreme language of the universe. If you wanna understand the universe, math is the way. I embark on the same path and it's amazing

    • @kayush01
      @kayush01 4 ๋…„ ์ „ +12

      Manamrit Singh not really, mathematics is an abstract concept and it wonโ€™t make you understand the universe. It is more of a tool that you can use to โ€žunderstandโ€ the universe through physics. I know several brilliant mathematicians who decided to study physics when they understood the difference. Mathematics is not really that interesting when it comes to studying it. Itโ€™s the same as learning about black holes in physics, itโ€™s a very brief lecture compared to other stuff that might seem boring like mechanics, kinematics, rigid bodies, aerodynamics etc.

    • @yourboyskar
      @yourboyskar 4 ๋…„ ์ „ +1

      What if you donโ€™t want to grow up lolll

  • @Hgulix62
    @Hgulix62 4 ๋…„ ์ „ +226

    This is like when you start a new project or new year resolution. Everything is fine and simple at first, then progressively and unexpectedly everything turn to chaos

  • @Puzekat2
    @Puzekat2 9 ๊ฐœ์›” ์ „

    Iโ€™m gonna get the FBLA of my sons STEM HS in Florida to watch this video. Every high school math major should know this video and this equation and you just explained what pattern I havenโ€™t been seeing all my life I just never know its name.

  • @yurigansmith
    @yurigansmith ๊ฐœ์›” ์ „ +1

    The graph at 8:43 is amazing. Gonna rebuild it for myself.

  • @infinitiv525
    @infinitiv525 4 ๋…„ ์ „ +372

    I am so glad that some lad just woke up one day and decided: "You know what, I should do some research of dripping faucet."

    • @TheFredmac
      @TheFredmac 4 ๋…„ ์ „ +7

      That would be a lad that doesn't get government funding.

    • @blackdaan
      @blackdaan 4 ๋…„ ์ „ +5

      weed is good for some things...

    • @rtleitao78
      @rtleitao78 4 ๋…„ ์ „ +2

      You mean, instead of fixing it?

    • @BenjaminCronce
      @BenjaminCronce 4 ๋…„ ์ „

      you mean "woken up by a dripping faucet"?

  • @hidjedewitje
    @hidjedewitje 2 ๋…„ ์ „ +1175

    This concept is actually taught in engineering. Particularly in Control Engineering. It's taught because it gives a lot of intuition in nonlinear differential equations. These differential equations occur quite often in nature and in engineering problems when you have to model the dynamics of a system!

    • @DataJYdocs
      @DataJYdocs 2 ๋…„ ์ „ +18

      ie: the Lorenz Attractor.

    • @albertofoti4152
      @albertofoti4152 2 ๋…„ ์ „ +14

      Yep, I'm here because I'm studying for an exam ahah
      Non-linear Control and Aerospace applications

    • @GdeJ
      @GdeJ 2 ๋…„ ์ „ +4

      Here's another: Chua's circuit

    • @albertofoti4152
      @albertofoti4152 2 ๋…„ ์ „ +6

      @@GdeJ I am from Politecnico of Turin in Italy and we had the pleasure of having a lecture directly from Professor Chua.
      I think the Lorenz Attractor and the Chua Circuit are the most thought in control engineering degrees. Maybe talking about non linear systems behaviors we also have systems having limit cycles in the phase portrait, for example the Van Der Pol Oscillator

    • @GdeJ
      @GdeJ 2 ๋…„ ์ „ +6

      @@albertofoti4152 I'm from Federico II University! I just had an exam on non linear dynamics and control. Other than Van Der Pol oscillator, our professor mentioned also other relaxation-excitation oscillators, such as Fitzhugh-Nagumo and Hindmarsh-Rose models of a neuron.

  • @moumous87
    @moumous87 ๋…„ ์ „

    After 3 years, watching it again. Love this video!

  • @jaianeguimaraes129
    @jaianeguimaraes129 3 ๊ฐœ์›” ์ „ +1

    Um dos melhores videos que eu ja vi, muito obrigada por esse conteรบdo!!! Meu coraรงรฃo deu uma acelerada vendo o grafico sendo montado e eu conseguindo compreender o quao incrivel isso รฉ. Brabao demais

  • @thereal7118
    @thereal7118 3 ๋…„ ์ „ +238

    This video taught me how hard is it to slightly open a tap...

    • @egg250
      @egg250 3 ๋…„ ์ „ +1

      lmao

    • @reibian
      @reibian 3 ๋…„ ์ „ +1

      This video certainly โ€œopen slightlyโ€ very well.

  • @ShilpanGPatel
    @ShilpanGPatel 4 ๋…„ ์ „ +128

    I saw the video title and thought โ€œoh suuuuure this will change my lifeโ€, but wow I did not expect to be so taken aback by this. Something so fundamental which Iโ€™ve never heard about before!

    • @ayaipeeoiiu8151
      @ayaipeeoiiu8151 4 ๋…„ ์ „

      Shilpan Patel so you should subscribe to numberphile

  • @valiantwarrior4517
    @valiantwarrior4517 ๋…„ ์ „ +7

    If you look at larger fractal patterns of the Mandelbrot set, you can get a cool โ€œmagic eyeโ€ 3D effect. Particularly one called โ€œSeahorse Valley.โ€

  • @LordElijah
    @LordElijah 10 ๊ฐœ์›” ์ „ +1

    I got more knowledge from this dude than in more than almost my entire school career