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

2020 Хул 29-нд
10 010 416 Үзсэн тоо

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 🙌
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/ShawRobertDrippingFaucetAsAModelChaoticSystem1984_201811/mode/2up
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:01982004307021100. 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"

Сэтгэгдлүүд
  • I think this graph also represents the evolution of human intelligence. 👉Think about this: The same brain that created the theory of evolution had to first evolve itself.

    The ZachThe Zach8 цагийн өмнө
  • Thanks

    Mahir BalushiMahir Balushi11 цагийн өмнө
  • Whaaaaaaaaaaatttt

    Daniel EdwardsDaniel Edwards12 цагийн өмнө
  • I love watching Mandelbrot renderings. That graphic just blew my mind. Beauty has a measure - math itself.

    Brian KleinschmidtBrian Kleinschmidt12 цагийн өмнө
  • This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.

    Lion DeluxeLion Deluxe15 цагийн өмнө
  • this video is horrible. You keep conflating "the population" with "the percentage of the maximum possible population"

    mt2mgamesmt2mgames16 цагийн өмнө
  • 16:55 excited about chaos *HERESY* call the inquisiton

    MarreMarre19 цагийн өмнө
  • Showerthought: every civilization follows the same pattern , I would say we crossed the curve somewhere between 70s-90s

    Ruderaksha KarwaRuderaksha Karwa20 цагийн өмнө
  • So much complexity and we still don't believe there is God.

    Drawing MasterclassDrawing Masterclass20 цагийн өмнө
  • I keep hearing predictions that human populations will decline, but I don't think it is going to be anywhere near as soon as they think. We have been rising since the Black Plague supposedly.

    Shawn BechardShawn Bechard22 цагийн өмнө
  • I LOVED this topic! It's insane! I knew that Mandelbrot set was pretty particular on its own but this! I want to know more

    Nad GNad GӨдрийн өмнө
  • This is amazing! I'm familiar with the Mandelbrot set from decades ago, but is that 3D z-axis section a new discovery?

    Ish KabibbleIsh KabibbleӨдрийн өмнө
  • Look at me just 16 and finding out about this instead of 32 welp anyway I have to go troubleshoot my brain

    UhOhMeMeBiggestBoyUhOhMeMeBiggestBoyӨдрийн өмнө
  • I hurt myself in confusion. :(

    Xandea GalletaXandea GalletaӨдрийн өмнө
  • Spherical trigonometry will prove the Earth is flat. You haven't got the balls to research that truth.

    Dodd RougeauDodd RougeauӨдрийн өмнө
  • An application of math. Frustrating part of most math classes is the lack of application.

    R DoodyR DoodyӨдрийн өмнө
  • 19:39 10^10^100 Googolplex

    Leandro PlacenciaLeandro PlacenciaӨдрийн өмнө
  • 10^10^100 Googolplex

    Leandro PlacenciaLeandro PlacenciaӨдрийн өмнө
  • BANG! .. My brain feels much better...

    Rotciv InoccicRotciv Inoccic2 өдрийн өмнө
  • It's the same about the human population. And it seems like we're at the peek right now and going down. That constant is like the pi of fractals

    Netemp WitempNetemp Witemp2 өдрийн өмнө
  • School only teaches you the minimum you need to start the next grade. It doesn't teach you to think or be intelligent and never will. Look at how fast kids learn until they start school and then are held back from learning at the same pace by being forced to do it "the way I tell you".

    deck monkeydeck monkey2 өдрийн өмнө
  • I want to thank you for your channel honestly. I rarely ever leave comments, but I am so IMPRESSED AND APPRECIATIVE for your work. You are bringing science out to the public forum so we, as a population, can engage in science. Science needs funding. It is what it is, and the content you provide is structured in a way for the general public can understand the unique and awe-inspiring physics that this universe has. FROM MY HEART THANK YOU FOR DOING YOUR BEST TO HELP THE HUMAN RACE EVOLVE.

    Jason BrunhardJason Brunhard2 өдрийн өмнө
  • Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.

    The RodestarrThe Rodestarr2 өдрийн өмнө
  • Which software did he use for plotting his graphs? 3:45

    ichich2 өдрийн өмнө
  • Amazing. Thenks for the outstanding explanation of a pretty complex subject (for lay people)!

    Naz FrideNaz Fride2 өдрийн өмнө
  • If everyone will become vegetarian, there is no hunting or poaching and no disasters then we can find the date of extinction of a specific species 😯😯😯😯😯😯. This is mind blowing

    Subhadeep DasSubhadeep Das2 өдрийн өмнө
  • Your calculation is wrong

    Simranjeet SinghSimranjeet Singh2 өдрийн өмнө
  • Can I still answer the question

    Ssenyonjo JirehSsenyonjo Jireh3 өдрийн өмнө
  • Can I still answer the question

    Ssenyonjo JirehSsenyonjo Jireh3 өдрийн өмнө
  • out of all the possibilities z-axis was the least expected

    Chindulur Sai KaushikChindulur Sai Kaushik3 өдрийн өмнө
  • we need "chaos" in schools, not the other chaos 😅

    Scripted FramesScripted Frames3 өдрийн өмнө
  • "Chaos"

    Scripted FramesScripted Frames3 өдрийн өмнө
  • This video proved me that I am a dumb

    Scripted FramesScripted Frames3 өдрийн өмнө
  • This video proved me that I am a dumb, I didn't even understand a bit as a 11th grades student

    Scripted FramesScripted Frames3 өдрийн өмнө
  • Rabbits times rabbits divided by coyotes plus hawks minus fox equals WTF are you talking about and who cares,...not even the rabbits care!

    Leo VerranLeo Verran3 өдрийн өмнө
  • This video was so enlightening! Thank you! I love how we can visually see the fractal from a simple equation, and this is exactly how I perceive the universe. "As above, so below"

    Karan JassalKaran Jassal3 өдрийн өмнө
  • hod up, someone has to tell me the graphing app that he used

    twobadtwobad3 өдрийн өмнө
  • God man your 37 and only just found out about this. I'm 35 and just found out about it. Up your game dude

    Miagi FodderMiagi Fodder3 өдрийн өмнө
  • this vid has saved my essay project 😂i've been learning how to determine period doubling in the last couple of months. But i had little clue that so many real life phenomena exhibits the bifurcation doubling behaviour. Impressed!

    Xing YuXing Yu3 өдрийн өмнө
  • I don’t get any of this but it sounds awesome

    FBI AgentFBI Agent3 өдрийн өмнө
  • The content is very good, a wonderful man with interesting knowledge

    Iron work PaulIron work Paul3 өдрийн өмнө
  • holy shiet thats beautiful

    Fuzzy AnklesFuzzy Ankles3 өдрийн өмнө
  • Life is a simulation confirmed

    fffrikkie 123fffrikkie 1234 өдрийн өмнө
  • what software is he using?

    Ishita VyavahareIshita Vyavahare4 өдрийн өмнө
  • how does it apply to the Covid-19 waves?

    Paolo ScaramuzzinoPaolo Scaramuzzino4 өдрийн өмнө
  • Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing

    O_0O_04 өдрийн өмнө
  • I've heard a ton about the Mandelbrot set over the years...but when he rotated it into 3 dimensions and it matched with the bifurcation diagram, my brain literally melted.

    Brian KemeryBrian Kemery4 өдрийн өмнө
  • ROWAN???

    KG GuitarKG Guitar4 өдрийн өмнө
  • first 10 seconds and i went dumb

    Anthony TranAnthony Tran4 өдрийн өмнө
  • When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere

    Simon LovelaceSimon Lovelace4 өдрийн өмнө
  • Amazing!!!

    Juan David BarradaJuan David Barrada4 өдрийн өмнө
  • Wow I love the way you presented this topic so visually.

    dolf1n1dolf1n14 өдрийн өмнө
  • Veritasium : video ratio movie producer : ''m i joke to you

    Rocket ZingRocket Zing4 өдрийн өмнө
  • how many leaves on a tree ? - search - MNred Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation

    ash channanash channan5 өдрийн өмнө
  • What if all these fundamental constants are such weird numbers (4.669, 3.1415..., and so on) because the computer universe.exe runs on uses something other than base 10?

    MilkymalkMilkymalk5 өдрийн өмнө
  • Everything is under control of God. Everything, under His calculation. Assalamualaikum

    adib zadib z5 өдрийн өмнө
  • Huh

    XRay PlaysXRay Plays5 өдрийн өмнө
  • I'm just now fi ding your videos and its creating chaos in my marriage! I feel a couple bifurcation coming on. Any sugar mommas out there wanna help me get to 4.6669!? 😜 But in all seriousness, your videos are awesome!

    Phillip PlyerPhillip Plyer5 өдрийн өмнө
  • I dont get it U just talk too much

    stevesteve5 өдрийн өмнө
  • I struggled to understand this just like many people. But look up Feigenbaum Number on Numberphile, it'll make this easier to understand slightly

    PhineasPhineas5 өдрийн өмнө
  • I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..

    John WorthingtonJohn Worthington5 өдрийн өмнө
  • All we have to do now is track and follow every bunny rabbit to see if this is true

    Mensa XMensa X5 өдрийн өмнө
  • In what day did god made this?😁

    rendzisrendzis5 өдрийн өмнө
  • Can you make a video about this equation with human population, where will be the equilibrium?

    mazhar chromemazhar chrome5 өдрийн өмнө
  • It's like programming life

    unityeltunityelt5 өдрийн өмнө
  • OMG! I bet he was the most hated guy in school !

    Slow MotionSlow Motion6 өдрийн өмнө
  • Is world an illusion make a video sir

    Pula VijayaPula Vijaya6 өдрийн өмнө
  • This is insane. I've never seen something visualized like this.

    Peacocks & Polar BearsPeacocks & Polar Bears6 өдрийн өмнө
  • Thanks. I love this channel. No one explains this stuff.

    korteks visceralzenkorteks visceralzen6 өдрийн өмнө
  • I was an ecology major in undergrad and everyone else thought we just went around hugging trees...

    Betsy LarcomBetsy Larcom6 өдрийн өмнө
  • Chaos is natural order.

    Bare Bear HandsBare Bear Hands6 өдрийн өмнө
  • And no one thinks there is a creator that did all this by design? All these links and ratios no one can explain the existence of, and we think it all just came about by accident...

    Eric SwensonEric Swenson6 өдрийн өмнө
  • so random numbers are not so random.

    Rohit NeemwalRohit Neemwal6 өдрийн өмнө
  • universal constants are just some values given to simulator to simulate our universe.hece we are in simulator

    Rohit NeemwalRohit Neemwal6 өдрийн өмнө
  • so , we are in simulation .

    Rohit NeemwalRohit Neemwal6 өдрийн өмнө
  • The mandelbrook fractal looks lika a turtle:)

    StevenSteven6 өдрийн өмнө
  • I guess the made up/unexplained answer of "42" we get to hear about has something to do with this universal constant of "4.669", I'm not sure though.

    Vinyas SinghVinyas Singh6 өдрийн өмнө
  • You should make a podcast

    Xer RXer R6 өдрийн өмнө
  • I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.

    O Templo de ShakaO Templo de Shaka7 өдрийн өмнө
  • There is no chaos. Everything has a pattern at certain perspective.

    Hein HtetHein Htet7 өдрийн өмнө
  • That kinda looks like how a tree 🌳 grows lol cool

    Martin Da MonarchMartin Da Monarch7 өдрийн өмнө
  • Seeeeriously fascinating!!!! 😲😲

    deltdelt7 өдрийн өмнө
  • Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago

    Ethan EvansEthan Evans7 өдрийн өмнө
  • Did you upload the vid ultra-wide just for me? :D

    CallMeBeepCallMeBeep7 өдрийн өмнө
  • This is the last time I watch any of your videos sober, 😒

    Kelvin FranciscoKelvin Francisco7 өдрийн өмнө
  • Now someone still thinks we live in a simulation?

    Zee YZee Y7 өдрийн өмнө
  • What kind of math is that?? Initially you said X is no. of rabbits, then you choose X=0.4, how's that possible?? Now, if R is the rate of growth, population next year isn't X*R, but X*(1+R). Further if suggest that the rate of growth will depend on the present population, the R, for any year, will be expressed as a function of (Ps, Pp) where Ps is the saturation population assuming limited resources and Pp is the present population for that particular year. Therefore, Xn=RX(1-X) is incorrect.

    Rohan DongreRohan Dongre7 өдрийн өмнө
    • The X is the percentage of population the theoretical maximum of the population. It makes sense to choose it arbitrarily, since what we care about is the value of X when it stabilises. And it will stabilise to the same value whether we choose it to be 0.4 or 0.9 or anything between 0 and 1. And secondly, it does make sense to multiply by the growth rate, as it makes an exponential model. The math here has been established since the 1970s, there are papers on this, of course it's correct.

      Segala NicolasSegala Nicolas7 өдрийн өмнө
  • me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man

    bereket taffessebereket taffesse7 өдрийн өмнө
  • so this is how the multiverse go

    PillowPillow7 өдрийн өмнө
    • multiverse

      PillowPillow7 өдрийн өмнө
    • No, this has nothing to do with that. But if you want something that feels like the multiverse, you should check out Veritasium's video on the Many Worlds theory of physics

      Segala NicolasSegala Nicolas7 өдрийн өмнө
  • Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.

    MichaelMichael7 өдрийн өмнө
  • THATS RIGHT!!! OH this got me so excited! :) Apply it to the cosmos and when a star releases energy to its surrounding planets. Chaos , adaptation to environment, then order but it evolves and branches out. The law of life. So many layers lol

    GodGod7 өдрийн өмнө
  • 13:44 oh god it's the zodiac killer

    FractalFractal7 өдрийн өмнө
  • Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.

    Mugtba MoamedMugtba Moamed8 өдрийн өмнө
  • How do you guys come up with such things.

    Random XRandom X8 өдрийн өмнө
  • The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp

    Connor EyerConnor Eyer8 өдрийн өмнө
  • mind blown and the day hasn't even started yet. thanks mate!

    troeteimarschtroeteimarsch8 өдрийн өмнө
  • Order begets chaos, chaos begets order.

    Chris IncorvatiChris Incorvati8 өдрийн өмнө
  • You adquired a new tittle: Chaotic (Neutral)

    ZygorgZygorg8 өдрийн өмнө
  • You just blew my mind.

    Carlos Handojo SantosaCarlos Handojo Santosa8 өдрийн өмнө
  • The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason

    Holyfield BarrettHolyfield Barrett8 өдрийн өмнө
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