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

29 jan. 2020
10 001 281 Weergaven

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"

Reacties
  • 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 KabibbleUur geleden
  • Look at me just 16 and finding out about this instead of 32 welp anyway I have to go troubleshoot my brain

    UhOhMeMeBiggestBoyUhOhMeMeBiggestBoy2 uur geleden
  • I hurt myself in confusion. :(

    Xandea GalletaXandea Galleta5 uur geleden
  • Spherical trigonometry will prove the Earth is flat. You haven't got the balls to research that truth.

    Dodd RougeauDodd Rougeau5 uur geleden
  • An application of math. Frustrating part of most math classes is the lack of application.

    R DoodyR Doody7 uur geleden
  • 19:39 10^10^100 Googolplex

    Leandro PlacenciaLeandro Placencia14 uur geleden
  • 10^10^100 Googolplex

    Leandro PlacenciaLeandro Placencia14 uur geleden
  • BANG! .. My brain feels much better...

    Rotciv InoccicRotciv Inoccic17 uur geleden
  • 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 Witemp20 uur geleden
  • 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 monkeyDag geleden
  • 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 BrunhardDag geleden
  • Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.

    The RodestarrThe RodestarrDag geleden
  • Which software did he use for plotting his graphs? 3:45

    ichichDag geleden
  • Amazing. Thenks for the outstanding explanation of a pretty complex subject (for lay people)!

    Naz FrideNaz FrideDag geleden
  • 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 DasDag geleden
  • Your calculation is wrong

    Simranjeet SinghSimranjeet SinghDag geleden
  • Can I still answer the question

    Ssenyonjo JirehSsenyonjo JirehDag geleden
  • Can I still answer the question

    Ssenyonjo JirehSsenyonjo JirehDag geleden
  • out of all the possibilities z-axis was the least expected

    Chindulur Sai KaushikChindulur Sai KaushikDag geleden
  • we need "chaos" in schools, not the other chaos 😅

    Scripted FramesScripted FramesDag geleden
  • "Chaos"

    Scripted FramesScripted FramesDag geleden
  • This video proved me that I am a dumb

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

    Scripted FramesScripted FramesDag geleden
  • 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 Verran2 dagen geleden
  • 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 Jassal2 dagen geleden
  • hod up, someone has to tell me the graphing app that he used

    twobadtwobad2 dagen geleden
  • 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 Fodder2 dagen geleden
  • 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 Yu2 dagen geleden
  • I don’t get any of this but it sounds awesome

    FBI AgentFBI Agent2 dagen geleden
  • The content is very good, a wonderful man with interesting knowledge

    Iron work PaulIron work Paul2 dagen geleden
  • holy shiet thats beautiful

    Fuzzy AnklesFuzzy Ankles2 dagen geleden
  • Life is a simulation confirmed

    fffrikkie 123fffrikkie 1232 dagen geleden
  • what software is he using?

    Ishita VyavahareIshita Vyavahare2 dagen geleden
  • how does it apply to the Covid-19 waves?

    Paolo ScaramuzzinoPaolo Scaramuzzino2 dagen geleden
  • Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing

    O_0O_02 dagen geleden
  • 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 Kemery3 dagen geleden
  • ROWAN???

    KG GuitarKG Guitar3 dagen geleden
  • first 10 seconds and i went dumb

    Anthony TranAnthony Tran3 dagen geleden
  • When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere

    Simon LovelaceSimon Lovelace3 dagen geleden
  • Amazing!!!

    Juan David BarradaJuan David Barrada3 dagen geleden
  • Wow I love the way you presented this topic so visually.

    dolf1n1dolf1n13 dagen geleden
  • Veritasium : video ratio movie producer : ''m i joke to you

    Rocket ZingRocket Zing3 dagen geleden
  • how many leaves on a tree ? - search - NLworld Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation

    ash channanash channan3 dagen geleden
  • 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?

    MilkymalkMilkymalk3 dagen geleden
  • Everything is under control of God. Everything, under His calculation. Assalamualaikum

    adib zadib z3 dagen geleden
  • Huh

    XRay PlaysXRay Plays3 dagen geleden
  • 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 Plyer3 dagen geleden
  • I dont get it U just talk too much

    stevesteve3 dagen geleden
  • I struggled to understand this just like many people. But look up Feigenbaum Number on Numberphile, it'll make this easier to understand slightly

    PhineasPhineas4 dagen geleden
  • I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..

    John WorthingtonJohn Worthington4 dagen geleden
  • All we have to do now is track and follow every bunny rabbit to see if this is true

    Mensa XMensa X4 dagen geleden
  • In what day did god made this?😁

    rendzisrendzis4 dagen geleden
  • Can you make a video about this equation with human population, where will be the equilibrium?

    mazhar chromemazhar chrome4 dagen geleden
  • It's like programming life

    unityeltunityelt4 dagen geleden
  • OMG! I bet he was the most hated guy in school !

    Slow MotionSlow Motion4 dagen geleden
  • Is world an illusion make a video sir

    Pula VijayaPula Vijaya4 dagen geleden
  • This is insane. I've never seen something visualized like this.

    Peacocks & Polar BearsPeacocks & Polar Bears4 dagen geleden
  • Thanks. I love this channel. No one explains this stuff.

    korteks visceralzenkorteks visceralzen5 dagen geleden
  • I was an ecology major in undergrad and everyone else thought we just went around hugging trees...

    Betsy LarcomBetsy Larcom5 dagen geleden
  • Chaos is natural order.

    Bare Bear HandsBare Bear Hands5 dagen geleden
  • 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 Swenson5 dagen geleden
  • so random numbers are not so random.

    Rohit NeemwalRohit Neemwal5 dagen geleden
  • universal constants are just some values given to simulator to simulate our universe.hece we are in simulator

    Rohit NeemwalRohit Neemwal5 dagen geleden
  • so , we are in simulation .

    Rohit NeemwalRohit Neemwal5 dagen geleden
  • The mandelbrook fractal looks lika a turtle:)

    StevenSteven5 dagen geleden
  • 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 Singh5 dagen geleden
  • You should make a podcast

    Xer RXer R5 dagen geleden
  • I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.

    O Templo de ShakaO Templo de Shaka5 dagen geleden
  • There is no chaos. Everything has a pattern at certain perspective.

    Hein HtetHein Htet5 dagen geleden
  • That kinda looks like how a tree 🌳 grows lol cool

    Martin Da MonarchMartin Da Monarch5 dagen geleden
  • Seeeeriously fascinating!!!! 😲😲

    deltdelt6 dagen geleden
  • Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago

    Ethan EvansEthan Evans6 dagen geleden
  • Did you upload the vid ultra-wide just for me? :D

    CallMeBeepCallMeBeep6 dagen geleden
  • This is the last time I watch any of your videos sober, 😒

    Kelvin FranciscoKelvin Francisco6 dagen geleden
  • Now someone still thinks we live in a simulation?

    Zee YZee Y6 dagen geleden
  • 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 Dongre6 dagen geleden
    • 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 Nicolas6 dagen geleden
  • me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man

    bereket taffessebereket taffesse6 dagen geleden
  • so this is how the multiverse go

    PillowPillow6 dagen geleden
    • multiverse

      PillowPillow6 dagen geleden
    • 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 Nicolas6 dagen geleden
  • Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.

    MichaelMichael6 dagen geleden
  • 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

    GodGod6 dagen geleden
  • 13:44 oh god it's the zodiac killer

    FractalFractal6 dagen geleden
  • Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.

    Mugtba MoamedMugtba Moamed6 dagen geleden
  • How do you guys come up with such things.

    Random XRandom X6 dagen geleden
  • The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp

    Connor EyerConnor Eyer6 dagen geleden
  • mind blown and the day hasn't even started yet. thanks mate!

    troeteimarschtroeteimarsch6 dagen geleden
  • Order begets chaos, chaos begets order.

    Chris IncorvatiChris Incorvati6 dagen geleden
  • You adquired a new tittle: Chaotic (Neutral)

    ZygorgZygorg6 dagen geleden
  • You just blew my mind.

    Carlos Handojo SantosaCarlos Handojo Santosa6 dagen geleden
  • The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason

    Holyfield BarrettHolyfield Barrett7 dagen geleden
  • The anti-life/death equation?

    GrandAdmiral ZodGrandAdmiral Zod7 dagen geleden
  • rx - the population will grow exponentially rx - is a linear equation

    ライアンライアン7 dagen geleden
    • @ライアン but it is exponential, because x(n+1)=r*x(n) is equivalent to x(n)=r^n so it's an exponential model because it's raised to a power. Anyway, the math here is correct

      Segala NicolasSegala Nicolas6 dagen geleden
    • @Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies

      ライアンライアン6 dagen geleden
    • It is a linear *differential* equation, which translates to an exponential solution.

      Релёкс84Релёкс846 dagen geleden
  • The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter

    reckless bosereckless bose7 dagen geleden
  • What happened to the contest after covid hit? Did the winner get to go?

    Maeby MooreMaeby Moore7 dagen geleden
  • The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand

    Beulah WestBeulah West7 dagen geleden
  • The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year

    Brittany BakerBrittany Baker7 dagen geleden
  • I'm going to be so honest here. What the hell did I just watch and how do I feel even less about myself

    RealJustinCaseRealJustinCase7 dagen geleden
  • Chaos is so subjective

    H o t r e t a r d e d c h i XH o t r e t a r d e d c h i X7 dagen geleden
  • Overpopulation debukned.

    Shoedi LShoedi L7 dagen geleden
    • What do you mean ? That's not the point of the video, and I'm not sure what there is to debunk about overpopulation

      Segala NicolasSegala Nicolas6 dagen geleden
  • CERN. August 1991. I believe it was few 6th.... But, yes, it was Switzerland's CERN that quietly switched on the first research website in the aim of studying particle based physics--atom smashing! Love it.

    USNBRENDONUSNBRENDON7 dagen geleden
  • YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9

    Manuel Sánchez de IñigoManuel Sánchez de Iñigo7 dagen geleden
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