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

29 gen 2020
9 996 076 visualizzazioni

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"

Commenti
  • 19:39 10^10^100 Googolplex

    Leandro PlacenciaLeandro PlacenciaOra fa
  • 10^10^100 Googolplex

    Leandro PlacenciaLeandro PlacenciaOra fa
  • BANG! .. My brain feels much better...

    Rotciv InoccicRotciv Inoccic4 ore fa
  • 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 Witemp7 ore fa
  • 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 monkey13 ore fa
  • 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 Brunhard17 ore fa
  • Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.

    The RodestarrThe Rodestarr17 ore fa
  • Which software did he use for plotting his graphs? 3:45

    ichich18 ore fa
  • Amazing. Thenks for the outstanding explanation of a pretty complex subject (for lay people)!

    Naz FrideNaz Fride22 ore fa
  • 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 Das22 ore fa
  • Your calculation is wrong

    Simranjeet SinghSimranjeet SinghGiorno fa
  • Can I still answer the question

    Ssenyonjo JirehSsenyonjo JirehGiorno fa
  • Can I still answer the question

    Ssenyonjo JirehSsenyonjo JirehGiorno fa
  • out of all the possibilities z-axis was the least expected

    Chindulur Sai KaushikChindulur Sai KaushikGiorno fa
  • we need "chaos" in schools, not the other chaos 😅

    Scripted FramesScripted FramesGiorno fa
  • "Chaos"

    Scripted FramesScripted FramesGiorno fa
  • This video proved me that I am a dumb

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

    Scripted FramesScripted FramesGiorno fa
  • 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 VerranGiorno fa
  • 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 JassalGiorno fa
  • hod up, someone has to tell me the graphing app that he used

    twobadtwobadGiorno fa
  • 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 FodderGiorno fa
  • 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 YuGiorno fa
  • I don’t get any of this but it sounds awesome

    FBI AgentFBI AgentGiorno fa
  • The content is very good, a wonderful man with interesting knowledge

    Iron work PaulIron work PaulGiorno fa
  • holy shiet thats beautiful

    Fuzzy AnklesFuzzy AnklesGiorno fa
  • Life is a simulation confirmed

    fffrikkie 123fffrikkie 1232 giorni fa
  • what software is he using?

    Ishita VyavahareIshita Vyavahare2 giorni fa
  • how does it apply to the Covid-19 waves?

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

    O_0O_02 giorni fa
  • 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 Kemery2 giorni fa
  • ROWAN???

    KG GuitarKG Guitar2 giorni fa
  • first 10 seconds and i went dumb

    Anthony TranAnthony Tran2 giorni fa
  • When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere

    Simon LovelaceSimon Lovelace2 giorni fa
  • Amazing!!!

    Juan David BarradaJuan David Barrada2 giorni fa
  • Wow I love the way you presented this topic so visually.

    dolf1n1dolf1n12 giorni fa
  • Veritasium : video ratio movie producer : ''m i joke to you

    Rocket ZingRocket Zing2 giorni fa
  • how many leaves on a tree ? - search - ITworlds Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation

    ash channanash channan3 giorni fa
  • 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 giorni fa
  • Everything is under control of God. Everything, under His calculation. Assalamualaikum

    adib zadib z3 giorni fa
  • Huh

    XRay PlaysXRay Plays3 giorni fa
  • 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 giorni fa
  • I dont get it U just talk too much

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

    PhineasPhineas3 giorni fa
  • I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..

    John WorthingtonJohn Worthington3 giorni fa
  • All we have to do now is track and follow every bunny rabbit to see if this is true

    Mensa XMensa X3 giorni fa
  • In what day did god made this?😁

    rendzisrendzis3 giorni fa
  • Can you make a video about this equation with human population, where will be the equilibrium?

    mazhar chromemazhar chrome4 giorni fa
  • It's like programming life

    unityeltunityelt4 giorni fa
  • OMG! I bet he was the most hated guy in school !

    Slow MotionSlow Motion4 giorni fa
  • Is world an illusion make a video sir

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

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

    korteks visceralzenkorteks visceralzen4 giorni fa
  • I was an ecology major in undergrad and everyone else thought we just went around hugging trees...

    Betsy LarcomBetsy Larcom4 giorni fa
  • Chaos is natural order.

    Bare Bear HandsBare Bear Hands4 giorni fa
  • 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 Swenson4 giorni fa
  • so random numbers are not so random.

    Rohit NeemwalRohit Neemwal4 giorni fa
  • universal constants are just some values given to simulator to simulate our universe.hece we are in simulator

    Rohit NeemwalRohit Neemwal4 giorni fa
  • so , we are in simulation .

    Rohit NeemwalRohit Neemwal4 giorni fa
  • The mandelbrook fractal looks lika a turtle:)

    StevenSteven4 giorni fa
  • 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 giorni fa
  • You should make a podcast

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

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

    Hein HtetHein Htet5 giorni fa
  • That kinda looks like how a tree 🌳 grows lol cool

    Martin Da MonarchMartin Da Monarch5 giorni fa
  • Seeeeriously fascinating!!!! 😲😲

    deltdelt5 giorni fa
  • Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago

    Ethan EvansEthan Evans5 giorni fa
  • Did you upload the vid ultra-wide just for me? :D

    CallMeBeepCallMeBeep5 giorni fa
  • This is the last time I watch any of your videos sober, 😒

    Kelvin FranciscoKelvin Francisco5 giorni fa
  • Now someone still thinks we live in a simulation?

    Zee YZee Y5 giorni fa
  • 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 Dongre5 giorni fa
    • 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 Nicolas5 giorni fa
  • me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man

    bereket taffessebereket taffesse5 giorni fa
  • so this is how the multiverse go

    PillowPillow6 giorni fa
    • multiverse

      PillowPillow5 giorni fa
    • 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 Nicolas5 giorni fa
  • Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.

    MichaelMichael6 giorni fa
  • 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 giorni fa
  • 13:44 oh god it's the zodiac killer

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

    Mugtba MoamedMugtba Moamed6 giorni fa
  • How do you guys come up with such things.

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

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

    troeteimarschtroeteimarsch6 giorni fa
  • Order begets chaos, chaos begets order.

    Chris IncorvatiChris Incorvati6 giorni fa
  • You adquired a new tittle: Chaotic (Neutral)

    ZygorgZygorg6 giorni fa
  • You just blew my mind.

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

    Holyfield BarrettHolyfield Barrett6 giorni fa
  • The anti-life/death equation?

    GrandAdmiral ZodGrandAdmiral Zod6 giorni fa
  • rx - the population will grow exponentially rx - is a linear equation

    ライアンライアン6 giorni fa
    • @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 Nicolas5 giorni fa
    • @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5 giorni fa
    • It is a linear *differential* equation, which translates to an exponential solution.

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

    reckless bosereckless bose6 giorni fa
  • What happened to the contest after covid hit? Did the winner get to go?

    Maeby MooreMaeby Moore6 giorni fa
  • The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand

    Beulah WestBeulah West6 giorni fa
  • The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year

    Brittany BakerBrittany Baker6 giorni fa
  • I'm going to be so honest here. What the hell did I just watch and how do I feel even less about myself

    RealJustinCaseRealJustinCase6 giorni fa
  • 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 X6 giorni fa
  • Overpopulation debukned.

    Shoedi LShoedi L6 giorni fa
    • 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 Nicolas5 giorni fa
  • 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.

    USNBRENDONUSNBRENDON6 giorni fa
  • YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9

    Manuel Sánchez de IñigoManuel Sánchez de Iñigo6 giorni fa
  • RIGHT NOW I AM STUDYING SAME IN MY T.Y BSc

    Scispace FactsScispace Facts6 giorni fa
  • Design ..by God

    Abdullah BhamAbdullah Bham7 giorni fa
  • I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.

    John DalzellJohn Dalzell7 giorni fa
  • When I say chaos, you say fogginbom, chaos

    tylor andersontylor anderson7 giorni fa
  • I didnt understand anything

    Mad ManiacMad Maniac7 giorni fa
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