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

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: Code for interactives is available below...
Animations, coding, interactives in this video by Jonny Hyman 🙌
Try the code yourself:
James Gleick, Chaos
Steven Strogatz, Nonlinear Dynamics and Chaos
May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976).
Robert Shaw, The Dripping Faucet as a Model Chaotic System
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).
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. 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: "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4" "Busy World" "Children of Mystery"


  • Scripted Frames
    Scripted FramesVor 2 Stunden

    we need "chaos" in schools, not the other chaos 😅

  • Scripted Frames
    Scripted FramesVor 2 Stunden


  • Scripted Frames
    Scripted FramesVor 2 Stunden

    This video proved me that I am a dumb

  • Scripted Frames
    Scripted FramesVor 2 Stunden

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

  • Leo Verran
    Leo VerranVor 2 Stunden

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

  • Karan Jassal
    Karan JassalVor 4 Stunden

    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"

  • twobad
    twobadVor 6 Stunden

    hod up, someone has to tell me the graphing app that he used

  • Miagi Fodder
    Miagi FodderVor 6 Stunden

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

  • Xing Yu
    Xing YuVor 7 Stunden

    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!

  • FBI Agent
    FBI AgentVor 7 Stunden

    I don’t get any of this but it sounds awesome

  • Iron work Paul
    Iron work PaulVor 9 Stunden

    The content is very good, a wonderful man with interesting knowledge

  • Fuzzy Ankles
    Fuzzy AnklesVor 9 Stunden

    holy shiet thats beautiful

  • fffrikkie 123
    fffrikkie 123Vor 19 Stunden

    Life is a simulation confirmed

  • Ishita Vyavahare
    Ishita VyavahareVor 22 Stunden

    what software is he using?

  • Paolo Scaramuzzino
    Paolo ScaramuzzinoVor 23 Stunden

    how does it apply to the Covid-19 waves?

  • O_0
    O_0Vor Tag

    Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing

  • Brian Kemery
    Brian KemeryVor Tag

    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.

  • KG Guitar
    KG GuitarVor Tag


  • Anthony Tran
    Anthony TranVor Tag

    first 10 seconds and i went dumb

  • Simon Lovelace
    Simon LovelaceVor Tag

    When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere

  • Juan David Barrada
    Juan David BarradaVor Tag


  • dolf1n1
    dolf1n1Vor Tag

    Wow I love the way you presented this topic so visually.

  • Rocket Zing
    Rocket ZingVor Tag

    Veritasium : video ratio movie producer : ''m i joke to you

  • ash channan
    ash channanVor Tag

    how many leaves on a tree ? - search - DElevel Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation

  • Milkymalk
    MilkymalkVor Tag

    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?

  • adib z
    adib zVor Tag

    Everything is under control of God. Everything, under His calculation. Assalamualaikum

  • XRay Plays
    XRay PlaysVor Tag


  • Phillip Plyer
    Phillip PlyerVor Tag

    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!

  • steve
    steveVor Tag

    I dont get it U just talk too much

  • Phineas
    PhineasVor 2 Tage

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

  • John Worthington
    John WorthingtonVor 2 Tage

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

  • Mensa X
    Mensa XVor 2 Tage

    All we have to do now is track and follow every bunny rabbit to see if this is true

  • rendzis
    rendzisVor 2 Tage

    In what day did god made this?😁

  • mazhar chrome
    mazhar chromeVor 2 Tage

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

  • unityelt
    unityeltVor 2 Tage

    It's like programming life

  • Slow Motion
    Slow MotionVor 2 Tage

    OMG! I bet he was the most hated guy in school !

  • Pula Vijaya
    Pula VijayaVor 3 Tage

    Is world an illusion make a video sir

  • Peacocks & Polar Bears
    Peacocks & Polar BearsVor 3 Tage

    This is insane. I've never seen something visualized like this.

  • korteks visceralzen
    korteks visceralzenVor 3 Tage

    Thanks. I love this channel. No one explains this stuff.

  • Betsy Larcom
    Betsy LarcomVor 3 Tage

    I was an ecology major in undergrad and everyone else thought we just went around hugging trees...

  • Bare Bear Hands
    Bare Bear HandsVor 3 Tage

    Chaos is natural order.

  • Eric Swenson
    Eric SwensonVor 3 Tage

    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...

  • Rohit Neemwal
    Rohit NeemwalVor 3 Tage

    so random numbers are not so random.

  • Rohit Neemwal
    Rohit NeemwalVor 3 Tage

    universal constants are just some values given to simulator to simulate our universe.hece we are in simulator

  • Rohit Neemwal
    Rohit NeemwalVor 3 Tage

    so , we are in simulation .

  • Steven
    StevenVor 3 Tage

    The mandelbrook fractal looks lika a turtle:)

  • Vinyas Singh
    Vinyas SinghVor 3 Tage

    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.

  • Xer R
    Xer RVor 3 Tage

    You should make a podcast

  • O Templo de Shaka
    O Templo de ShakaVor 3 Tage

    I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.

  • Hein Htet
    Hein HtetVor 3 Tage

    There is no chaos. Everything has a pattern at certain perspective.

  • Martin Da Monarch
    Martin Da MonarchVor 3 Tage

    That kinda looks like how a tree 🌳 grows lol cool

  • delt
    deltVor 4 Tage

    Seeeeriously fascinating!!!! 😲😲

  • Ethan Evans
    Ethan EvansVor 4 Tage

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

  • CallMeBeep
    CallMeBeepVor 4 Tage

    Did you upload the vid ultra-wide just for me? :D

  • Kelvin Francisco
    Kelvin FranciscoVor 4 Tage

    This is the last time I watch any of your videos sober, 😒

  • Zee Y
    Zee YVor 4 Tage

    Now someone still thinks we live in a simulation?

  • Rohan Dongre
    Rohan DongreVor 4 Tage

    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.

  • Segala Nicolas

    Segala Nicolas

    Vor 4 Tage

    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.

  • bereket taffesse
    bereket taffesseVor 4 Tage

    me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man

  • Pillow
    PillowVor 4 Tage

    so this is how the multiverse go

  • Pillow


    Vor 4 Tage


  • Segala Nicolas

    Segala Nicolas

    Vor 4 Tage

    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

  • Michael
    MichaelVor 4 Tage

    Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.

  • God
    GodVor 4 Tage

    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

  • Fractal
    FractalVor 4 Tage

    13:44 oh god it's the zodiac killer

  • Mugtba Moamed
    Mugtba MoamedVor 4 Tage

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

  • Random X
    Random XVor 4 Tage

    How do you guys come up with such things.

  • Connor Eyer
    Connor EyerVor 4 Tage

    The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp

  • troeteimarsch
    troeteimarschVor 4 Tage

    mind blown and the day hasn't even started yet. thanks mate!

  • Chris Incorvati
    Chris IncorvatiVor 5 Tage

    Order begets chaos, chaos begets order.

  • Zygorg
    ZygorgVor 5 Tage

    You adquired a new tittle: Chaotic (Neutral)

  • Carlos Handojo Santosa
    Carlos Handojo SantosaVor 5 Tage

    You just blew my mind.

  • Holyfield Barrett
    Holyfield BarrettVor 5 Tage

    The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason

  • GrandAdmiral Zod
    GrandAdmiral ZodVor 5 Tage

    The anti-life/death equation?

  • ライアン
    ライアンVor 5 Tage

    rx - the population will grow exponentially rx - is a linear equation

  • Segala Nicolas

    Segala Nicolas

    Vor 4 Tage

    @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

  • ライアン


    Vor 4 Tage

    @Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies

  • Релёкс84


    Vor 4 Tage

    It is a linear *differential* equation, which translates to an exponential solution.

  • reckless bose
    reckless boseVor 5 Tage

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

  • Maeby Moore
    Maeby MooreVor 5 Tage

    What happened to the contest after covid hit? Did the winner get to go?

  • Beulah West
    Beulah WestVor 5 Tage

    The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand

  • Brittany Baker
    Brittany BakerVor 5 Tage

    The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year

  • RealJustinCase
    RealJustinCaseVor 5 Tage

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

  • H o t r e t a r d e d c h i X
    H o t r e t a r d e d c h i XVor 5 Tage

    Chaos is so subjective

  • Shoedi L
    Shoedi LVor 5 Tage

    Overpopulation debukned.

  • Segala Nicolas

    Segala Nicolas

    Vor 4 Tage

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

    USNBRENDONVor 5 Tage

    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.

  • Manuel Sánchez de Iñigo
    Manuel Sánchez de IñigoVor 5 Tage

    YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9

  • Scispace Facts
    Scispace FactsVor 5 Tage


  • Abdullah Bham
    Abdullah BhamVor 5 Tage

    Design God

  • John Dalzell
    John DalzellVor 5 Tage

    I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.

  • tylor anderson
    tylor andersonVor 5 Tage

    When I say chaos, you say fogginbom, chaos

  • Mad Maniac
    Mad ManiacVor 6 Tage

    I didnt understand anything

  • mark ryan Jervoso
    mark ryan JervosoVor 6 Tage

    When that needle happens on the chaotic part..then there will Thanos comes..

  • naysay02
    naysay02Vor 6 Tage

    These numbers are living things. This is extraordinary.

  • Olli Bruno
    Olli BrunoVor 6 Tage

    The real Question ist: how to apply this to the Stock market?

  • Kryptonicul
    KryptoniculVor 6 Tage

    Am i the only whos life is actually being changed by this stuff?? Its the only thing i can think about like all different types of infinity. Usually when im doing any task in my daily life ill spring into action or rather my brain does and starts think about how something can be infinite or is it infinite or can it be connected to infinity. The worst case of this is so simple but its almost hindering me, almost every two minutes in math class my brain just spits out "theres infinite amount of numbers in between ___ and ___" or "if you keep using that equation it will go for infinity" or even sometimes i try to make an infinite something like writing how many zeros after 0.0 before running out of room and having to put a 1 at the end. Tomorrow or maybe monday in class im going to use the mandelbrot equation to try and draw a small taste of a man made mandbrot set. Although I know I will be restricted by how much room I have on the page or whatever im drawing on. I almost feel restricted by reality or something. Considering everyone has ever told me that infinity is impossible to comprehend I seriously want to comprehend it or hear it or see it or just do anything that i could actually interact my sense with infinity. Of coure this will never happen considering there is no real infinity or at least not that we can "comprehend"

  • Manners PUBGM
    Manners PUBGMVor 6 Tage

    The only reason we call it chaos is because in order to see the chaos as a constant you would need to be in a higher dimension.

  • Kim-André Johansen

    Kim-André Johansen

    Vor 4 Tage

    Yes! But maths can take us there 🙂

  • Leif Schmit-Kallas
    Leif Schmit-KallasVor 6 Tage

    The correct name for a population of rabbits is Fluffle.

  • Basil Al-jaml
    Basil Al-jamlVor 6 Tage

    what is the name of the plotting tool at 3:07 ?

  • pudpud kirkpatrick
    pudpud kirkpatrickVor 6 Tage

    The sweltering ketchup fortuitously correct because kitty internationally chew within a wonderful dragonfly. fabulous, abrasive windshield

  • Snow Ko Oo
    Snow Ko OoVor 6 Tage

    click on the video Panik : Oh god , i am so dumb, i will not be able to change the view on the world Pause the video and.. click on comment section Kalm: yhh at least....i know i am not aloooone😜

  • A Man With Suspenders
    A Man With SuspendersVor 6 Tage

    4.669 hehehe funny number.

  • Jonas Fermefors
    Jonas FermeforsVor 6 Tage

    I haven't thought about Mandelbrot sets since I was 20 and they delivered the coolest graphics on the new VGA-card. The Mandelbrot set already has something organic about it, but this takes it to a new level: the actual underpinnings of the universe. The clickbait-like title was true. Blew my mind.

  • Enzhou Zutzut
    Enzhou ZutzutVor 7 Tage

    This video makes me feel genius even though I don't understand any of it.

  • Axel From Group Therapy
    Axel From Group TherapyVor 7 Tage

    Am i the only one who sees the graph similar to the Darwin´s tree of life?

  • Shark Falcon
    Shark FalconVor 7 Tage

    Amazing science communicator. Heads of to you sir!