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"


  • Nad G
    Nad G35 minuti fa

    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

  • Ish Kabibble
    Ish Kabibble6 ore fa

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

  • UhOhMeMeBiggestBoy
    UhOhMeMeBiggestBoy7 ore fa

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

  • Xandea Galleta
    Xandea Galleta10 ore fa

    I hurt myself in confusion. :(

  • Dodd Rougeau
    Dodd Rougeau11 ore fa

    Spherical trigonometry will prove the Earth is flat. You haven't got the balls to research that truth.

  • R Doody
    R Doody12 ore fa

    An application of math. Frustrating part of most math classes is the lack of application.

  • Leandro Placencia
    Leandro Placencia20 ore fa

    19:39 10^10^100 Googolplex

  • Leandro Placencia
    Leandro Placencia20 ore fa

    10^10^100 Googolplex

  • Rotciv Inoccic
    Rotciv Inoccic23 ore fa

    BANG! .. My brain feels much better...

  • Netemp Witemp
    Netemp WitempGiorno 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

  • deck monkey
    deck monkeyGiorno 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".

  • Jason Brunhard
    Jason BrunhardGiorno 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.

  • The Rodestarr
    The RodestarrGiorno fa

    Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.

  • ich
    ichGiorno fa

    Which software did he use for plotting his graphs? 3:45

  • Naz Fride
    Naz FrideGiorno fa

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

  • Subhadeep Das
    Subhadeep DasGiorno 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

  • Simranjeet Singh
    Simranjeet SinghGiorno fa

    Your calculation is wrong

  • Ssenyonjo Jireh
    Ssenyonjo JirehGiorno fa

    Can I still answer the question

  • Ssenyonjo Jireh
    Ssenyonjo JirehGiorno fa

    Can I still answer the question

  • Chindulur Sai Kaushik
    Chindulur Sai Kaushik2 giorni fa

    out of all the possibilities z-axis was the least expected

  • Scripted Frames
    Scripted Frames2 giorni fa

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

  • Scripted Frames
    Scripted Frames2 giorni fa


  • Scripted Frames
    Scripted Frames2 giorni fa

    This video proved me that I am a dumb

  • Scripted Frames
    Scripted Frames2 giorni fa

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

  • Leo Verran
    Leo Verran2 giorni 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!

  • Karan Jassal
    Karan Jassal2 giorni 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"

  • twobad
    twobad2 giorni fa

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

  • Miagi Fodder
    Miagi Fodder2 giorni 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

  • Xing Yu
    Xing Yu2 giorni 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!

  • FBI Agent
    FBI Agent2 giorni fa

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

  • Iron work Paul
    Iron work Paul2 giorni fa

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

  • Fuzzy Ankles
    Fuzzy Ankles2 giorni fa

    holy shiet thats beautiful

  • fffrikkie 123
    fffrikkie 1232 giorni fa

    Life is a simulation confirmed

  • Ishita Vyavahare
    Ishita Vyavahare3 giorni fa

    what software is he using?

  • Paolo Scaramuzzino
    Paolo Scaramuzzino3 giorni fa

    how does it apply to the Covid-19 waves?

  • O_0
    O_03 giorni fa

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

  • Brian Kemery
    Brian Kemery3 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.

  • KG Guitar
    KG Guitar3 giorni fa


  • Anthony Tran
    Anthony Tran3 giorni fa

    first 10 seconds and i went dumb

  • Simon Lovelace
    Simon Lovelace3 giorni fa

    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 Barrada3 giorni fa


  • dolf1n1
    dolf1n13 giorni fa

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

  • Rocket Zing
    Rocket Zing3 giorni fa

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

  • ash channan
    ash channan3 giorni fa

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

  • Milkymalk
    Milkymalk3 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?

  • adib z
    adib z3 giorni fa

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

  • XRay Plays
    XRay Plays4 giorni fa


  • Phillip Plyer
    Phillip Plyer4 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!

  • steve
    steve4 giorni fa

    I dont get it U just talk too much

  • Phineas
    Phineas4 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

  • John Worthington
    John Worthington4 giorni fa

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

  • Mensa X
    Mensa X4 giorni fa

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

  • rendzis
    rendzis4 giorni fa

    In what day did god made this?😁

  • mazhar chrome
    mazhar chrome4 giorni fa

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

  • unityelt
    unityelt4 giorni fa

    It's like programming life

  • Slow Motion
    Slow Motion5 giorni fa

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

  • Pula Vijaya
    Pula Vijaya5 giorni fa

    Is world an illusion make a video sir

  • Peacocks & Polar Bears
    Peacocks & Polar Bears5 giorni fa

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

  • korteks visceralzen
    korteks visceralzen5 giorni fa

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

  • Betsy Larcom
    Betsy Larcom5 giorni fa

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

  • Bare Bear Hands
    Bare Bear Hands5 giorni fa

    Chaos is natural order.

  • Eric Swenson
    Eric Swenson5 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...

  • Rohit Neemwal
    Rohit Neemwal5 giorni fa

    so random numbers are not so random.

  • Rohit Neemwal
    Rohit Neemwal5 giorni fa

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

  • Rohit Neemwal
    Rohit Neemwal5 giorni fa

    so , we are in simulation .

  • Steven
    Steven5 giorni fa

    The mandelbrook fractal looks lika a turtle:)

  • Vinyas Singh
    Vinyas Singh5 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.

  • Xer R
    Xer R5 giorni fa

    You should make a podcast

  • O Templo de Shaka
    O Templo de Shaka5 giorni fa

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

  • Hein Htet
    Hein Htet5 giorni fa

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

  • Martin Da Monarch
    Martin Da Monarch6 giorni fa

    That kinda looks like how a tree 🌳 grows lol cool

  • delt
    delt6 giorni fa

    Seeeeriously fascinating!!!! 😲😲

  • Ethan Evans
    Ethan Evans6 giorni fa

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

  • CallMeBeep
    CallMeBeep6 giorni fa

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

  • Kelvin Francisco
    Kelvin Francisco6 giorni fa

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

  • Zee Y
    Zee Y6 giorni fa

    Now someone still thinks we live in a simulation?

  • Rohan Dongre
    Rohan Dongre6 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.

  • Segala Nicolas

    Segala Nicolas

    6 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.

  • bereket taffesse
    bereket taffesse6 giorni fa

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

  • Pillow
    Pillow6 giorni fa

    so this is how the multiverse go

  • Pillow


    6 giorni fa


  • Segala Nicolas

    Segala Nicolas

    6 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

  • Michael
    Michael6 giorni fa

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

  • God
    God6 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

  • Fractal
    Fractal6 giorni fa

    13:44 oh god it's the zodiac killer

  • Mugtba Moamed
    Mugtba Moamed6 giorni fa

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

  • Random X
    Random X7 giorni fa

    How do you guys come up with such things.

  • Connor Eyer
    Connor Eyer7 giorni fa

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

  • troeteimarsch
    troeteimarsch7 giorni fa

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

  • Chris Incorvati
    Chris Incorvati7 giorni fa

    Order begets chaos, chaos begets order.

  • Zygorg
    Zygorg7 giorni fa

    You adquired a new tittle: Chaotic (Neutral)

  • Carlos Handojo Santosa
    Carlos Handojo Santosa7 giorni fa

    You just blew my mind.

  • Holyfield Barrett
    Holyfield Barrett7 giorni fa

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

  • GrandAdmiral Zod
    GrandAdmiral Zod7 giorni fa

    The anti-life/death equation?

  • ライアン
    ライアン7 giorni fa

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

  • Segala Nicolas

    Segala Nicolas

    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

  • ライアン


    6 giorni fa

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

  • Релёкс84


    6 giorni fa

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

  • reckless bose
    reckless bose7 giorni fa

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

  • Maeby Moore
    Maeby Moore7 giorni fa

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

  • Beulah West
    Beulah West7 giorni fa

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

  • Brittany Baker
    Brittany Baker7 giorni fa

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

  • RealJustinCase
    RealJustinCase7 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

  • 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 X7 giorni fa

    Chaos is so subjective

  • Shoedi L
    Shoedi L7 giorni fa

    Overpopulation debukned.

  • Segala Nicolas

    Segala Nicolas

    6 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

    USNBRENDON7 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.

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