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"

  • ich

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

  • Naz Fride
    Naz Fride

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

  • Subhadeep Das
    Subhadeep Das

    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 Singh

    Your calculation is wrong

  • Ssenyonjo Jireh
    Ssenyonjo Jireh

    Can I still answer the question

  • Ssenyonjo Jireh
    Ssenyonjo Jireh

    Can I still answer the question

  • Chindulur Sai Kaushik
    Chindulur Sai Kaushik

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

  • Scripted Frames
    Scripted Frames

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

  • Scripted Frames
    Scripted Frames


  • Scripted Frames
    Scripted Frames

    This video proved me that I am a dumb

  • Scripted Frames
    Scripted Frames

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

  • Leo Verran
    Leo Verran

    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 Jassal

    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

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

  • Miagi Fodder
    Miagi Fodder

    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 Yu

    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 Agent

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

  • Iron work Paul
    Iron work Paul

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

  • Fuzzy Ankles
    Fuzzy Ankles

    holy shiet thats beautiful

  • fffrikkie 123
    fffrikkie 123

    Life is a simulation confirmed

  • Ishita Vyavahare
    Ishita Vyavahare

    what software is he using?

  • Paolo Scaramuzzino
    Paolo Scaramuzzino

    how does it apply to the Covid-19 waves?

  • O_0

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

  • Brian Kemery
    Brian Kemery

    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 Guitar


  • Anthony Tran
    Anthony Tran

    first 10 seconds and i went dumb

  • Simon Lovelace
    Simon Lovelace

    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 Barrada


  • dolf1n1

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

  • Rocket Zing
    Rocket Zing

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

  • ash channan
    ash channan

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

  • Milkymalk

    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 z

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

  • XRay Plays
    XRay Plays


  • Phillip Plyer
    Phillip Plyer

    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

    I dont get it U just talk too much

  • Phineas

    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 Worthington

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

  • Mensa X
    Mensa X

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

  • rendzis

    In what day did god made this?😁

  • mazhar chrome
    mazhar chrome

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

  • unityelt

    It's like programming life

  • Slow Motion
    Slow Motion

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

  • Pula Vijaya
    Pula Vijaya

    Is world an illusion make a video sir

  • Peacocks & Polar Bears
    Peacocks & Polar Bears

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

  • korteks visceralzen
    korteks visceralzen

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

  • Betsy Larcom
    Betsy Larcom

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

  • Bare Bear Hands
    Bare Bear Hands

    Chaos is natural order.

  • Eric Swenson
    Eric Swenson

    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 Neemwal

    so random numbers are not so random.

  • Rohit Neemwal
    Rohit Neemwal

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

  • Rohit Neemwal
    Rohit Neemwal

    so , we are in simulation .

  • Steven

    The mandelbrook fractal looks lika a turtle:)

  • Vinyas Singh
    Vinyas Singh

    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 R

    You should make a podcast

  • O Templo de Shaka
    O Templo de Shaka

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

  • Hein Htet
    Hein Htet

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

  • Martin Da Monarch
    Martin Da Monarch

    That kinda looks like how a tree 🌳 grows lol cool

  • delt

    Seeeeriously fascinating!!!! 😲😲

  • Ethan Evans
    Ethan Evans

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

  • CallMeBeep

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

  • Kelvin Francisco
    Kelvin Francisco

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

  • Zee Y
    Zee Y

    Now someone still thinks we live in a simulation?

  • Rohan Dongre
    Rohan Dongre

    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

      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 taffesse

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

  • Pillow

    so this is how the multiverse go

    • Pillow


    • Segala Nicolas
      Segala Nicolas

      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

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

  • God

    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

    13:44 oh god it's the zodiac killer

  • Mugtba Moamed
    Mugtba Moamed

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

  • Random X
    Random X

    How do you guys come up with such things.

  • Connor Eyer
    Connor Eyer

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

  • troeteimarsch

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

  • Chris Incorvati
    Chris Incorvati

    Order begets chaos, chaos begets order.

  • Zygorg

    You adquired a new tittle: Chaotic (Neutral)

  • Carlos Handojo Santosa
    Carlos Handojo Santosa

    You just blew my mind.

  • Holyfield Barrett
    Holyfield Barrett

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

  • GrandAdmiral Zod
    GrandAdmiral Zod

    The anti-life/death equation?

  • ライアン

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

    • Segala Nicolas
      Segala Nicolas

      @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

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

    • Релёкс84

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

  • reckless bose
    reckless bose

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

  • Maeby Moore
    Maeby Moore

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

  • Beulah West
    Beulah West

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

  • Brittany Baker
    Brittany Baker

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

  • RealJustinCase

    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 X

    Chaos is so subjective

  • Shoedi L
    Shoedi L

    Overpopulation debukned.

    • Segala Nicolas
      Segala Nicolas

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


    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 Iñigo

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

  • Scispace Facts
    Scispace Facts


  • Abdullah Bham
    Abdullah Bham

    Design God

  • John Dalzell
    John Dalzell

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

  • tylor anderson
    tylor anderson

    When I say chaos, you say fogginbom, chaos

  • Mad Maniac
    Mad Maniac

    I didnt understand anything

  • mark ryan Jervoso
    mark ryan Jervoso

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

  • naysay02

    These numbers are living things. This is extraordinary.

  • Olli Bruno
    Olli Bruno

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

  • Kryptonicul

    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 PUBGM

    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

      Yes! But maths can take us there 🙂

  • Leif Schmit-Kallas
    Leif Schmit-Kallas

    The correct name for a population of rabbits is Fluffle.

  • Basil Al-jaml
    Basil Al-jaml

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