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"


  • IvĂĄn
    Ivån2 orë më parë

    Now my mind has fallen into a fascinating chaos

  • Tom Russell
    Tom Russell10 orë më parë

    kudos to you and your curiosity

  • Nenad ИХ XC Shuput
    Nenad ИХ XC Shuput10 orë më parë

    Not even this guy knows exactly what he is saying đŸ€ŁđŸ€Ł

  • charlie3k
    charlie3k12 orë më parë

    i watched this high and i feel like my mind entered a new dimension

  • Fairyplay
    Fairyplay15 orë më parë

    This video has become really relevant with covid lol (at least the R part at the beginning)

  • Ray Skudlark
    Ray Skudlark16 orë më parë

    I find it odd that ever since I can remember I have been trying to figure out this pattern 2 4 8 16 32 64 128 256 512 1024 as high as I could reach. And now to be learning all of this much later in life it really makes you wonder!? Thanks for the content man I have been watching and learning with you for I think what 8 or 9 years now and you have been a constant reminder I'm not the only one kicking these ideas around. I have been poor my whole life and never had a chance to apply my brain the way I wanted to. And being in low income areas it hard to have these kind of conversations with anyone. So thanks for doing this man really you and Micheal Vsauce I only hope the best to you guys.

  • C Harris
    C Harris18 orë më parë

    Finally the math that I already forgotten since high school looks interesting

  • Mathew Jackson
    Mathew Jackson19 orë më parë

    So I'm on the toilet, when you push more, more flow will come out but not all at once and evenly, then eventually your muscles can't take the stress and less flow will come out. Then your muscles recharge and you go at it again maybe harder or softer... Equation works in everything

  • Omid Khoshravan Azar
    Omid Khoshravan Azar19 orë më parë

    I don’t know why but this whole video felt like an unskippable ad

  • Maulau Craw
    Maulau Craw21 orë më parë

    Reverse this connection(selectablly applythe inverse function) and you have a fantastic modulus you can use to chart on an overlay the explicit proficiency to levels of implicit practicality of the teacher-student relevancy thereof.

  • bumfartbumfart2
    bumfartbumfart2Ditë më parë

    i hope you have won some awards for your films

  • The Zach
    The ZachDitë më parë

    I think this graph also represents the evolution of human intelligence. 👉Think about this: The same brain that created the theory of evolution had to first evolve itself.

  • Mahir Balushi
    Mahir BalushiDitë më parë


  • Daniel Edwards
    Daniel EdwardsDitë më parë


  • Brian Kleinschmidt
    Brian KleinschmidtDitë më parë

    I love watching Mandelbrot renderings. That graphic just blew my mind. Beauty has a measure - math itself.

  • Lion Deluxe
    Lion DeluxeDitë më parë

    This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.

  • mt2mgames
    mt2mgamesDitë më parë

    this video is horrible. You keep conflating "the population" with "the percentage of the maximum possible population"

  • Marre
    MarreDitë më parë

    16:55 excited about chaos *HERESY* call the inquisiton

  • Ruderaksha Karwa
    Ruderaksha KarwaDitë më parë

    Showerthought: every civilization follows the same pattern , I would say we crossed the curve somewhere between 70s-90s

  • Drawing Masterclass
    Drawing MasterclassDitë më parë

    So much complexity and we still don't believe there is God.

  • Shawn Bechard
    Shawn BechardDitë më parë

    I keep hearing predictions that human populations will decline, but I don't think it is going to be anywhere near as soon as they think. We have been rising since the Black Plague supposedly.

  • Nad G
    Nad GDitë më parë

    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 Kabibble2 ditë më parë

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

  • UhOhMeMeBiggestBoy
    UhOhMeMeBiggestBoy2 ditë më parë

    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 Galleta2 ditë më parë

    I hurt myself in confusion. :(

  • Dodd Rougeau
    Dodd Rougeau2 ditë më parë

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

  • R Doody
    R Doody2 ditë më parë

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

  • Leandro Placencia
    Leandro Placencia2 ditë më parë

    19:39 10^10^100 Googolplex

  • Leandro Placencia
    Leandro Placencia2 ditë më parë

    10^10^100 Googolplex

  • Rotciv Inoccic
    Rotciv Inoccic2 ditë më parë

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

  • Netemp Witemp
    Netemp Witemp3 ditë më parë

    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 monkey3 ditë më parë

    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 Brunhard3 ditë më parë

    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 Rodestarr3 ditë më parë

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

  • ich
    ich3 ditë më parë

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

  • Naz Fride
    Naz Fride3 ditë më parë

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

  • Subhadeep Das
    Subhadeep Das3 ditë më parë

    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

  • oh no

    oh no

    17 orë më parë

    this has nothing to do with vegetarians??

  • Simranjeet Singh
    Simranjeet Singh3 ditë më parë

    Your calculation is wrong

  • Ssenyonjo Jireh
    Ssenyonjo Jireh3 ditë më parë

    Can I still answer the question

  • Ssenyonjo Jireh
    Ssenyonjo Jireh3 ditë më parë

    Can I still answer the question

  • Chindulur Sai Kaushik
    Chindulur Sai Kaushik3 ditë më parë

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

  • Scripted Frames
    Scripted Frames4 ditë më parë

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

  • Scripted Frames
    Scripted Frames4 ditë më parë


  • Scripted Frames
    Scripted Frames4 ditë më parë

    This video proved me that I am a dumb

  • Scripted Frames
    Scripted Frames4 ditë më parë

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

  • Leo Verran
    Leo Verran4 ditë më parë

    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 Jassal4 ditë më parë

    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
    twobad4 ditë më parë

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

  • Miagi Fodder
    Miagi Fodder4 ditë më parë

    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 Yu4 ditë më parë

    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 Agent4 ditë më parë

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

  • Iron work Paul
    Iron work Paul4 ditë më parë

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

  • Fuzzy Ankles
    Fuzzy Ankles4 ditë më parë

    holy shiet thats beautiful

  • fffrikkie 123
    fffrikkie 1234 ditë më parë

    Life is a simulation confirmed

  • Ishita Vyavahare
    Ishita Vyavahare5 ditë më parë

    what software is he using?

  • Paolo Scaramuzzino
    Paolo Scaramuzzino5 ditë më parë

    how does it apply to the Covid-19 waves?

  • O_0
    O_05 ditë më parë

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

  • Brian Kemery
    Brian Kemery5 ditë më parë

    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 Guitar5 ditë më parë


  • Anthony Tran
    Anthony Tran5 ditë më parë

    first 10 seconds and i went dumb

  • Simon Lovelace
    Simon Lovelace5 ditë më parë

    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 Barrada5 ditë më parë


  • dolf1n1
    dolf1n15 ditë më parë

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

  • Rocket Zing
    Rocket Zing5 ditë më parë

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

  • ash channan
    ash channan5 ditë më parë

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

  • Milkymalk
    Milkymalk5 ditë më parë

    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 z5 ditë më parë

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

  • XRay Plays
    XRay Plays5 ditë më parë


  • Phillip Plyer
    Phillip Plyer6 ditë më parë

    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
    steve6 ditë më parë

    I dont get it U just talk too much

  • Phineas
    Phineas6 ditë më parë

    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 Worthington6 ditë më parë

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

  • Mensa X
    Mensa X6 ditë më parë

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

  • rendzis
    rendzis6 ditë më parë

    In what day did god made this?😁

  • mazhar chrome
    mazhar chrome6 ditë më parë

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

  • unityelt
    unityelt6 ditë më parë

    It's like programming life

  • Slow Motion
    Slow Motion7 ditë më parë

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

  • Pula Vijaya
    Pula Vijaya7 ditë më parë

    Is world an illusion make a video sir

  • Peacocks & Polar Bears
    Peacocks & Polar Bears7 ditë më parë

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

  • korteks visceralzen
    korteks visceralzen7 ditë më parë

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

  • Betsy Larcom
    Betsy Larcom7 ditë më parë

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

  • Bare Bear Hands
    Bare Bear Hands7 ditë më parë

    Chaos is natural order.

  • Eric Swenson
    Eric Swenson7 ditë më parë

    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 Neemwal7 ditë më parë

    so random numbers are not so random.

  • Rohit Neemwal
    Rohit Neemwal7 ditë më parë

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

  • Rohit Neemwal
    Rohit Neemwal7 ditë më parë

    so , we are in simulation .

  • Steven
    Steven7 ditë më parë

    The mandelbrook fractal looks lika a turtle:)

  • Vinyas Singh
    Vinyas Singh7 ditë më parë

    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 R7 ditë më parë

    You should make a podcast

  • O Templo de Shaka
    O Templo de Shaka7 ditë më parë

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

  • Hein Htet
    Hein Htet7 ditë më parë

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

  • Martin Da Monarch
    Martin Da Monarch7 ditë më parë

    That kinda looks like how a tree 🌳 grows lol cool

  • delt
    delt8 ditë më parë

    Seeeeriously fascinating!!!! đŸ˜ČđŸ˜Č

  • Ethan Evans
    Ethan Evans8 ditë më parë

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

  • CallMeBeep
    CallMeBeep8 ditë më parë

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

  • Kelvin Francisco
    Kelvin Francisco8 ditë më parë

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

  • Zee Y
    Zee Y8 ditë më parë

    Now someone still thinks we live in a simulation?

  • Rohan Dongre
    Rohan Dongre8 ditë më parë

    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

    8 ditë më parë

    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 taffesse8 ditë më parë

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

  • Pillow
    Pillow8 ditë më parë

    so this is how the multiverse go

  • Pillow


    8 ditë më parë


  • Segala Nicolas

    Segala Nicolas

    8 ditë më parë

    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

Faqja Tjeter