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"


  1. Fairyplay


    Саат мурун

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

  2. Ray Skudlark

    Ray Skudlark

    3 саат мурун

    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.

  3. C Harris

    C Harris

    5 саат мурун

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

  4. Mathew Jackson

    Mathew Jackson

    5 саат мурун

    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

  5. Omid Khoshravan Azar

    Omid Khoshravan Azar

    6 саат мурун

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

  6. Maulau Craw

    Maulau Craw

    8 саат мурун

    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.

  7. bumfartbumfart2


    12 саат мурун

    i hope you have won some awards for your films

  8. The Zach

    The Zach

    15 саат мурун

    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.

  9. Mahir Balushi

    Mahir Balushi

    18 саат мурун


  10. Daniel Edwards

    Daniel Edwards

    19 саат мурун


  11. Brian Kleinschmidt

    Brian Kleinschmidt

    19 саат мурун

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

  12. Lion Deluxe

    Lion Deluxe

    22 саат мурун

    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.

  13. mt2mgames


    23 саат мурун

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

  14. Marre


    Күн мурун

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

  15. Ruderaksha Karwa

    Ruderaksha Karwa

    Күн мурун

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

  16. Drawing Masterclass

    Drawing Masterclass

    Күн мурун

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

  17. Shawn Bechard

    Shawn Bechard

    Күн мурун

    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.

  18. Nad G

    Nad G

    Күн мурун

    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

  19. Ish Kabibble

    Ish Kabibble

    Күн мурун

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

  20. UhOhMeMeBiggestBoy


    Күн мурун

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

  21. Xandea Galleta

    Xandea Galleta

    Күн мурун

    I hurt myself in confusion. :(

  22. Dodd Rougeau

    Dodd Rougeau

    Күн мурун

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

  23. R Doody

    R Doody

    Күн мурун

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

  24. Leandro Placencia

    Leandro Placencia

    2 күн мурун

    19:39 10^10^100 Googolplex

  25. Leandro Placencia

    Leandro Placencia

    2 күн мурун

    10^10^100 Googolplex

  26. Rotciv Inoccic

    Rotciv Inoccic

    2 күн мурун

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

  27. Netemp Witemp

    Netemp Witemp

    2 күн мурун

    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

  28. deck monkey

    deck monkey

    2 күн мурун

    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".

  29. Jason Brunhard

    Jason Brunhard

    2 күн мурун

    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.

  30. The Rodestarr

    The Rodestarr

    2 күн мурун

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

  31. ich


    2 күн мурун

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

  32. Naz Fride

    Naz Fride

    3 күн мурун

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

  33. Subhadeep Das

    Subhadeep Das

    3 күн мурун

    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

      4 саат мурун

      this has nothing to do with vegetarians??

  34. Simranjeet Singh

    Simranjeet Singh

    3 күн мурун

    Your calculation is wrong

  35. Ssenyonjo Jireh

    Ssenyonjo Jireh

    3 күн мурун

    Can I still answer the question

  36. Ssenyonjo Jireh

    Ssenyonjo Jireh

    3 күн мурун

    Can I still answer the question

  37. Chindulur Sai Kaushik

    Chindulur Sai Kaushik

    3 күн мурун

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

  38. Scripted Frames

    Scripted Frames

    3 күн мурун

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

  39. Scripted Frames

    Scripted Frames

    3 күн мурун


  40. Scripted Frames

    Scripted Frames

    3 күн мурун

    This video proved me that I am a dumb

  41. Scripted Frames

    Scripted Frames

    3 күн мурун

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

  42. Leo Verran

    Leo Verran

    3 күн мурун

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

  43. Karan Jassal

    Karan Jassal

    3 күн мурун

    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"

  44. twobad


    3 күн мурун

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

  45. Miagi Fodder

    Miagi Fodder

    3 күн мурун

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

  46. Xing Yu

    Xing Yu

    3 күн мурун

    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!

  47. FBI Agent

    FBI Agent

    3 күн мурун

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

  48. Iron work Paul

    Iron work Paul

    3 күн мурун

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

  49. Fuzzy Ankles

    Fuzzy Ankles

    3 күн мурун

    holy shiet thats beautiful

  50. fffrikkie 123

    fffrikkie 123

    4 күн мурун

    Life is a simulation confirmed

  51. Ishita Vyavahare

    Ishita Vyavahare

    4 күн мурун

    what software is he using?

  52. Paolo Scaramuzzino

    Paolo Scaramuzzino

    4 күн мурун

    how does it apply to the Covid-19 waves?

  53. O_0


    4 күн мурун

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

  54. Brian Kemery

    Brian Kemery

    4 күн мурун

    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.

  55. KG Guitar

    KG Guitar

    4 күн мурун


  56. Anthony Tran

    Anthony Tran

    4 күн мурун

    first 10 seconds and i went dumb

  57. Simon Lovelace

    Simon Lovelace

    4 күн мурун

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

  58. Juan David Barrada

    Juan David Barrada

    4 күн мурун


  59. dolf1n1


    5 күн мурун

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

  60. Rocket Zing

    Rocket Zing

    5 күн мурун

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

  61. ash channan

    ash channan

    5 күн мурун

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

  62. Milkymalk


    5 күн мурун

    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?

  63. adib z

    adib z

    5 күн мурун

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

  64. XRay Plays

    XRay Plays

    5 күн мурун


  65. Phillip Plyer

    Phillip Plyer

    5 күн мурун

    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!

  66. steve


    5 күн мурун

    I dont get it U just talk too much

  67. Phineas


    5 күн мурун

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

  68. John Worthington

    John Worthington

    5 күн мурун

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

  69. Mensa X

    Mensa X

    6 күн мурун

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

  70. rendzis


    6 күн мурун

    In what day did god made this?😁

  71. mazhar chrome

    mazhar chrome

    6 күн мурун

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

  72. unityelt


    6 күн мурун

    It's like programming life

  73. Slow Motion

    Slow Motion

    6 күн мурун

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

  74. Pula Vijaya

    Pula Vijaya

    6 күн мурун

    Is world an illusion make a video sir

  75. Peacocks & Polar Bears

    Peacocks & Polar Bears

    6 күн мурун

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

  76. korteks visceralzen

    korteks visceralzen

    6 күн мурун

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

  77. Betsy Larcom

    Betsy Larcom

    6 күн мурун

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

  78. Bare Bear Hands

    Bare Bear Hands

    6 күн мурун

    Chaos is natural order.

  79. Eric Swenson

    Eric Swenson

    7 күн мурун

    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...

  80. Rohit Neemwal

    Rohit Neemwal

    7 күн мурун

    so random numbers are not so random.

  81. Rohit Neemwal

    Rohit Neemwal

    7 күн мурун

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

  82. Rohit Neemwal

    Rohit Neemwal

    7 күн мурун

    so , we are in simulation .

  83. Steven


    7 күн мурун

    The mandelbrook fractal looks lika a turtle:)

  84. Vinyas Singh

    Vinyas Singh

    7 күн мурун

    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.

  85. Xer R

    Xer R

    7 күн мурун

    You should make a podcast

  86. O Templo de Shaka

    O Templo de Shaka

    7 күн мурун

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

  87. Hein Htet

    Hein Htet

    7 күн мурун

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

  88. Martin Da Monarch

    Martin Da Monarch

    7 күн мурун

    That kinda looks like how a tree 🌳 grows lol cool

  89. delt


    7 күн мурун

    Seeeeriously fascinating!!!! 😲😲

  90. Ethan Evans

    Ethan Evans

    7 күн мурун

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

  91. CallMeBeep


    7 күн мурун

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

  92. Kelvin Francisco

    Kelvin Francisco

    7 күн мурун

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

  93. Zee Y

    Zee Y

    8 күн мурун

    Now someone still thinks we live in a simulation?

  94. Rohan Dongre

    Rohan Dongre

    8 күн мурун

    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

      7 күн мурун

      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.

  95. bereket taffesse

    bereket taffesse

    8 күн мурун

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

  96. Pillow


    8 күн мурун

    so this is how the multiverse go

    • Pillow


      7 күн мурун


    • Segala Nicolas

      Segala Nicolas

      7 күн мурун

      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

  97. Michael


    8 күн мурун

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

  98. God


    8 күн мурун

    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

  99. Fractal


    8 күн мурун

    13:44 oh god it's the zodiac killer

  100. Mugtba Moamed

    Mugtba Moamed

    8 күн мурун

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