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

99 183 zhlédnutí 10M

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. Jesus Reynoso
    Jesus Reynoso
    Před 4 hodinami

    Why if you have a bunch a gay rabbits?

  2. Man of Morbihan
    Man of Morbihan
    Před 4 hodinami

    I don't understand what he is saying but it sounds very interesting....

  3. James Paddock
    James Paddock
    Před 12 hodinami

    0:00 *eating rabbit stew on a fractal*

  4. Jeff M
    Jeff M
    Před 22 hodinami

    Universal constants are defined in the simulation parameters.

  5. Eric Newsom
    Eric Newsom
    Před dnem

    This explains mosquitoes on the Texas gulf coast.

  6. Cian Foley
    Cian Foley
    Před dnem

    Amazing videos.

  7. Multi Da
    Multi Da
    Před dnem

    Still want to return to monkey?

  8. Sharim Almaas
    Sharim Almaas
    Před dnem

    Can anyone please tell me which app he is using to plot those beautiful graphs??🥺😭

  9. iamdope
    Před dnem

    Which software he used to illustrate graph? Any idea?

  10. FractAlkemist
    Před dnem

    Interesting how it can "predict" population flux - can this also apply to Covid, the multiple "waves" we get??

  11. Johan Du Toit
    Johan Du Toit
    Před 2 dny

    I need to get in contact with you. Got something pretty amazing to share. Thanks for this video!

  12. Iván
    Před 2 dny

    Now my mind has fallen into a fascinating chaos

  13. Tom Russell
    Tom Russell
    Před 2 dny

    kudos to you and your curiosity

  14. Nenad ИС XC Shuput
    Nenad ИС XC Shuput
    Před 2 dny

    Not even this guy knows exactly what he is saying 🤣🤣

  15. charlie3k
    Před 2 dny

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

  16. Fairyplay
    Před 2 dny

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

  17. Ray Skudlark
    Ray Skudlark
    Před 2 dny

    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.

  18. C Harris
    C Harris
    Před 2 dny

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

  19. Mathew Jackson
    Mathew Jackson
    Před 2 dny

    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

  20. Omid Khoshravan Azar
    Omid Khoshravan Azar
    Před 2 dny

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

  21. Maulau Craw
    Maulau Craw
    Před 3 dny

    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.

  22. bumfartbumfart2
    Před 3 dny

    i hope you have won some awards for your films

  23. The Zach
    The Zach
    Před 3 dny

    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.

  24. Mahir Balushi
    Mahir Balushi
    Před 3 dny


  25. Daniel Edwards
    Daniel Edwards
    Před 3 dny


  26. Brian Kleinschmidt
    Brian Kleinschmidt
    Před 3 dny

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

  27. Lion Deluxe
    Lion Deluxe
    Před 3 dny

    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.

  28. mt2mgames
    Před 3 dny

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

  29. Marre
    Před 3 dny

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

  30. Ruderaksha Karwa
    Ruderaksha Karwa
    Před 3 dny

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

  31. Drawing Masterclass
    Drawing Masterclass
    Před 3 dny

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

  32. Shawn Bechard
    Shawn Bechard
    Před 3 dny

    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.

  33. Nad G
    Nad G
    Před 4 dny

    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

  34. Ish Kabibble
    Ish Kabibble
    Před 4 dny

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

  35. UhOhMeMeBiggestBoy
    Před 4 dny

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

  36. Xandea Galleta
    Xandea Galleta
    Před 4 dny

    I hurt myself in confusion. :(

  37. Dodd Rougeau
    Dodd Rougeau
    Před 4 dny

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

  38. R Doody
    R Doody
    Před 4 dny

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

  39. Leandro Placencia
    Leandro Placencia
    Před 4 dny

    19:39 10^10^100 Googolplex

  40. Leandro Placencia
    Leandro Placencia
    Před 4 dny

    10^10^100 Googolplex

  41. Rotciv Inoccic
    Rotciv Inoccic
    Před 5 dny

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

  42. Netemp Witemp
    Netemp Witemp
    Před 5 dny

    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

  43. deck monkey
    deck monkey
    Před 5 dny

    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".

  44. Jason Brunhard
    Jason Brunhard
    Před 5 dny

    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.

  45. The Rodestarr
    The Rodestarr
    Před 5 dny

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

  46. ich
    Před 5 dny

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

  47. Naz Fride
    Naz Fride
    Před 5 dny

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

  48. Subhadeep Das
    Subhadeep Das
    Před 5 dny

    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

    1. oh no
      oh no
      Před 2 dny

      this has nothing to do with vegetarians??

  49. Simranjeet Singh
    Simranjeet Singh
    Před 5 dny

    Your calculation is wrong

  50. Ssenyonjo Jireh
    Ssenyonjo Jireh
    Před 6 dny

    Can I still answer the question

  51. Ssenyonjo Jireh
    Ssenyonjo Jireh
    Před 6 dny

    Can I still answer the question

  52. Chindulur Sai Kaushik
    Chindulur Sai Kaushik
    Před 6 dny

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

  53. Scripted Frames
    Scripted Frames
    Před 6 dny

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

  54. Scripted Frames
    Scripted Frames
    Před 6 dny


  55. Scripted Frames
    Scripted Frames
    Před 6 dny

    This video proved me that I am a dumb

  56. Scripted Frames
    Scripted Frames
    Před 6 dny

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

  57. Leo Verran
    Leo Verran
    Před 6 dny

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

  58. Karan Jassal
    Karan Jassal
    Před 6 dny

    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"

  59. twobad
    Před 6 dny

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

  60. Miagi Fodder
    Miagi Fodder
    Před 6 dny

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

  61. Xing Yu
    Xing Yu
    Před 6 dny

    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!

  62. FBI Agent
    FBI Agent
    Před 6 dny

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

  63. Iron work Paul
    Iron work Paul
    Před 6 dny

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

  64. Fuzzy Ankles
    Fuzzy Ankles
    Před 6 dny

    holy shiet thats beautiful

  65. fffrikkie 123
    fffrikkie 123
    Před 7 dny

    Life is a simulation confirmed

  66. Ishita Vyavahare
    Ishita Vyavahare
    Před 7 dny

    what software is he using?

  67. Paolo Scaramuzzino
    Paolo Scaramuzzino
    Před 7 dny

    how does it apply to the Covid-19 waves?

  68. O_0
    Před 7 dny

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

  69. Brian Kemery
    Brian Kemery
    Před 7 dny

    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.

  70. KG Guitar
    KG Guitar
    Před 7 dny


  71. Anthony Tran
    Anthony Tran
    Před 7 dny

    first 10 seconds and i went dumb

  72. Simon Lovelace
    Simon Lovelace
    Před 7 dny

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

  73. Juan David Barrada
    Juan David Barrada
    Před 7 dny


  74. dolf1n1
    Před 7 dny

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

  75. Rocket Zing
    Rocket Zing
    Před 7 dny

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

  76. ash channan
    ash channan
    Před 8 dny

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

  77. Milkymalk
    Před 8 dny

    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?

  78. adib z
    adib z
    Před 8 dny

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

  79. XRay Plays
    XRay Plays
    Před 8 dny


  80. Phillip Plyer
    Phillip Plyer
    Před 8 dny

    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!

  81. steve
    Před 8 dny

    I dont get it U just talk too much

  82. Phineas
    Před 8 dny

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

  83. John Worthington
    John Worthington
    Před 8 dny

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

  84. Mensa X
    Mensa X
    Před 8 dny

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

  85. rendzis
    Před 8 dny

    In what day did god made this?😁

  86. mazhar chrome
    mazhar chrome
    Před 8 dny

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

  87. unityelt
    Před 8 dny

    It's like programming life

  88. Slow Motion
    Slow Motion
    Před 9 dny

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

  89. Pula Vijaya
    Pula Vijaya
    Před 9 dny

    Is world an illusion make a video sir

  90. Peacocks & Polar Bears
    Peacocks & Polar Bears
    Před 9 dny

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

  91. korteks visceralzen
    korteks visceralzen
    Před 9 dny

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

  92. Betsy Larcom
    Betsy Larcom
    Před 9 dny

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

  93. Bare Bear Hands
    Bare Bear Hands
    Před 9 dny

    Chaos is natural order.

  94. Eric Swenson
    Eric Swenson
    Před 9 dny

    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...

  95. Rohit Neemwal
    Rohit Neemwal
    Před 9 dny

    so random numbers are not so random.

  96. Rohit Neemwal
    Rohit Neemwal
    Před 9 dny

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

  97. Rohit Neemwal
    Rohit Neemwal
    Před 9 dny

    so , we are in simulation .

  98. Steven
    Před 9 dny

    The mandelbrook fractal looks lika a turtle:)

  99. Vinyas Singh
    Vinyas Singh
    Před 9 dny

    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.

  100. Xer R
    Xer R
    Před 9 dny

    You should make a podcast