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

98 849 Weergaven 10 mln.

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. Leandro Placencia
    Leandro Placencia
    7 uur geleden

    19:39 10^10^100 Googolplex

  2. Leandro Placencia
    Leandro Placencia
    7 uur geleden

    10^10^100 Googolplex

  3. Rotciv Inoccic
    Rotciv Inoccic
    10 uur geleden

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

  4. Netemp Witemp
    Netemp Witemp
    13 uur geleden

    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

  5. deck monkey
    deck monkey
    19 uur geleden

    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".

  6. Jason Brunhard
    Jason Brunhard
    23 uur geleden

    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.

  7. The Rodestarr
    The Rodestarr
    23 uur geleden

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

  8. ich
    Dag geleden

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

  9. Naz Fride
    Naz Fride
    Dag geleden

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

  10. Subhadeep Das
    Subhadeep Das
    Dag geleden

    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

  11. Simranjeet Singh
    Simranjeet Singh
    Dag geleden

    Your calculation is wrong

  12. Ssenyonjo Jireh
    Ssenyonjo Jireh
    Dag geleden

    Can I still answer the question

  13. Ssenyonjo Jireh
    Ssenyonjo Jireh
    Dag geleden

    Can I still answer the question

  14. Chindulur Sai Kaushik
    Chindulur Sai Kaushik
    Dag geleden

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

  15. Scripted Frames
    Scripted Frames
    Dag geleden

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

  16. Scripted Frames
    Scripted Frames
    Dag geleden


  17. Scripted Frames
    Scripted Frames
    Dag geleden

    This video proved me that I am a dumb

  18. Scripted Frames
    Scripted Frames
    Dag geleden

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

  19. Leo Verran
    Leo Verran
    Dag geleden

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

  20. Karan Jassal
    Karan Jassal
    Dag geleden

    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"

  21. twobad
    Dag geleden

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

  22. Miagi Fodder
    Miagi Fodder
    Dag geleden

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

  23. Xing Yu
    Xing Yu
    Dag geleden

    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!

  24. FBI Agent
    FBI Agent
    Dag geleden

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

  25. Iron work Paul
    Iron work Paul
    Dag geleden

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

  26. Fuzzy Ankles
    Fuzzy Ankles
    2 dagen geleden

    holy shiet thats beautiful

  27. fffrikkie 123
    fffrikkie 123
    2 dagen geleden

    Life is a simulation confirmed

  28. Ishita Vyavahare
    Ishita Vyavahare
    2 dagen geleden

    what software is he using?

  29. Paolo Scaramuzzino
    Paolo Scaramuzzino
    2 dagen geleden

    how does it apply to the Covid-19 waves?

  30. O_0
    2 dagen geleden

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

  31. Brian Kemery
    Brian Kemery
    2 dagen geleden

    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.

  32. KG Guitar
    KG Guitar
    2 dagen geleden


  33. Anthony Tran
    Anthony Tran
    2 dagen geleden

    first 10 seconds and i went dumb

  34. Simon Lovelace
    Simon Lovelace
    2 dagen geleden

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

  35. Juan David Barrada
    Juan David Barrada
    2 dagen geleden


  36. dolf1n1
    3 dagen geleden

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

  37. Rocket Zing
    Rocket Zing
    3 dagen geleden

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

  38. ash channan
    ash channan
    3 dagen geleden

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

  39. Milkymalk
    3 dagen geleden

    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?

  40. adib z
    adib z
    3 dagen geleden

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

  41. XRay Plays
    XRay Plays
    3 dagen geleden


  42. Phillip Plyer
    Phillip Plyer
    3 dagen geleden

    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!

  43. steve
    3 dagen geleden

    I dont get it U just talk too much

  44. Phineas
    3 dagen geleden

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

  45. John Worthington
    John Worthington
    3 dagen geleden

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

  46. Mensa X
    Mensa X
    4 dagen geleden

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

  47. rendzis
    4 dagen geleden

    In what day did god made this?😁

  48. mazhar chrome
    mazhar chrome
    4 dagen geleden

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

  49. unityelt
    4 dagen geleden

    It's like programming life

  50. Slow Motion
    Slow Motion
    4 dagen geleden

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

  51. Pula Vijaya
    Pula Vijaya
    4 dagen geleden

    Is world an illusion make a video sir

  52. Peacocks & Polar Bears
    Peacocks & Polar Bears
    4 dagen geleden

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

  53. korteks visceralzen
    korteks visceralzen
    4 dagen geleden

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

  54. Betsy Larcom
    Betsy Larcom
    4 dagen geleden

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

  55. Bare Bear Hands
    Bare Bear Hands
    4 dagen geleden

    Chaos is natural order.

  56. Eric Swenson
    Eric Swenson
    5 dagen geleden

    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...

  57. Rohit Neemwal
    Rohit Neemwal
    5 dagen geleden

    so random numbers are not so random.

  58. Rohit Neemwal
    Rohit Neemwal
    5 dagen geleden

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

  59. Rohit Neemwal
    Rohit Neemwal
    5 dagen geleden

    so , we are in simulation .

  60. Steven
    5 dagen geleden

    The mandelbrook fractal looks lika a turtle:)

  61. Vinyas Singh
    Vinyas Singh
    5 dagen geleden

    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.

  62. Xer R
    Xer R
    5 dagen geleden

    You should make a podcast

  63. O Templo de Shaka
    O Templo de Shaka
    5 dagen geleden

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

  64. Hein Htet
    Hein Htet
    5 dagen geleden

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

  65. Martin Da Monarch
    Martin Da Monarch
    5 dagen geleden

    That kinda looks like how a tree 🌳 grows lol cool

  66. delt
    5 dagen geleden

    Seeeeriously fascinating!!!! 😲😲

  67. Ethan Evans
    Ethan Evans
    5 dagen geleden

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

  68. CallMeBeep
    5 dagen geleden

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

  69. Kelvin Francisco
    Kelvin Francisco
    5 dagen geleden

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

  70. Zee Y
    Zee Y
    6 dagen geleden

    Now someone still thinks we live in a simulation?

  71. Rohan Dongre
    Rohan Dongre
    6 dagen geleden

    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.

    1. Segala Nicolas
      Segala Nicolas
      6 dagen geleden

      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.

  72. bereket taffesse
    bereket taffesse
    6 dagen geleden

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

  73. Pillow
    6 dagen geleden

    so this is how the multiverse go

    1. Pillow
      5 dagen geleden


    2. Segala Nicolas
      Segala Nicolas
      6 dagen geleden

      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

  74. Michael
    6 dagen geleden

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

  75. God
    6 dagen geleden

    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

  76. Fractal
    6 dagen geleden

    13:44 oh god it's the zodiac killer

  77. Mugtba Moamed
    Mugtba Moamed
    6 dagen geleden

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

  78. Random X
    Random X
    6 dagen geleden

    How do you guys come up with such things.

  79. Connor Eyer
    Connor Eyer
    6 dagen geleden

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

  80. troeteimarsch
    6 dagen geleden

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

  81. Chris Incorvati
    Chris Incorvati
    6 dagen geleden

    Order begets chaos, chaos begets order.

  82. Zygorg
    6 dagen geleden

    You adquired a new tittle: Chaotic (Neutral)

  83. Carlos Handojo Santosa
    Carlos Handojo Santosa
    6 dagen geleden

    You just blew my mind.

  84. Holyfield Barrett
    Holyfield Barrett
    6 dagen geleden

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

  85. GrandAdmiral Zod
    GrandAdmiral Zod
    6 dagen geleden

    The anti-life/death equation?

  86. ライアン
    6 dagen geleden

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

    1. Segala Nicolas
      Segala Nicolas
      6 dagen geleden

      @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

    2. ライアン
      6 dagen geleden

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

    3. Релёкс84
      6 dagen geleden

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

  87. reckless bose
    reckless bose
    6 dagen geleden

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

  88. Maeby Moore
    Maeby Moore
    6 dagen geleden

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

  89. Beulah West
    Beulah West
    6 dagen geleden

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

  90. Brittany Baker
    Brittany Baker
    6 dagen geleden

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

  91. RealJustinCase
    6 dagen geleden

    I'm going to be so honest here. What the hell did I just watch and how do I feel even less about myself

  92. 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
    6 dagen geleden

    Chaos is so subjective

  93. Shoedi L
    Shoedi L
    6 dagen geleden

    Overpopulation debukned.

    1. Segala Nicolas
      Segala Nicolas
      6 dagen geleden

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

    7 dagen geleden

    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.

  95. Manuel Sánchez de Iñigo
    Manuel Sánchez de Iñigo
    7 dagen geleden

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

  96. Scispace Facts
    Scispace Facts
    7 dagen geleden


  97. Abdullah Bham
    Abdullah Bham
    7 dagen geleden

    Design God

  98. John Dalzell
    John Dalzell
    7 dagen geleden

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

  99. tylor anderson
    tylor anderson
    7 dagen geleden

    When I say chaos, you say fogginbom, chaos

  100. Mad Maniac
    Mad Maniac
    7 dagen geleden

    I didnt understand anything