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. Janak Brahmbhatt

    Janak Brahmbhatt

    Πριν 3 ώρες

    Me: understands less than 5% of what he said Also me: life changed

  2. Will Statmen

    Will Statmen

    Πριν 4 ώρες

    I feel what he’s talking about is basically the old Chinese philosophical idea of ying&yang

  3. Udgin Fufsa

    Udgin Fufsa

    Πριν 4 ώρες

    It is clear from your story (useful in all respects!), that you have not read the book of the Belarusian physicist Fursa E.Ya. : "The history of the future ...", in 2 volumes, published in Minsk in 2011. (T.1. By the laws of nature. T.2. By the laws of reason). It is also about "tricks of chaos" in the world order. See, for example, vol. 2, pp. 282-284. /See I-net/.There you will find a lot of interesting things that can be useful in your work. Tell about it in your videos.

  4. The SlowMotion

    The SlowMotion

    Πριν 7 ώρες

    3D Mandelbrot, awesome 😎

  5. Pavin Hautavanija

    Pavin Hautavanija

    Πριν 8 ώρες

    As in Quran mentioned وَلَقَدۡ خَلَقۡنَا ٱلۡإِنسَـٰنَ مِن سُلَـٰلَةࣲ مِّن طِینࣲ وَلَقَدۡ خَلَقۡنَا ٱلۡإِنسَٰنَ مِن سُلَٰلَةٖ مِّن طِينٖ ١٢ • Abdul Haleem: We created man from an essence of clay, (12) ثُمَّ جَعَلۡنَـٰهُ نُطۡفَةࣰ فِی قَرَارࣲ مَّكِینࣲ ثُمَّ جَعَلۡنَٰهُ نُطۡفَةٗ فِي قَرَارٖ مَّكِينٖ ١٣ • Abdul Haleem: then We placed him as a drop of fluid in a safe place, (13) 23:12-13 Al-Mu'minun, Ayah 12-13

  6. Nofer Trunions

    Nofer Trunions

    Πριν 8 ώρες

    Growth rate of infection disease, COVIC 19? Unexpected oscillations???

  7. CreativeCraft -

    CreativeCraft -

    Πριν 8 ώρες

    also color blindness will change the way you see the world

  8. OneEye Man

    OneEye Man

    Πριν 8 ώρες

    Could this apply to economics?

  9. Shota Toriumi

    Shota Toriumi

    Πριν 9 ώρες

    I am so grateful to be alive today. My girlfriend saved my life last night. This is a selfie I took in the emergency room after having a severe allergic reaction to almonds. I went into anaphylaxis, meaning my face, my lips, my eyes, my tongue, and my throat all started swelling up rapidly, making it almost impossible for me to breathe. I also had a rash all over my entire body, and I was extremely red. Staying alive had never felt more difficult. At one point, my nasal passage was completely blocked, and it was getting more and more difficult to breathe. They shot me up with Benadryl, steroids, they gave me a breathing tube, and even other stuff that I can’t even remember, and it caused all of the swelling and the rash to go away. Because this was a severe allergic reaction, I need to continue taking steroids and Benadryl for the next week, because it is possible that the allergic reactions could come back at any point over the next week. The steroids and Benadryl make me feel like a zombie, and I really want to take care of my health, so this will be my main focus over the next week. I want to thank my amazing girlfriend, who made the decision to take me to the emergency room the second I started feeling itchy. I was hesitant about going, because I didn’t even want to believe this was actually happening. If it weren’t for my girlfriend driving me to the emergency room only minutes after eating the almonds, there is a good chance that I wouldn’t have made it according to the doctor. This has been without a doubt the hardest few days of my life, but I also look at them as the most important few days of my life. These moments have reminded me about what’s really important in life, and it has made me so grateful to even be here on this earth. I will be prioritizing my health over the next week, and I’ll post updates about how I feel. Thank you all for being patient during these difficult times. This week has been NUTS (too soon for jokes? 😅)

  10. EyyMunchian


    Πριν 13 ώρες

    Unreal Engine but cosmic used by God lol

  11. Roman Frey

    Roman Frey

    Πριν 14 ώρες

    i watched the whole thing sure that i would get something out of it...wrong

  12. Luschient 007

    Luschient 007

    Πριν 15 ώρες

    One word What

  13. K C

    K C

    Πριν 15 ώρες

    "This equation will change how you see the world" - it Robert May, or it Robert May not.

  14. Konstantinos


    Πριν 17 ώρες

    So, Are we living in a simulation ?

  15. pool Boy

    pool Boy

    Πριν 20 ώρες

    Bifurcation or Dichotomy?

    • Jeffrey.Dahmer.Dinner.Survivor


      Πριν 20 ώρες


  16. Franz Liszt

    Franz Liszt

    Πριν 22 ώρες

    Chaos is a ladder

  17. István Deme

    István Deme

    Πριν 23 ώρες

    I'd really like to read some meaningful comments but all the top comments are just bs. :( Comments should be categorized and let users switch between them.

  18. Anustup Biswas

    Anustup Biswas

    Πριν ημέρα

    Which graphing software is used here?

  19. Alexander H.

    Alexander H.

    Πριν ημέρα

    I'm mostly impressed by his epic house.

  20. WhiteChocolateMocha


    Πριν ημέρα

    As the world population grows, there'll statistically be at least one idiot who will eat an infected bat

  21. David Steadman

    David Steadman

    Πριν ημέρα

    I been watching C-19 since the end of Jan, and the first thing I locked on to was the ratio smh. I find this science intriguing. I am also curious about the fluid cylinders, and heat part of the video. It looks very similar to harmonics, and I'm thinking that as it gets hotter, its activity rate increases. I wish there was an extended, more in depth video covering that aspect.

  22. ssunkite1


    Πριν ημέρα

    What language is he speaking?

  23. Bon Summers

    Bon Summers

    Πριν ημέρα

    Pronouncing the 'T' of Mandelbrot sounds so crass. Come on, pronounce in French or Polish, it's silent.

  24. Robert E, Andrews

    Robert E, Andrews

    Πριν ημέρα

    Survival is in question, when we don't apply what is known in the social sciences. The reptilian portion of our brain, coupled with arms proliferation, spells doom. Why elect leaders who flunked science and ethics? We do so at our increasing peril.

  25. K J

    K J

    Πριν ημέρα

    If chaos was predictable and more so, controllable, who would benefit?

  26. J Flat Hat

    J Flat Hat

    Πριν ημέρα

    Beautiful description Of reality. To find out causality you need to use actual science dude.

  27. Farweasel


    Πριν ημέρα

    How cool is that ...................... the equation (1-x) kills rabbits. Who said maths is useless.

  28. Jordan Wyatt

    Jordan Wyatt

    Πριν ημέρα

    This is literally the equation to why we have periods in our life where everything seems to be going smoothly and then chaotic. Anytime there's a consonant ratio between the values, you experience harmony; vice versa, anytime there's a dissonant ratio between the values, we experience chaos. There's also proof of this in the way we hear music, interestingly. If I were to record myself hitting a drum (tuned to any frequency) and then play it rapidly, I can make a constant stream of notes. If I speed it up fast enough, you begin to hear it sound like a vibration. Faster than that and it creates a note based on how fast or slow it's played. Is this feeling freaky yet? Imagine now adding another drum playing alongside the preexisting drum with another constant stream of notes. In the space it takes the 1st drummer to play 2 notes, the other is playing 3 giving us a 3:2 ratio. Speed these up together and we begin to hear an interval of a perfect 5th between the two notes. There is no limit to # of ratios (hemiolas). Once you add another player, there are now 3 notes heard and harmony is formed. So mathematically, percussionists make the world go 'round.

  29. Onder Ozenc

    Onder Ozenc

    Πριν ημέρα

    I met the simpler version of this subject when I was preparing for my exam in optics : non-linear response of the dialectrics to the intensity of the applied sinusoidal signal.

  30. Parsley Tooth

    Parsley Tooth

    Πριν ημέρα

    Does anybody know what software is being used to represent the values here? I'm looking for something to visualise data (that isn't R).

  31. Randall Flagg

    Randall Flagg

    Πριν ημέρα

    This explains why I could stare for hours into a strobe light whilst tripping lysergic, & change everything with the strobe pulse rate. I noticed that I was affixing to the "every other strobe" flash. It's interesting to discover "constants of nature" in math when I could barely pass Algebra. Instead of doing a 12 step formula & showing my work, I solved the problems in my head with 3-4 steps. Mandelbrot is fascinating, as we are all never ending energy, able to delve into oneself, just don't go too deep, or at least, leave a mental rope to climb back out, lest you get lost like Syd Barrett. Fun Facts: Spinning an empty aluminum can fast enough magically creates an electromagnetic field. Unwinding Scotch Tape in a vacuum chamber creates X-Rays. Human hearts & brains emit radiation that surrounds the body. Twins brains can sometimes tap into one another like Wi-Fi...or so I'm told

    • erikpoephoofd


      Πριν ημέρα

      "Human hearts & brains emit radiation that surrounds the body. " Do you mean something else than infra red radiation? "Twins brains can sometimes tap into one another like Wi-Fi...or so I'm told" I'm pretty sure this is not possible. Just because twins have the same DNA does not mean brains can magically do telepathy. If that was possible, evolution would have created the means for humans to talk telepathically, since this would be a huge benefit for survival chances.

  32. Guilherme Torquato

    Guilherme Torquato

    Πριν ημέρα

    Incredible! A “must see again” video



    Πριν ημέρα

    i read about this in a famous book (chaos by john gleick) and this vid was posted the very next day

  34. Hassanajdari


    Πριν 2 ημέρες

    Dude I thought I was good in science lmao

  35. Soul Trap

    Soul Trap

    Πριν 2 ημέρες

    Fantastic graphics. Beautiful mathematics:)

  36. Blade Runner

    Blade Runner

    Πριν 2 ημέρες

    I lived 53 years without hearing about the Feigenbaum Constant, even though I enjoy math. Now - do I have to expect to hear about it in decreasing time intervals who comply to the factor 4.669 ?

  37. Ameer Hamza

    Ameer Hamza

    Πριν 2 ημέρες

    Imma pretend that i understood that...

  38. Groth Holmes

    Groth Holmes

    Πριν 2 ημέρες

    3:27 AM Me: hunched over the sink My mom: why are you STILL up? Me: SHHH! I’VE ALMOST GOT A CHAOTIC SYSTEM!

  39. gregoryg72


    Πριν 2 ημέρες

    @Veristasium In the beginning of the video you say that if the population of rabbits doubled every year then the population of rabbits would grow exponentially forever. That's a geometric progression, not an exponential progression.

  40. Dazza dizzy

    Dazza dizzy

    Πριν 2 ημέρες

    yeah I got lost around the 1:00minute mark

  41. Hank Jay

    Hank Jay

    Πριν 2 ημέρες

    Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.

  42. yandere himesama

    yandere himesama

    Πριν 3 ημέρες

    This is pure statistics

  43. abijithr quora

    abijithr quora

    Πριν 3 ημέρες

    Mind blowing and.... (i should probably expand my vocabulary)

  44. Martin Blank

    Martin Blank

    Πριν 3 ημέρες

    Lost me within a minute - define x, dude! If x is anything more than 1 in that first equation then it oscillates. I think he meant that x < 1, but why? I already understand chaos theory but I gave up in under 5 mins because he never defined his terms. Usually a great show but he slipped up here.

  45. Lee's Uploads

    Lee's Uploads

    Πριν 3 ημέρες

    Its the golden ratio. The algo to the universe

  46. TBNRRests


    Πριν 3 ημέρες

    matches the reverse psychology pattern in order of sequence (,) is the answer correct? yes - truth, no - lie, yes - either truth or telling truth because you think I know you think I'm lying, no - either lie or telling lie because you think that I'm lying, so you think I believe it is yes and so on

  47. Томас Кинг

    Томас Кинг

    Πριν 3 ημέρες

    Я могу поговорить с русскими?

  48. Joe D

    Joe D

    Πριν 3 ημέρες

    Kangaroos have bifurcated penises, HyperKangaroos have mandelbrot penises.... is my take-away.

  49. Mark Liebergall

    Mark Liebergall

    Πριν 3 ημέρες

    Thanks for an exceptional presentation. You seem to have a doppelganger. The actor who plays the veterinarian on Schitt's Creek is your double, especially in later seasons when he has similar facial hair as you. He looks, sounds and moves just like you. WOW.

  50. Apollyon


    Πριν 3 ημέρες


  51. Balazs Kovacs

    Balazs Kovacs

    Πριν 4 ημέρες

    Hi there! What is the app that you used to create that simulation? Many thanks!

  52. Arnob Das

    Arnob Das

    Πριν 4 ημέρες

    Thank you, I'll make more chaos in school from now

  53. Zonlander


    Πριν 4 ημέρες

    Yeah, looks like a Tadpole.

  54. Gdjnx Gdk

    Gdjnx Gdk

    Πριν 4 ημέρες

    Who has cooked using Duck fat ? Just spent the day grilling Duck breast starting off on the cast iron griddle in duck fat for some tanning lotion before hitting the grill. #bbqpitboys

  55. JustMoseyinAround


    Πριν 4 ημέρες

    Thanks for the James Gleick recommendation

  56. Bruno Oliveira

    Bruno Oliveira

    Πριν 4 ημέρες

    Da vinci code guys... just read it



    Πριν 4 ημέρες

    عمري 18 عام ... حسنن أضن أن ٢٩.٩% من المعلومات لم يمكنني إستعابها ولكن شكرا

  58. WielkiTana


    Πριν 4 ημέρες

    That's why Europe is going to extinct, most countries have reached levels very close to 1 fertility rate below which is only extinction

  59. stanisław b.

    stanisław b.

    Πριν 4 ημέρες

    I once saw in my mathbook somethink about fractals but we sciped it :(

  60. Moritz Hofmann

    Moritz Hofmann

    Πριν 4 ημέρες

    @you - How about the filaments. The Superclusters of the galaxy distribution - it's not uniformly, but could it be the chaotic part ? - I'm not a mathematican neither a physicist, but what about doing calculations WITH that number on at least 3 axes ? Wouldn't "look" the "chaotic" parts like the filaments and voids? (not thinking of perculiar speeds etc)

  61. Frederick Drenning

    Frederick Drenning

    Πριν 4 ημέρες

    Incredibly interesting thank you so much!

  62. Kevin Valadez

    Kevin Valadez

    Πριν 4 ημέρες

    happy birthday Benoit Mandelbrot!

  63. Venkat


    Πριν 4 ημέρες

    Today is his birthday :)

  64. Saurav Mukherjee

    Saurav Mukherjee

    Πριν 4 ημέρες

    I am 10 and i accualy understand this also I am a nerd

  65. sjallard


    Πριν 5 ημέρες

    Does this equation decribe fast toasts?

  66. Gary Z

    Gary Z

    Πριν 5 ημέρες

    why is it "chaotic" and not cause and effect?

  67. Romualdo Barajas

    Romualdo Barajas

    Πριν 5 ημέρες


  68. Tim Tam1123

    Tim Tam1123

    Πριν 5 ημέρες

    What is n?

  69. Wintana Welday

    Wintana Welday

    Πριν 5 ημέρες

    I think there’s a mistake @0:45 : 2x is not an exponential function but a linear therefore the population doesn’t double every year rather grow in a constant rate... I’m sorry if I was wrong but it confused me... if x doubled each year the equation should have been 2^x

    • Wintana Welday

      Wintana Welday

      Πριν 4 ημέρες

      @George Brantley I thank you

    • George Brantley

      George Brantley

      Πριν 4 ημέρες

      The equation is recursive, not absolute. The video says x[n+1] = 2*x[n], which does in fact double each year. You might be thinking of the equation y = 2*x, which is linear. But y = 2*x is very different from x[n+1] = 2*x[n].

  70. Chaosgremlin


    Πριν 5 ημέρες

    You look tired dude.

  71. Jerbi B

    Jerbi B

    Πριν 5 ημέρες


  72. Tomi Antenna

    Tomi Antenna

    Πριν 5 ημέρες

    You reaaally wanted to show off your fancy home there, didn't ya.

  73. Hoonin’ n Poonin’

    Hoonin’ n Poonin’

    Πριν 5 ημέρες

    Is it just me or does the song playing at 15:00 remind you of halo. Not the melody/chords just the percussion a little bit.

  74. Manuel Aravena

    Manuel Aravena

    Πριν 5 ημέρες

    0:51 number of rabbits does not grow exponentially it is linear

  75. Sonnier Goo

    Sonnier Goo

    Πριν 6 ημέρες

    “Perfectly balanced, as all things should be”.-Thanos

  76. Andres Samuel Abreu Prado

    Andres Samuel Abreu Prado

    Πριν 6 ημέρες

    Poor rabbit

  77. Diego del busto

    Diego del busto

    Πριν 6 ημέρες

    What did he use to graph this

  78. Rory Smith

    Rory Smith

    Πριν 6 ημέρες

    They should also teach quantum field theory so kids would understand particles don't really exist. Life changing stuff.

  79. Douglas Balduino

    Douglas Balduino

    Πριν 6 ημέρες

    When he twisted that bitch I lost it

  80. Nathan Benatti Silva

    Nathan Benatti Silva

    Πριν 6 ημέρες

    what program do you used to do Mandelbrot set like this ? i want to mess with it a bit

  81. Daniel Skilton

    Daniel Skilton

    Πριν 6 ημέρες

    All this makes perfect sense, but only to him.

  82. Daniel Skilton

    Daniel Skilton

    Πριν 6 ημέρες

    He's just putting he's phone number up there

  83. QuantumCHRIST 0

    QuantumCHRIST 0

    Πριν 6 ημέρες fibonachi sequence fit in?

  84. Dennis Hartigan

    Dennis Hartigan

    Πριν 6 ημέρες

    A brain skeleton

  85. avtar singh

    avtar singh

    Πριν 6 ημέρες

    I understanded every single thing and i m just 16

  86. avtar singh

    avtar singh

    Πριν 6 ημέρες


  87. Pranav


    Πριν 6 ημέρες

    what if we make 11 the new ten

  88. Blarg


    Πριν 6 ημέρες

    how to open google calculator how to open google calculator

  89. tim johnson

    tim johnson

    Πριν 7 ημέρες

    changing the initial population as done in video has me wondering how this can be applied to algorithms that trade stocks and mean reversion, for instance he says we can ignore the initial population, so how would a computer trade and forecast based on that ?

  90. Чудик


    Πριν 7 ημέρες

    Математика хорошо, но в природе происходят процессы не зависимо от придуманных людьми формул. Если говорить о кроликах, то их популяция будет зависеть от погодных условий и количества хищников. И это всё взаимосвязано: засуха уменьшает количество кроликов и автоматически уменьшает количество хищников. И обратный процесс при обильном росте растительности. И процесс увеличения не будет бесконечным. Он достигнет некоего уровня и будет колебаться около него. А если ещё учесть наличие болезней, то уровень будет ещё ниже. А если взять для примера Австралию, где у кроликов почти нет врагов, то их популяция может достигнуть огромных размеров. Вот поэтому приходиться людям бороться с кроликами вместо природных хищников.

  91. William Ives

    William Ives

    Πριν 7 ημέρες

    The periodical dripping does not increase to chaotic, The increase of unknown variables results a lack of information to create a sound equation. Kaos is provably Impossible by this statement:- Reality, follows Rules... Kaos, is the absence of Rules...!

    • Kit Mooney

      Kit Mooney

      Πριν 4 ημέρες

      Chaos as in "Chaos Theory." Chaotic Systems are deterministic. They are only apparently random.,fractals%2C%20and%20self%2Dorganization.



    Πριν 7 ημέρες

    That Equation does not take into account one thing, Humans and guns.

  93. Skyler Knight

    Skyler Knight

    Πριν 7 ημέρες

    I don’t understand what he’s talking about but I desperately want to

    • vescent


      Πριν 5 ημέρες


  94. Occam's Razor

    Occam's Razor

    Πριν 7 ημέρες

    To define God, all one needs to do is describe the reason for the existence of the Mandlebrot set. For all intents and purposes, God is the Mandlebrot set. It's not a living, conscious being. Simply the fact that sometimes, math aligns in a beautiful pattern, and we're all merely a single data point in that set.

  95. you tube

    you tube

    Πριν 7 ημέρες

    Hi, very interesting video! I watched it twice and then I did some math: A particular population is stable (no oscillation) if R*(1-X) = 1. That means you can calculate the needed X to a given R or vice versa with R = 1/(1-X) or X = 1-(1/R). With that pair of numbers you can get a stable population in an unstable area! In your video you mentioned the starting value doesn't matter, the population will reach its given convergence. You demonstrated that fact with the small slider. But: if you move the slider in a way that it hits this one special number (every given R has a partner X where the population becomes stable), then there is the magic and the starting population leads to stability :)

  96. Trekzuko. iwnl

    Trekzuko. iwnl

    Πριν 7 ημέρες


  97. Hamza Victor

    Hamza Victor

    Πριν 7 ημέρες

    How come I didn't hear about this Feigenbaum constant till I'm 33 years? Wow, this video really explained so much. Seeing the Mandelbrodt Fractals from the Bifurcation perspective is really beautiful. The Mandelbrodt fractals are just a simple 2D representation of the Bifurcation concept.

  98. Pure Pressure

    Pure Pressure

    Πριν 7 ημέρες

    Does this correlate at all with prime number distribution

  99. walid stonebreaker

    walid stonebreaker

    Πριν 7 ημέρες


  100. Austin Eli

    Austin Eli

    Πριν 7 ημέρες

    all of the dislikes are the people who dont know who mandelbrot is yet