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

9 925 478 Megtekintés

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"

  • Design God

    Abdullah BhamAbdullah Bham9 perccel
  • I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.

    John DalzellJohn Dalzell38 perccel
  • When I say chaos, you say fogginbom, chaos

    tylor andersontylor anderson49 perccel
  • I didnt understand anything

    Mad ManiacMad Maniac2 órája
  • When that needle happens on the chaotic part..then there will Thanos comes..

    mark ryan Jervosomark ryan Jervoso2 órája
  • These numbers are living things. This is extraordinary.

    naysay02naysay025 órája
  • The real Question ist: how to apply this to the Stock market?

    Olli BrunoOlli Bruno5 órája
  • Am i the only whos life is actually being changed by this stuff?? Its the only thing i can think about like all different types of infinity. Usually when im doing any task in my daily life ill spring into action or rather my brain does and starts think about how something can be infinite or is it infinite or can it be connected to infinity. The worst case of this is so simple but its almost hindering me, almost every two minutes in math class my brain just spits out "theres infinite amount of numbers in between ___ and ___" or "if you keep using that equation it will go for infinity" or even sometimes i try to make an infinite something like writing how many zeros after 0.0 before running out of room and having to put a 1 at the end. Tomorrow or maybe monday in class im going to use the mandelbrot equation to try and draw a small taste of a man made mandbrot set. Although I know I will be restricted by how much room I have on the page or whatever im drawing on. I almost feel restricted by reality or something. Considering everyone has ever told me that infinity is impossible to comprehend I seriously want to comprehend it or hear it or see it or just do anything that i could actually interact my sense with infinity. Of coure this will never happen considering there is no real infinity or at least not that we can "comprehend"

    KryptoniculKryptonicul5 órája
  • The only reason we call it chaos is because in order to see the chaos as a constant you would need to be in a higher dimension.

    Manners PUBGMManners PUBGM7 órája
  • The correct name for a population of rabbits is Fluffle.

    Leif Schmit-KallasLeif Schmit-Kallas9 órája
  • what is the name of the plotting tool at 3:07 ?

    Basil Al-jamlBasil Al-jaml13 órája
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    pudpud kirkpatrickpudpud kirkpatrick14 órája
  • click on the video Panik : Oh god , i am so dumb, i will not be able to change the view on the world Pause the video and.. click on comment section Kalm: yhh at least....i know i am not aloooone😜

    Snow Ko OoSnow Ko Oo18 órája
  • 4.669 hehehe funny number.

    CerberusCerberus23 órája
  • I haven't thought about Mandelbrot sets since I was 20 and they delivered the coolest graphics on the new VGA-card. The Mandelbrot set already has something organic about it, but this takes it to a new level: the actual underpinnings of the universe. The clickbait-like title was true. Blew my mind.

    Jonas FermeforsJonas FermeforsNapja
  • This video makes me feel genius even though I don't understand any of it.

    Enzhou ZutzutEnzhou ZutzutNapja
  • Am i the only one who sees the graph similar to the Darwin´s tree of life?

    Axel From Group TherapyAxel From Group TherapyNapja
  • Amazing science communicator. Heads of to you sir!

    Shark FalconShark FalconNapja
  • Wish I had seen this video when I was taking Dynamical Systems in college :/

    Jack BarbeyJack BarbeyNapja
  • Bout to watch this fired af Hope it kick starts my physics degree

    O RiddleO RiddleNapja
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    Brian SegoviaBrian SegoviaNapja
  • So... we don't really need to worry about humans overpopulating the planet?

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  • I gave up 1:35 in 🥲

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    Esther CookEsther CookNapja
  • Nice video

    Tommaso D'EsteTommaso D'Este2 napja
  • You may know a lot about Math, Physics etc... But this video doesn't really "change how people see the world". Not for the vast majority anyway. To achieve that, it needs to be simplified and shown. Sadly, none of these happened. Good luck with your future videos

    Kouzoulos14Kouzoulos142 napja
    • @Vad3r from ur answer it seems tht u are too dumb to even understand what i m saying... me, the "dumb". have a great day/night all of u

      Kouzoulos14Kouzoulos148 órája
    • so basically you mean you were too dumb to understand it and therefore it's bad

      Vad3rVad3r13 órája
  • So what you're saying is releasing an endemic pandemic wasn't worth it?

    DigotaDigota2 napja
  • Chaos is my all-time favorite book. Next would be "Genius"

    Orion NashOrion Nash2 napja
  • you lost me at “This one simple eQUaTioN”

    Greggy DyGreggy Dy2 napja
  • should i understand this video?! :)

    LcxLcx2 napja
  • Thats crazy, I know the answer is cern but this video was a year

    Jason SpadesJason Spades2 napja
  • 0:58 the video ended for me

    Camilo DelgadoCamilo Delgado2 napja
  • Dude one flaw though. at r>=4 the equation will break and return negative values(eventually)[well it may show very quickly or a lot later]. Why did you not show that. I mean if complex numbers are real then it returning negatives values might also mean something intutive about our world. Ok genuine question though. When it returns negative values is it still cyclic or it completely breaks and goes near infinity. Never mind. Opened calculator it goes near negative infinity. Though ok is there a way to make it repeat while it is still negative. Like maybe it has some repetition in negative numbers too. What if we use complex numbers in the equations

    pravin raopravin rao2 napja
  • Ok I am in highschool but i am pretty sure calling it fundamental constant of nature feels wrong. I think we can make equations and systems which take there previous state as input for there current state (and do anything) and get different constant. Just intuition i don't know anything. but it feels like you can relate previous thing to next thing and get constant. no wait though. Why would it be a constant then. If you are randomly relating stuff why should it be a constant.

    pravin raopravin rao2 napja
    • Iterate it the way we have. So like you mean if we take previous value as input for the next value. So if single hump. Then no matter what we do. Ok what if i define a completely weird non algebraic function . Like without squares or multiplication . Will that work too. Ok though sin(x) can actually be written as a algebraic polynomial cause of Taylor series. So well anything can be written as that if we use Taylor series. Maybe something with polynomials. What if we use something which can't be approximated using Taylor series. WHAT IF WE USE A DERIVATIVE WHICH DON'T HAVE A ANTI DERIVATIVE. TO MAKE A FUNCTION(by manually computing that function on computer . ) LIKE WE CAN'T FIND A NEAT LITTLE FORMULA FOR IT IF THERE IS NO ANTI DERIVATIVE. WILL THE CONSTANT STILL EMERGE IF THERE IS A SINGLE HUMP. though what does similar mean does it just mean that new value is function of previous value.

      pravin raopravin rao2 napja
    • 15:30 huh that's pretty weird. Then it might actually be constant of nature or something. something is converging i think somewhere . Like something averages out somehow

      pravin raopravin rao2 napja
  • Ok just watch 3lbue1browns video on complex numbers and you would understand it. Z (n+1) =Z (n)^2 +C Squaring complex is just rotating it by doubling it's angle and it's magnitude is squared. the C we add act's like subtraction probably from the total magnitude of complex number . So it just keeps rotating and getting subtracted perodically

    pravin raopravin rao2 napja
  • If my girlfriend was an equation.

    JusemanJuseman2 napja
  • "I am so excited by chaos!" 2020: "Oh really..?"

    Dreaming OneDreaming One2 napja
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    Jose MedinaJose Medina2 napja
  • Wut?

    Error 10110Error 101102 napja
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    Jasper EcbJasper Ecb2 napja
  • Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).

    FollowIfYouSwallowFollowIfYouSwallow2 napja
  • chaos knight in dota has varying critacal dmg (from 1.2-2.8) and lifesteal (20-120%) but i also am 23 and never heard of the particular constant 4.669

    Stefan PapdiStefan Papdi2 napja
  • someone can tell me what is the program at minute 2:47? the program of graphs

    Derek Da LuzDerek Da Luz2 napja
  • Cool hyper dimensional Pringle you got there

    Diego MoDiego Mo2 napja
  • Good work! I Think you should have brought up more examples. Trees, rivers, brocooli and our lugns:)

    Dan ielDan iel2 napja
  • Can you explain what is happening at 0:16 in your video? It's right after the equation appears and before you start speaking. Am I crazy, or does the environment suddenly look different and then suddenly normal.

    Ed GarzaroEd Garzaro2 napja
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    mario yumario yu2 napja
  • i can assure you that not even half of the viewers understand enything 😂

    Ismail MoufidIsmail Moufid2 napja
  • Nyc Trick: 2:14

    AayushAayush2 napja
  • Thanks man

    Toon Vd WielenToon Vd Wielen2 napja
  • Fantastic video. The section where the parabola is hand-drawn and the numbers punched into a calculator could have been substituted with a graphic showing how the height of the parabola is determined by r, and, how successive values are obtained by using the last y as the next x (reflected on the line y=x).

    DevilCouldCareDevilCouldCare2 napja
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    Donnie BakerDonnie Baker2 napja
  • Ok.....explain why when you multiply two negative get a positive number....? That one does my head in.

    Andrew ThomasAndrew Thomas3 napja
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    Willy MadisonWilly Madison3 napja
  • I watched this high and now I'm certain we live in a simulation.

    Flip MoreFlip More3 napja
  • when we give full confidence and faith that we already knew these things as a baby knows Calculus or trig as the baby begins to walk. trust your abilities and doubt not.

    Alberto HidalgoAlberto Hidalgo3 napja
  • *y = mx + b has entered the chat*

    Beavalian _osuBeavalian _osu3 napja
  • I played with this formula in a spreadsheet, and observed that with a carefully picked initial population of nx = (r-1)/r I could maintain balance with enormous grow rates.

    Tom Georg EriksenTom Georg Eriksen3 napja
  • i guess life really is entropy. time for another bong rip brb

    Samuel MasonSamuel Mason3 napja
  • Sorry I left. it started I could follow . Then , it took a Ph D. to follow . So.... Try the K.I.S.S. method ( Keep it simple stupid).

    NicolasNicolas3 napja
  • Funny, the whole time I was watching this, I wonder why I never saw this in school

    James iPadJames iPad3 napja
    • I think because this is a part of chaos. We student are not capable of handling chaos

  • But how does it descend into chaos if the pattern happens every time at a specific value

    EvatanEvatan3 napja
  • I stopped understanding when he started with the numbers... looks cool though

    Harryboi 64Harryboi 643 napja
    • Same lol

      Kylie NelsonKylie Nelson3 napja
  • I read about this in Nonlinear Dynamics

    AkileshAkilesh3 napja
  • The answer to the question is CERN.

    Steven EatonSteven Eaton3 napja
  • i. understand

    giagia4 napja
  • This is what feels like after death

    Aditya KishoreAditya Kishore4 napja

    Oruga MargoOruga Margo4 napja
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    Elnora WinnElnora Winn4 napja
  • OMG...the camera man or woman is a vampire or vampiress

    Charge0CompleteCharge0Complete4 napja
  • this guy is the madest scientist ever

    みみきP officialみみきP official4 napja
  • i can`t stop thinking of epicnpcman`s fisherman.... (help)

    65 - Sebastian Fretes65 - Sebastian Fretes4 napja
  • So many equations and models that repeat throughout life. Almost like it was programmed that way.

    A LA L4 napja
  • 11:40 heartbeat pulse????

    Fernando MtlvoFernando Mtlvo4 napja

    RobRob4 napja
  • “Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. ” ― Nikola Tesla.

    MarkoMarko4 napja
  • good video

    DomiNickelDomiNickel4 napja
  • There should be a completely different field called the Mathematics of Nature. It's fascinating

    Nebuchadnezzar QuellcrisNebuchadnezzar Quellcris4 napja
    • Mathematics itself is already nature. Why is this so hard for people to grasp? Is this forbidden knowledge? Lol

      NativeNative2 napja
    • “Applied” usually implies that, For future reference.

      Pirkulator _Pirkulator _3 napja
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    Jeremy DelgadoJeremy Delgado4 napja
  • Look at Nassim Haramein's physics and his holofractalographic principle and you'll see that this can be applied on the universal scale as well as quantum scale

    Zte PhoneZte Phone5 napja
  • My teacher in High School used to tell us that Every second thing in this Universe works on a mathematical pattern that is yet to be run down by us ... It all boils down to the fact that the people who actually worked on finding such patterns are the names that you may recall once the words Physics or Mathematics hits your mind (Say Einstein or Newton)... Nice Video Derek! ... The first time it really blew my mind but the second time, I was able to really relate it...

    Lavnish KumarLavnish Kumar5 napja
  • I understand nothing 😥

    Govind Anand PathakGovind Anand Pathak5 napja
  • We got graphs within graphs within graphs.

    Colm Óg GildernewColm Óg Gildernew5 napja
  • can this equation be used to predict earthquakes?

    Damon Von BohnDamon Von Bohn5 napja
  • apply this in music & cymatics and see what you get

    DarkSession van ArtDarkSession van Art5 napja
  • I'm at 14:34 now. You put a lot of effort. It's making me worked out. How is it that you're not famous of anything is what I'd like to say but dude you have a good idea about the thing you're doing

    Sammy MoktanSammy Moktan5 napja
  • Dude I'm at 17:39 you're really smart and are using good tricks but why do you not have a good fanbase? I could do something about it

    Sammy MoktanSammy Moktan5 napja
  • Why are you using sounds and music to create emotions? That's not very fun ya

    Sammy MoktanSammy Moktan5 napja
  • genius! thank you!

    3263927 contra3263927 contra5 napja
  • can i represent this equation with geogebra?

    Vitaly GrashchenkovVitaly Grashchenkov5 napja
  • How relevant is the R number today... in a pandemic!!

    Abdullah Ali AkhtarAbdullah Ali Akhtar5 napja
  • why did I rewatch this video feeling It has been 5 years since I've seen this

    Hemanth ReddyHemanth Reddy5 napja
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    Kyra VijsmaKyra Vijsma6 napja
  • cool vid, bro, but it kinda felt only like an appetizer

    Dr. GreenThumbsDr. GreenThumbs6 napja
  • Here's a mad thought - the universe has gone through several different periods of expansion and quantum events are probabilistic. Could that related to chaos and the Feigenbaum constant?

    GrizabeeblesGrizabeebles6 napja
  • So pringles. Got it

    Lil WolfyLil Wolfy6 napja
  • Me: sees the graph My brain: haha pp

    Caleb LarsonCaleb Larson6 napja
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