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

เผยแพร่เมื่อ 29 ม.ค. 2020
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.
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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"


  • what is the name of the plotting tool at 3:07 ?

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  • 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😜

  • 4.669 hehehe funny number.

  • 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.

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

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

  • Amazing science communicator. Heads of to you sir!

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

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

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  • 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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  • Nice video

  • 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

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

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

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

  • you lost me at “This one simple eQUaTioN”

  • should i understand this video?! :)

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

  • 0:58 the video ended for me

  • 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

  • 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.

    • 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.

    • 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

  • 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

  • If my girlfriend was an equation.

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

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  • Wut?

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  • Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).

  • 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

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

  • Cool hyper dimensional Pringle you got there

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

  • 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.

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  • i can assure you that not even half of the viewers understand enything 😂

  • Nyc Trick: 2:14

  • Thanks man

  • 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).

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

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  • I watched this high and now I'm certain we live in a simulation.

  • 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.

  • *y = mx + b has entered the chat*

  • 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.

  • i guess life really is entropy. time for another bong rip brb

  • 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).

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

    • 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

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

  • I read about this in Nonlinear Dynamics

  • The answer to the question is CERN.

  • i. understand

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  • OMG...the camera man or woman is a vampire or vampiress

  • this guy is the madest scientist ever

  • i can`t stop thinking of epicnpcman`s fisherman.... (help)

  • So many equations and models that repeat throughout life. Almost like it was programmed that way.

  • 11:40 heartbeat pulse????


  • “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.

  • good video

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

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

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

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  • 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

  • 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...

  • I understand nothing 😥

  • We got graphs within graphs within graphs.

  • can this equation be used to predict earthquakes?

  • apply this in music & cymatics and see what you get

  • 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

  • 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

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

  • can this be applied to coronavirus?

  • genius! thank you!

  • can i represent this equation with geogebra?

  • How relevant is the R number today... in a pandemic!!

  • why did I rewatch this video feeling It has been 5 years since I've seen this

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  • cool vid, bro, but it kinda felt only like an appetizer

  • 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?

  • So pringles. Got it

  • Me: sees the graph My brain: haha pp

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  • How did I get to 52 without hearing about it❗❓❗❓❗🚓🚔👮⚽

  • why dont you use this to find the 0,6 of human population?

  • The most "particularly active group of rabbits" would be at the Playboy mansion!

  • Спасибо за субтитры

  • What did you use to graph the equation?

  • What graphing software is used?

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  • Calls chaos gets constant... Hmmm...