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

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Pirms Gada

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"

John Dalzell
John Dalzell Pirms 14 Minūtes
I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.
tylor anderson
tylor anderson Pirms 24 Minūtes
When I say chaos, you say fogginbom, chaos
Mad Maniac
Mad Maniac Pirms Stundas
I didnt understand anything
mark ryan Jervoso
mark ryan Jervoso Pirms Stundas
When that needle happens on the chaotic part..then there will Thanos comes..
naysay02 Pirms 4 Stundām
These numbers are living things. This is extraordinary.
Olli Bruno
Olli Bruno Pirms 4 Stundām
The real Question ist: how to apply this to the Stock market?
Kryptonicul Pirms 5 Stundām
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"
Manners PUBGM
Manners PUBGM Pirms 7 Stundām
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.
Leif Schmit-Kallas
Leif Schmit-Kallas Pirms 8 Stundām
The correct name for a population of rabbits is Fluffle.
Basil Al-jaml
Basil Al-jaml Pirms 12 Stundām
what is the name of the plotting tool at 3:07 ?
pudpud kirkpatrick
pudpud kirkpatrick Pirms 14 Stundām
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Snow Ko Oo
Snow Ko Oo Pirms 17 Stundām
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😜
Cerberus Pirms 23 Stundām
4.669 hehehe funny number.
Jonas Fermefors
Jonas Fermefors Pirms dienas
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.
Enzhou Zutzut
Enzhou Zutzut Pirms dienas
This video makes me feel genius even though I don't understand any of it.
Axel From Group Therapy
Axel From Group Therapy Pirms dienas
Am i the only one who sees the graph similar to the Darwin´s tree of life?
Shark Falcon
Shark Falcon Pirms dienas
Amazing science communicator. Heads of to you sir!
Jack Barbey
Jack Barbey Pirms dienas
Wish I had seen this video when I was taking Dynamical Systems in college :/
O Riddle
O Riddle Pirms dienas
Bout to watch this fired af Hope it kick starts my physics degree
Brian Segovia
Brian Segovia Pirms dienas
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Marc030320 Pirms dienas
So... we don't really need to worry about humans overpopulating the planet?
유유보현 Pirms dienas
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Emily uwu
Emily uwu Pirms dienas
I gave up 1:35 in 🥲
Hola Como Estas
Hola Como Estas Pirms dienas
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Esther Cook
Esther Cook Pirms dienas
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Tommaso D'Este
Tommaso D'Este Pirms dienas
Nice video
Kouzoulos14 Pirms 2 dienām
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
Kouzoulos14 Pirms 8 Stundām
@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
Vad3r Pirms 13 Stundām
so basically you mean you were too dumb to understand it and therefore it's bad
Digota Pirms 2 dienām
So what you're saying is releasing an endemic pandemic wasn't worth it?
Orion Nash
Orion Nash Pirms 2 dienām
Chaos is my all-time favorite book. Next would be "Genius"
Greggy Dy
Greggy Dy Pirms 2 dienām
you lost me at “This one simple eQUaTioN”
Lcx Pirms 2 dienām
should i understand this video?! :)
Jason Spades
Jason Spades Pirms 2 dienām
Thats crazy, I know the answer is cern but this video was a year
Camilo Delgado
Camilo Delgado Pirms 2 dienām
0:58 the video ended for me
pravin rao
pravin rao Pirms 2 dienām
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 rao
pravin rao Pirms 2 dienām
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 rao
pravin rao Pirms 2 dienām
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 rao
pravin rao Pirms 2 dienām
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 rao
pravin rao Pirms 2 dienām
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
Juseman Pirms 2 dienām
If my girlfriend was an equation.
Dreaming One
Dreaming One Pirms 2 dienām
"I am so excited by chaos!" 2020: "Oh really..?"
Jose Medina
Jose Medina Pirms 2 dienām
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Error 10110
Error 10110 Pirms 2 dienām
Jasper Ecb
Jasper Ecb Pirms 2 dienām
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FollowIfYouSwallow Pirms 2 dienām
Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).
Stefan Papdi
Stefan Papdi Pirms 2 dienām
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
Derek Da Luz
Derek Da Luz Pirms 2 dienām
someone can tell me what is the program at minute 2:47? the program of graphs
Diego Mo
Diego Mo Pirms 2 dienām
Cool hyper dimensional Pringle you got there
Dan iel
Dan iel Pirms 2 dienām
Good work! I Think you should have brought up more examples. Trees, rivers, brocooli and our lugns:)
Ed Garzaro
Ed Garzaro Pirms 2 dienām
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.
mario yu
mario yu Pirms 2 dienām
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Ismail Moufid
Ismail Moufid Pirms 2 dienām
i can assure you that not even half of the viewers understand enything 😂
Aayush Pirms 2 dienām
Nyc Trick: 2:14
Toon Vd Wielen
Toon Vd Wielen Pirms 2 dienām
Thanks man
DevilCouldCare Pirms 2 dienām
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).
Donnie Baker
Donnie Baker Pirms 2 dienām
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Andrew Thomas
Andrew Thomas Pirms 2 dienām
Ok.....explain why when you multiply two negative get a positive number....? That one does my head in.
Willy Madison
Willy Madison Pirms 3 dienām
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Flip More
Flip More Pirms 3 dienām
I watched this high and now I'm certain we live in a simulation.
Alberto Hidalgo
Alberto Hidalgo Pirms 3 dienām
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.
Beavalian _osu
Beavalian _osu Pirms 3 dienām
*y = mx + b has entered the chat*
Tom Georg Eriksen
Tom Georg Eriksen Pirms 3 dienām
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.
Samuel Mason
Samuel Mason Pirms 3 dienām
i guess life really is entropy. time for another bong rip brb
Nicolas Pirms 3 dienām
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).
James iPad
James iPad Pirms 3 dienām
Funny, the whole time I was watching this, I wonder why I never saw this in school
Makyr Pirms dienas
I think because this is a part of chaos. We student are not capable of handling chaos
Evatan Pirms 3 dienām
But how does it descend into chaos if the pattern happens every time at a specific value
Harryboi 64
Harryboi 64 Pirms 3 dienām
I stopped understanding when he started with the numbers... looks cool though
Kylie Nelson
Kylie Nelson Pirms 3 dienām
Same lol
Akilesh Pirms 3 dienām
I read about this in Nonlinear Dynamics
Steven Eaton
Steven Eaton Pirms 3 dienām
The answer to the question is CERN.
gia Pirms 4 dienām
i. understand
Aditya Kishore
Aditya Kishore Pirms 4 dienām
This is what feels like after death
Oruga Margo
Oruga Margo Pirms 4 dienām
Elnora Winn
Elnora Winn Pirms 4 dienām
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Charge0Complete Pirms 4 dienām
OMG...the camera man or woman is a vampire or vampiress
みみきP official
みみきP official Pirms 4 dienām
this guy is the madest scientist ever
65 - Sebastian Fretes
65 - Sebastian Fretes Pirms 4 dienām
i can`t stop thinking of epicnpcman`s fisherman.... (help)
A L Pirms 4 dienām
So many equations and models that repeat throughout life. Almost like it was programmed that way.
Fernando Mtlvo
Fernando Mtlvo Pirms 4 dienām
11:40 heartbeat pulse????
Rob Pirms 4 dienām
Marko Pirms 4 dienām
“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.
DomiNickel Pirms 4 dienām
good video
Nebuchadnezzar Quellcris
Nebuchadnezzar Quellcris Pirms 4 dienām
There should be a completely different field called the Mathematics of Nature. It's fascinating
Native Pirms 2 dienām
Mathematics itself is already nature. Why is this so hard for people to grasp? Is this forbidden knowledge? Lol
Pirkulator _
Pirkulator _ Pirms 3 dienām
“Applied” usually implies that, For future reference.
Jeremy Delgado
Jeremy Delgado Pirms 4 dienām
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Zte Phone
Zte Phone Pirms 4 dienām
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
Lavnish Kumar
Lavnish Kumar Pirms 5 dienām
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...
Govind Anand Pathak
Govind Anand Pathak Pirms 5 dienām
I understand nothing 😥
Colm Óg Gildernew
Colm Óg Gildernew Pirms 5 dienām
We got graphs within graphs within graphs.
Damon Von Bohn
Damon Von Bohn Pirms 5 dienām
can this equation be used to predict earthquakes?
DarkSession van Art
DarkSession van Art Pirms 5 dienām
apply this in music & cymatics and see what you get
Sammy Moktan
Sammy Moktan Pirms 5 dienām
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 Moktan
Sammy Moktan Pirms 5 dienām
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 Moktan
Sammy Moktan Pirms 5 dienām
Why are you using sounds and music to create emotions? That's not very fun ya
3263927 contra
3263927 contra Pirms 5 dienām
genius! thank you!
Vitaly Grashchenkov
Vitaly Grashchenkov Pirms 5 dienām
can i represent this equation with geogebra?
Abdullah Ali Akhtar
Abdullah Ali Akhtar Pirms 5 dienām
How relevant is the R number today... in a pandemic!!
Hemanth Reddy
Hemanth Reddy Pirms 5 dienām
why did I rewatch this video feeling It has been 5 years since I've seen this
Kyra Vijsma
Kyra Vijsma Pirms 6 dienām
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Dr. GreenThumbs
Dr. GreenThumbs Pirms 6 dienām
cool vid, bro, but it kinda felt only like an appetizer
Grizabeebles Pirms 6 dienām
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?
Lil Wolfy
Lil Wolfy Pirms 6 dienām
So pringles. Got it
Caleb Larson
Caleb Larson Pirms 6 dienām
Me: sees the graph My brain: haha pp
david rab
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