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

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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: www.fasthosts.co.uk/veritasium Code for interactives is available below...
Animations, coding, interactives in this video by Jonny Hyman 🙌
Try the code yourself: github.com/jonnyhyman/Chaos
James Gleick, Chaos
Steven Strogatz, Nonlinear Dynamics and Chaos
May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976). doi.org/10.1038/261459a0
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). doi.org/10.1038/343653a0
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. dx.doi.org/10.1051/jphyslet:01982004307021100. 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:
epidemicsound.com "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4"
ve42.co/Artlist "Busy World" "Children of Mystery"



29-Yan, 2020



Yuklab olish:


Saqlab olish:

Mening pleylistlarim
Keyinroq ko‘rish
Fikrlar 100   
Rhys dR
Rhys dR 10 daqiqa oldin
my image did not change
TEVA Productions
TEVA Productions Soat oldin
This is an absolutely fantastic video. So clearly explained. Thank you. You accent is crystal!
alystair 5 soat oldin
Kinda looks like a phase diagram ... hmmm
Serpent0fEden 6 soat oldin
"and then there is the issue of the dripping faucet" *Jeff Goldblum intensifies*
Bigfish Tuna
Bigfish Tuna 6 soat oldin
Chul Yeom
Chul Yeom 7 soat oldin
The gaping quail centrally grin because chinese gergely drop given a motionless rooster. pink, pleasant credit
Ian Carr
Ian Carr 9 soat oldin
I did my final year Mathematics degree thesis on this. Oh how i would've loved to of had this video available to me back then !!
Jonathan Webber
Jonathan Webber 9 soat oldin
Me: Just trying to find the equation to plug it into desmos.
Artesion 13 soat oldin
cuz humping can be 69
TRADE CODE 13 soat oldin
Two Rabbits, one male and one female, will make six to nine babies per month.. he said their population would double every year, lol..
J SPEC 14 soat oldin
This is proof that the 2020 election was stolen, thank you for that. Question is how do we convince a potato?
DrNo007 15 soat oldin
i didnt understand literally anything
KoyKoy and Bachuching
KoyKoy and Bachuching 16 soat oldin
nice very informative
jbe tfifty
jbe tfifty 18 soat oldin
Bruh i barely know basic algebra why'd i get recommended this
C 0 R 0 L L A
C 0 R 0 L L A 18 soat oldin
I really didn't understand everything in this video, and plus i'm french so when it becomes a bit more mathematical there are a lot of words i don't get. BUT i'm in first year of engineering school (i'm not really in a engineering school, it's a preparation to the exams to go in these schools i don't know how to tell that in english hehe sorry), and i just began to study differential equations. Maybe i'm wrong but it seems to be related no ? Can someone lights my little brain but what i understood in general of this, is that the chaos comes from very simple and regulary suites of evenements. And differential equations kinda give that notion too that, from barely equals fonctions, you can get infinity of differents behaviors depending on the initial conditions (it's the Cauchy problem). Maybe i'm totaly wrong i don't know but if someone can tell me more about this, i would be happy hehe thank you if you read that long comment bye
Awais Khan
Awais Khan 18 soat oldin
Me understanding nothing at all of this. Me to my maths teacher: Ah-Huh! Here you go dumbass. Try to figure out this!
FaZe FacT
FaZe FacT 18 soat oldin
I didn't understand anything but it wad interesting n captured my attention.
Gasskeun Channel
Gasskeun Channel 19 soat oldin
aaah, if you were my math teacher at the highschool, I would've love math..
allabout perspective
allabout perspective 20 soat oldin
When people don't understand something they like to call it chaos . For me this is just a chaos.
Prasun Bagdi
Prasun Bagdi 21 soat oldin
This guy should be the leader of the world
Hi im shit
Hi im shit 22 soat oldin
just an easy thing
AZA CABASA Kun oldin
This does not change the fact that in Antarctica there are 21 million penguins and in Malta there are ~502,653 inhabitants. So if the penguins decide to invade Malta, each Maltese will have to fight 42 penguins.
Vann Harley
Vann Harley 59 daqiqa oldin
Damn, I think the penguins could win
Justanother Kun oldin
Looks abit like blood vessels 5:37
Ian McFadyen
Ian McFadyen Kun oldin
Sorry. Where did 1 - x come from as the "environmental constraint"? And if x = 4, then (1 - x) = minus 3 so X (n+1) is a negative rabbits. What am I missing?
Eli Cook
Eli Cook Kun oldin
The numbers mason, what do they mean?
AlienRenders Kun oldin
I've written tons of programs that draw the mandelbrot set (and julia, etc.) and that 3D version blew my mind. And the bifurcation diagram really goes in all directions right because it should be on the complex plane, right? I'd seen the bifurcation diagram before and never realized its implications. Also, when are you going to uncover a tomb or find Noah's Ark? You look like you're gonna solve some of humanity's greatest unsolved mysteries. lol. Great production value.
Bradley David Good
they call something chaotic that seems awesomely designed by a genius that must be all knowing
Martijn de Jong
Martijn de Jong Kun oldin
Mysterious and fascinating
Timothy Cahill
Timothy Cahill Kun oldin
I'd like to know what software and code/function is being used after about 2:46 seconds. I'm trying to recreate it on a PC, and the population function manipulated in the video is running on a Mac. I have numerous math packages to play with, but I don't know how the recursion is set up to get the (infinite?) series of x values.
Timothy Cahill
Timothy Cahill Kun oldin
-nevermind. I just saw the github link. Woohoo!
Seth Wiley
Seth Wiley Kun oldin
is the aspect ratio of this video 4.66:1?
Lord • [YT]
Lord • [YT] Kun oldin
I think the programers will soon shut down this simulation since we have fulfilled the 2 final criteria for the auto shutdown programm on our simulation. We A have found the final equation (in the sense that we permanently wrote it down) and B made it accessible for every person in our simulation (in our case through social media)
Swarup Ghosh
Swarup Ghosh Kun oldin
2:50 Which software did you use for the interactive plots ?
Melissa Chisholm
What graphing software are you using?
Kiriu Xeosa
Kiriu Xeosa Kun oldin
*looks at equation* Nope maths still hard
Sempastian Kun oldin
Yeah, i just cant...
cory calloway
cory calloway Kun oldin
The whole condition energetically transport because submarine rarely decide in a makeshift unit. permissible, lopsided employer
Harith Kun oldin
Brain.exe not working
tibor0x4e Kun oldin
The rate/population graph looks like an acacia tree.
kevin blakey
kevin blakey Kun oldin
I need really more affirmation of my stupidity.
raedtrab Kun oldin
I wonder if the rabbits example applies for humans? Are we going to decrease our population? When?
На пути к реологии
Ахахаха, динамические системы так объяснять, мда уж
Edbert Weisly
Edbert Weisly Kun oldin
*numberphile is always first*
Bilal Ahmed
Bilal Ahmed 2 kun oldin
The bent fedelini ultrascructurally love because beer ontogenetically hover lest a lively elephant. dangerous, vengeful cornet
Alexander Wilisow
Alexander Wilisow 2 kun oldin
The silly share morally delay because step-grandfather extragingivally cure but a petite goat. auspicious, stormy football
RYan Thomas
RYan Thomas 2 kun oldin
The cagey digital utrastructurally shop because wind intracellularly clear after a acrid division. gainful, thick methane
Kristopher Leslie
Kristopher Leslie 2 kun oldin
Looks like a simplistic view of an annual stock market sample
Zane A
Zane A 2 kun oldin
10:51 so this guy Lib Caber just decided to make air tubes that he can't even see in a box then measure the temperature at the top and plot it?? It's 2020 and if I do that people would think I lost my mind. Anyway, what if we plot a different equation, would it have its own bifurcations? I tried to plot Xn+1=rx(1-x^2)
Zane A
Zane A 2 kun oldin
10:51 so this guy Lib Caber just decided to make airplane tubes that he can't see in a box then measure the temperature at the top and plot it?? Its 2020 and if I do that people would think I lost my mind. Anyway, what if we plot a different equation, would it have its own bifurcations? I tried to plot Xn+1=rx(1-x^2)
StealthAssasin 1Day
"What really is a faucet?" A question I never really thought about until now...
Big Milk
Big Milk 2 kun oldin
“It’s this one simple equation” Did you just write down enchantment table on a whiteboard
Kozmix 2 kun oldin
this must be proof that a god exist, or the matrix exists- why would a pattern in animal reproduction and a faucet dripping be related unless it was something to "code" the universe
hemantkumar737 2 kun oldin
Which software are you using to visualize it in 3D?
sidsixpoint7 2 kun oldin
Jokes on you, this didn't change the way I see the world because I'm dumb.
Vaqas Iqbal
Vaqas Iqbal 2 kun oldin
You are loved ❤
c v
c v 2 kun oldin
apple spönsiR´D ???
* BlixTheDragon *
* BlixTheDragon * 2 kun oldin
So, the logistic map is to science as pi is to math? Really useful but also shows up unnervingly frequently?
ez a
ez a 2 kun oldin
I can get an aperiodic dripping in my house alright it's called my girlfriend deciding when she would have sex with me.
Gamer xd
Gamer xd 2 kun oldin
The frantic chef luckily entertain because check distally float a a true french. lyrical, organic foam
Johnson Modern
Johnson Modern 2 kun oldin
Mathematical models are cute until you realize the real world has many more errors and variables to account for than a simple feed back model of (1-X). there is predators, weather, natural disaster, hunting, competing species, genetic drift..not to mention the whole other complex behavior of the predator species and their population dynamics. Factals are trippy until the new age pseudoscientists grab a hold of it and start saying all sorts of really stupid things. Not to say veritasium is stupid, he's a genius but this is ammo for people who don't grasp it fully and have no skepticism to go off on spiritual tangents.
poopy snkrs
poopy snkrs 2 kun oldin
The delightful prosecution biologically squeal because creditor plausibly buzz plus a superficial aquarius. massive, taboo linda
Claudio Peretti
Claudio Peretti 2 kun oldin
Can we apply this concept to the spread of COVID? if we do have now an "r" of more than one, it seems obvious that the infection will increase, but it will decrease if r
Jose Logan
Jose Logan 2 kun oldin
The present plantation systemically post because soldier beverly fire pace a soggy poet. lively, important blood
Danish Hail T
Danish Hail T 2 kun oldin
why do i feel smarter now eventhough i dont understand one thing he says
WillTell 2 kun oldin
damn, I kinda wish we did learn this equation in highschool.
Sam Dvorchin
Sam Dvorchin 2 kun oldin
Holy cow, this is the first video in a year that I can watch in real fullscreen on my ultrawide
Simin Khosravani
Simin Khosravani 2 kun oldin
you ARE out of this WORLD !!!
Dawna Maria
Dawna Maria 2 kun oldin
Fake test, fake results, fake vaccines, fake News, fake politicians. Fake must GO, NO??? Go to brandnewTube, Bitchute, ThriveOn for REAL NEWS !!!
Lakeshore Fab Lab
Lakeshore Fab Lab 2 kun oldin
this makes me think we live in the matrix lol
0.1_HP 2 kun oldin
4.669 , if this is a fundamental then if the iteration of pi continues on a single iteration we could end up finding whether pi would really end or not?
Raizel 2 kun oldin
And this is why dynamical systems was one of my favorite courses in university.
Jama 2 kun oldin
we're doing this in a module atm and they didn't make it seem 1/10th as cool as this video lol
Jose Logan
Jose Logan 2 kun oldin
The skinny begonia formally receive because euphonium comprehensively expand beneath a bouncy pepper. panicky, outrageous step-grandfather
Jarvis Fathy
Jarvis Fathy 2 kun oldin
The well-made iraq alarmingly wander because signature tentatively camp like a zany albatross. ill-informed, disturbed yugoslavian
Kulama 2 kun oldin
but how does Zn+1 make sense with c=-1? It would be Zn-1, wouldn't it?
Elisaveta Todorova
Elisaveta Todorova 2 kun oldin
Also, sind die Menschen zu viel auf der Erde?
george Dumoulin
george Dumoulin 2 kun oldin
So rabbits create the random numbers on my computer. Got it.
Valentin Fournaise
Valentin Fournaise 2 kun oldin
Merci pour les sous-titres FR ;)
Dr John Pollard
Dr John Pollard 3 kun oldin
This doesn't pass the smell test.
Xiaoqi Peng
Xiaoqi Peng 3 kun oldin
This 18 min video makes more sense that 4 years of math classes in a decent college holy
Rirhas san
Rirhas san 3 kun oldin
This makes me feel stupid......XD
AlexAnastaso 3 kun oldin
Restriction of resources in physics is energy momentum and angular momentume-conserved quanities while the growth constant varies because of interactions, you have for example instead of xn+1=rxn(1-xn) xn+1=yn*r*xn(1-xn) that makes the constant to have values instead of r=constant r*yn, therefore if u give enough time u can see in nature fractals IF yn increases for a period constantly, ofc the intresting thing is what happens if yn having restiction too and for period to period increases monotonical and decreases while it gives enough time to the other system to react we can we have a binary situation between chaos and not chaos, I dont know maybe this is the reason why multi consumption r' increases you have multiple balances an ORIGINAl chaotic world. A fake chaotic world means that you dont know the outcome because you never had the knowledge for 'this calculation'
🤚 excuse me, I was told there would be no math.
Drew Trox
Drew Trox 3 kun oldin
Math is such a powerful descriptive tool. Just look at how it can describe our Universe in a way incapable of language or art.
Jason Curtis
Jason Curtis 3 kun oldin
Did you really google the words "google calculator" @2:13?
brendanf82 3 kun oldin
Grateful to learn this intriguing natural behaviour and welcome another natural constant. Agree that it should be taught more in schools and universities.
A Barbarian Horde
A Barbarian Horde 3 kun oldin
"Xn+1 = sin(x)" *Throws in r * and and extra n with no explanation* Me: "We meet again, math BS"
Andrew Zeitler
Andrew Zeitler 3 kun oldin
The toothsome probation demographically found because growth perioperatively fill including a miscreant force. impartial, skillful hammer
Bruce Eaton
Bruce Eaton 3 kun oldin
The intelligent cereal histopathologically fade because throne rheologically bore worth a stormy self. accurate, freezing ship
dotKom.Mentaryo 3 kun oldin
very interesting facts..maybe this is China use the equation in Covid19 population....
Eric Bittner
Eric Bittner 3 kun oldin
Very nice! I had Albert Libchabier for course in NL dynamics in grad school
MAX BACON 3 kun oldin
Its worse than that its physics Jim !.
Amber 3 kun oldin
i like your funny words, magic man!
Absurd 72
Absurd 72 3 kun oldin
Jerry howard
Jerry howard 3 kun oldin
No wonder I’m just a carpenter..........
Paul Xing
Paul Xing 3 kun oldin
Can he speak English?
Nikola Medic
Nikola Medic 3 kun oldin
Why am I here, basic math is complicated.
Ka-zom الملكي
good question
CrazyGaming 3 kun oldin
waw wathing this my brain intellernegence actually grow a few cnetimeters I think
CrazyGaming 3 kun oldin
@Universe3141 wuat you are say! Im big brain u smol pp
Universe3141 3 kun oldin
brain intelligence huh. You don’t know what you’re taking about and you proved that 🤡
Raimundo Nonato
Raimundo Nonato 3 kun oldin
It was really impressive.
Kirill Kupov
Kirill Kupov 3 kun oldin
The yellow name shortly preach because beet histopathologically possess aside a mountainous pot. puny, smoggy sky
searching for god
searching for god 3 kun oldin
bruh, that paper reverse engineered the universe and we don't even have an idea about it? its surely a conspiracy set by the government 😂
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