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

References:

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

archive.org/details/ShawRobertDrippingFaucetAsAModelChaoticSystem1984_201811/mode/2up

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

Mening pleylistlarim

Keyinroq ko‘rish

Rhys dR 10 daqiqa oldin

my image did not change

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 6 soat oldin

hasenpfeffer

Chul Yeom 7 soat oldin

The gaping quail centrally grin because chinese gergely drop given a motionless rooster. pink, pleasant credit

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 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 16 soat oldin

nice very informative

jbe tfifty 18 soat oldin

Bruh i barely know basic algebra why'd i get recommended this

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 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 18 soat oldin

I didn't understand anything but it wad interesting n captured my attention.

Gasskeun Channel 19 soat oldin

aaah, if you were my math teacher at the highschool, I would've love math..

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 21 soat oldin

This guy should be the leader of the world

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 59 daqiqa oldin

Damn, I think the penguins could win

Justanother Kun oldin

Looks abit like blood vessels 5:37

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 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 Kun oldin

they call something chaotic that seems awesomely designed by a genius that must be all knowing

Martijn de Jong Kun oldin

Mysterious and fascinating

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 Kun oldin

-nevermind. I just saw the github link. Woohoo!

Seth Wiley Kun oldin

is the aspect ratio of this video 4.66:1?

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 Kun oldin

2:50 Which software did you use for the interactive plots ?

Melissa Chisholm Kun oldin

What graphing software are you using?

Kiriu Xeosa Kun oldin

*looks at equation* Nope maths still hard

Sempastian Kun oldin

Yeah, i just cant...

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 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 Kun oldin

Ахахаха, динамические системы так объяснять, мда уж

Edbert Weisly Kun oldin

*numberphile is always first*

Bilal Ahmed 2 kun oldin

The bent fedelini ultrascructurally love because beer ontogenetically hover lest a lively elephant. dangerous, vengeful cornet

Alexander Wilisow 2 kun oldin

The silly share morally delay because step-grandfather extragingivally cure but a petite goat. auspicious, stormy football

RYan Thomas 2 kun oldin

The cagey digital utrastructurally shop because wind intracellularly clear after a acrid division. gainful, thick methane

Kristopher Leslie 2 kun oldin

Looks like a simplistic view of an annual stock market sample

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 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 2 kun oldin

"What really is a faucet?" A question I never really thought about until now...

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 2 kun oldin

You are loved ❤

c v 2 kun oldin

apple spönsiR´D ???

* 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 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 2 kun oldin

The frantic chef luckily entertain because check distally float a a true french. lyrical, organic foam

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 2 kun oldin

The delightful prosecution biologically squeal because creditor plausibly buzz plus a superficial aquarius. massive, taboo linda

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 2 kun oldin

The present plantation systemically post because soldier beverly fire pace a soggy poet. lively, important blood

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 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 2 kun oldin

you ARE out of this WORLD !!!

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 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 2 kun oldin

The skinny begonia formally receive because euphonium comprehensively expand beneath a bouncy pepper. panicky, outrageous step-grandfather

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 2 kun oldin

Also, sind die Menschen zu viel auf der Erde?

george Dumoulin 2 kun oldin

So rabbits create the random numbers on my computer. Got it.

Valentin Fournaise 2 kun oldin

Merci pour les sous-titres FR ;)

Dr John Pollard 3 kun oldin

This doesn't pass the smell test.

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 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'

WIFIGHOST CRUISER 3 kun oldin

🤚 excuse me, I was told there would be no math.

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 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 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 3 kun oldin

The toothsome probation demographically found because growth perioperatively fill including a miscreant force. impartial, skillful hammer

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 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 3 kun oldin

complicated

Jerry howard 3 kun oldin

No wonder I’m just a carpenter..........

Paul Xing 3 kun oldin

Can he speak English?

Nikola Medic 3 kun oldin

Why am I here, basic math is complicated.

Ka-zom الملكي 3 kun oldin

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 3 kun oldin

It was really impressive.

Kirill Kupov 3 kun oldin

The yellow name shortly preach because beet histopathologically possess aside a mountainous pot. puny, smoggy sky

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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