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

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"

Kommentarer

© 2010-2021 SEtoos Online video

Chul Yeom27 minuter sedan

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

Ian Carr2 timmar sedan

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 Webber2 timmar sedan

Me: Just trying to find the equation to plug it into desmos.

Artesion5 timmar sedan

cuz humping can be 69

TRADE CODE5 timmar sedan

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 SPEC7 timmar sedan

This is proof that the 2020 election was stolen, thank you for that. Question is how do we convince a potato?

DrNo0077 timmar sedan

i didnt understand literally anything

KoyKoy and Bachuching9 timmar sedan

nice very informative

jbe tfifty10 timmar sedan

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

C 0 R 0 L L A11 timmar sedan

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 Khan11 timmar sedan

Me understanding nothing at all of this. Me to my maths teacher: Ah-Huh! Here you go dumbass. Try to figure out this!

FaZe FacT11 timmar sedan

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

Gasskeun Channel12 timmar sedan

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

allabout perspective12 timmar sedan

When people don't understand something they like to call it chaos . For me this is just a chaos.

Prasun Bagdi14 timmar sedan

This guy should be the leader of the world

Hi im shit15 timmar sedan

just an easy thing

AZA CABASA19 timmar sedan

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.

Justanother20 timmar sedan

Looks abit like blood vessels 5:37

Ian McFadyen20 timmar sedan

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 Cook20 timmar sedan

The numbers mason, what do they mean?

AlienRenders21 timme sedan

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 Good22 timmar sedan

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

Martijn de Jong23 timmar sedan

Mysterious and fascinating

Timothy CahillDag sedan

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 CahillDag sedan

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

Seth WileyDag sedan

is the aspect ratio of this video 4.66:1?

Lord • [YT]Dag sedan

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 GhoshDag sedan

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

Melissa ChisholmDag sedan

What graphing software are you using?

Kiriu XeosaDag sedan

*looks at equation* Nope maths still hard

SempastianDag sedan

Yeah, i just cant...

cory callowayDag sedan

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HarithDag sedan

Brain.exe not working

tibor0x4eDag sedan

The rate/population graph looks like an acacia tree.

kevin blakeyDag sedan

I need really more affirmation of my stupidity.

raedtrabDag sedan

I wonder if the rabbits example applies for humans? Are we going to decrease our population? When?

На пути к реологииDag sedan

Ахахаха, динамические системы так объяснять, мда уж

Edbert WeislyDag sedan

*numberphile is always first*

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Kristopher LeslieDag sedan

Looks like a simplistic view of an annual stock market sample

Zane ADag sedan

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 ADag sedan

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 1DayDag sedan

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

Big MilkDag sedan

“It’s this one simple equation” Did you just write down enchantment table on a whiteboard

KozmixDag sedan

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

hemantkumar737Dag sedan

Which software are you using to visualize it in 3D?

sidsixpoint7Dag sedan

Jokes on you, this didn't change the way I see the world because I'm dumb.

Vaqas IqbalDag sedan

You are loved ❤

c v2 dagar sedan

apple spönsiR´D ???

* BlixTheDragon *2 dagar sedan

So, the logistic map is to science as pi is to math? Really useful but also shows up unnervingly frequently?

ez a2 dagar sedan

I can get an aperiodic dripping in my house alright it's called my girlfriend deciding when she would have sex with me.

Gamer xd2 dagar sedan

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Johnson Modern2 dagar sedan

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 snkrs2 dagar sedan

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Claudio Peretti2 dagar sedan

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 Logan2 dagar sedan

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Danish Hail T2 dagar sedan

why do i feel smarter now eventhough i dont understand one thing he says

WillTell2 dagar sedan

damn, I kinda wish we did learn this equation in highschool.

Sam Dvorchin2 dagar sedan

Holy cow, this is the first video in a year that I can watch in real fullscreen on my ultrawide

Simin Khosravani2 dagar sedan

you ARE out of this WORLD !!!

Dawna Maria2 dagar sedan

Fake test, fake results, fake vaccines, fake News, fake politicians. Fake must GO, NO??? Go to brandnewTube, Bitchute, ThriveOn for REAL NEWS !!!

Lakeshore Fab Lab2 dagar sedan

this makes me think we live in the matrix lol

0.1_HP2 dagar sedan

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?

Raizel2 dagar sedan

And this is why dynamical systems was one of my favorite courses in university.

Jama2 dagar sedan

we're doing this in a module atm and they didn't make it seem 1/10th as cool as this video lol

Jose Logan2 dagar sedan

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Kulama2 dagar sedan

but how does Zn+1 make sense with c=-1? It would be Zn-1, wouldn't it?

Elisaveta Todorova2 dagar sedan

Also, sind die Menschen zu viel auf der Erde?

george Dumoulin2 dagar sedan

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

Valentin Fournaise2 dagar sedan

Merci pour les sous-titres FR ;)

Dr John Pollard2 dagar sedan

This doesn't pass the smell test.

Xiaoqi Peng2 dagar sedan

This 18 min video makes more sense that 4 years of math classes in a decent college holy

Rirhas san2 dagar sedan

This makes me feel stupid......XD

AlexAnastaso2 dagar sedan

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 CRUISER2 dagar sedan

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

Drew Trox2 dagar sedan

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 Curtis2 dagar sedan

Did you really google the words "google calculator" @2:13?

brendanf822 dagar sedan

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 Horde2 dagar sedan

"Xn+1 = sin(x)" *Throws in r * and and extra n with no explanation* Me: "We meet again, math BS"

Andrew Zeitler2 dagar sedan

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Bruce Eaton3 dagar sedan

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dotKom.Mentaryo3 dagar sedan

very interesting facts..maybe this is China use the equation in Covid19 population....

Eric Bittner3 dagar sedan

Very nice! I had Albert Libchabier for course in NL dynamics in grad school

MAX BACON3 dagar sedan

Its worse than that its physics Jim !.

Amber3 dagar sedan

i like your funny words, magic man!

Absurd 723 dagar sedan

complicated

Jerry howard3 dagar sedan

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

Paul Xing3 dagar sedan

Can he speak English?

Nikola Medic3 dagar sedan

Why am I here, basic math is complicated.

Ka-zom الملكي3 dagar sedan

good question

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waw wathing this my brain intellernegence actually grow a few cnetimeters I think

CrazyGaming3 dagar sedan

@Universe3141 wuat you are say! Im big brain u smol pp

Universe31413 dagar sedan

brain intelligence huh. You don’t know what you’re taking about and you proved that 🤡

Raimundo Nonato3 dagar sedan

It was really impressive.

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searching for god3 dagar sedan

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 😂

Mana Rallego3 dagar sedan

12:45 So, the implantable cardioverter defibrillator was achieved by hell on earth for rabbits... One of these days, doomsguy will be coming for a special part of science, and they've had it coming.

sunkeet3 dagar sedan

unstable filter + sample rate lower than data

javed ansari3 dagar sedan

So... The computer isn't smart enough to make random numbers, he just follows a pattern 😂

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Virgin confirmed