# 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"

The Zach

Hace 8 horas

I think this graph also represents the evolution of human intelligence. 👉Think about this: The same brain that created the theory of evolution had to first evolve itself.

Mahir Balushi

Hace 11 horas

Thanks

Daniel Edwards

Hace 12 horas

Whaaaaaaaaaaatttt

Brian Kleinschmidt

Hace 12 horas

I love watching Mandelbrot renderings. That graphic just blew my mind. Beauty has a measure - math itself.

Lion Deluxe

Hace 15 horas

This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.

mt2mgames

Hace 16 horas

this video is horrible. You keep conflating "the population" with "the percentage of the maximum possible population"

Marre

Hace 18 horas

16:55 excited about chaos *HERESY* call the inquisiton

Ruderaksha Karwa

Hace 20 horas

Showerthought: every civilization follows the same pattern , I would say we crossed the curve somewhere between 70s-90s

Drawing Masterclass

Hace 20 horas

So much complexity and we still don't believe there is God.

Shawn Bechard

Hace 22 horas

I keep hearing predictions that human populations will decline, but I don't think it is going to be anywhere near as soon as they think. We have been rising since the Black Plague supposedly.

Nad G

Hace un día

I LOVED this topic! It's insane! I knew that Mandelbrot set was pretty particular on its own but this! I want to know more

Ish Kabibble

Hace un día

This is amazing! I'm familiar with the Mandelbrot set from decades ago, but is that 3D z-axis section a new discovery?

UhOhMeMeBiggestBoy

Hace un día

Look at me just 16 and finding out about this instead of 32 welp anyway I have to go troubleshoot my brain

Xandea Galleta

Hace un día

I hurt myself in confusion. :(

Dodd Rougeau

Hace un día

Spherical trigonometry will prove the Earth is flat. You haven't got the balls to research that truth.

R Doody

Hace un día

An application of math. Frustrating part of most math classes is the lack of application.

Leandro Placencia

Hace un día

19:39 10^10^100 Googolplex

Leandro Placencia

Hace un día

10^10^100 Googolplex

Rotciv Inoccic

Hace 2 días

BANG! .. My brain feels much better...

Netemp Witemp

Hace 2 días

It's the same about the human population. And it seems like we're at the peek right now and going down. That constant is like the pi of fractals

deck monkey

Hace 2 días

School only teaches you the minimum you need to start the next grade. It doesn't teach you to think or be intelligent and never will. Look at how fast kids learn until they start school and then are held back from learning at the same pace by being forced to do it "the way I tell you".

Jason Brunhard

Hace 2 días

I want to thank you for your channel honestly. I rarely ever leave comments, but I am so IMPRESSED AND APPRECIATIVE for your work. You are bringing science out to the public forum so we, as a population, can engage in science. Science needs funding. It is what it is, and the content you provide is structured in a way for the general public can understand the unique and awe-inspiring physics that this universe has. FROM MY HEART THANK YOU FOR DOING YOUR BEST TO HELP THE HUMAN RACE EVOLVE.

The Rodestarr

Hace 2 días

Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.

ich

Hace 2 días

Which software did he use for plotting his graphs? 3:45

Naz Fride

Hace 2 días

Amazing. Thenks for the outstanding explanation of a pretty complex subject (for lay people)!

Subhadeep Das

Hace 2 días

If everyone will become vegetarian, there is no hunting or poaching and no disasters then we can find the date of extinction of a specific species 😯😯😯😯😯😯. This is mind blowing

Simranjeet Singh

Hace 2 días

Your calculation is wrong

Ssenyonjo Jireh

Hace 3 días

Can I still answer the question

Ssenyonjo Jireh

Hace 3 días

Can I still answer the question

Chindulur Sai Kaushik

Hace 3 días

out of all the possibilities z-axis was the least expected

Scripted Frames

Hace 3 días

we need "chaos" in schools, not the other chaos 😅

Scripted Frames

Hace 3 días

"Chaos"

Scripted Frames

Hace 3 días

This video proved me that I am a dumb

Scripted Frames

Hace 3 días

This video proved me that I am a dumb, I didn't even understand a bit as a 11th grades student

Leo Verran

Hace 3 días

Rabbits times rabbits divided by coyotes plus hawks minus fox equals WTF are you talking about and who cares,...not even the rabbits care!

Karan Jassal

Hace 3 días

This video was so enlightening! Thank you! I love how we can visually see the fractal from a simple equation, and this is exactly how I perceive the universe. "As above, so below"

twobad

Hace 3 días

hod up, someone has to tell me the graphing app that he used

Miagi Fodder

Hace 3 días

God man your 37 and only just found out about this. I'm 35 and just found out about it. Up your game dude

Xing Yu

Hace 3 días

this vid has saved my essay project 😂i've been learning how to determine period doubling in the last couple of months. But i had little clue that so many real life phenomena exhibits the bifurcation doubling behaviour. Impressed!

FBI Agent

Hace 3 días

I don’t get any of this but it sounds awesome

Iron work Paul

Hace 3 días

The content is very good, a wonderful man with interesting knowledge

Fuzzy Ankles

Hace 3 días

holy shiet thats beautiful

fffrikkie 123

Hace 3 días

Life is a simulation confirmed

Ishita Vyavahare

Hace 4 días

what software is he using?

Paolo Scaramuzzino

Hace 4 días

how does it apply to the Covid-19 waves?

O_0

Hace 4 días

Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing

Brian Kemery

Hace 4 días

I've heard a ton about the Mandelbrot set over the years...but when he rotated it into 3 dimensions and it matched with the bifurcation diagram, my brain literally melted.

KG Guitar

Hace 4 días

ROWAN???

Anthony Tran

Hace 4 días

first 10 seconds and i went dumb

Simon Lovelace

Hace 4 días

When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere

Juan David Barrada

Hace 4 días

Amazing!!!

dolf1n1

Hace 4 días

Wow I love the way you presented this topic so visually.

Rocket Zing

Hace 4 días

Veritasium : video ratio movie producer : ''m i joke to you

ash channan

Hace 5 días

how many leaves on a tree ? - search - EScall Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation

Milkymalk

Hace 5 días

What if all these fundamental constants are such weird numbers (4.669, 3.1415..., and so on) because the computer universe.exe runs on uses something other than base 10?

adib z

Hace 5 días

Everything is under control of God. Everything, under His calculation. Assalamualaikum

XRay Plays

Hace 5 días

Huh

Phillip Plyer

Hace 5 días

I'm just now fi ding your videos and its creating chaos in my marriage! I feel a couple bifurcation coming on. Any sugar mommas out there wanna help me get to 4.6669!? 😜 But in all seriousness, your videos are awesome!

steve

Hace 5 días

I dont get it U just talk too much

Phineas

Hace 5 días

I struggled to understand this just like many people. But look up Feigenbaum Number on Numberphile, it'll make this easier to understand slightly

John Worthington

Hace 5 días

I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..

Mensa X

Hace 5 días

All we have to do now is track and follow every bunny rabbit to see if this is true

rendzis

Hace 5 días

In what day did god made this?😁

mazhar chrome

Hace 5 días

Can you make a video about this equation with human population, where will be the equilibrium?

unityelt

Hace 5 días

It's like programming life

Slow Motion

Hace 6 días

OMG! I bet he was the most hated guy in school !

Pula Vijaya

Hace 6 días

Is world an illusion make a video sir

Peacocks & Polar Bears

Hace 6 días

This is insane. I've never seen something visualized like this.

korteks visceralzen

Hace 6 días

Thanks. I love this channel. No one explains this stuff.

Betsy Larcom

Hace 6 días

I was an ecology major in undergrad and everyone else thought we just went around hugging trees...

Bare Bear Hands

Hace 6 días

Chaos is natural order.

Eric Swenson

Hace 6 días

And no one thinks there is a creator that did all this by design? All these links and ratios no one can explain the existence of, and we think it all just came about by accident...

Rohit Neemwal

Hace 6 días

so random numbers are not so random.

Rohit Neemwal

Hace 6 días

universal constants are just some values given to simulator to simulate our universe.hece we are in simulator

Rohit Neemwal

Hace 6 días

so , we are in simulation .

Steven

Hace 6 días

The mandelbrook fractal looks lika a turtle:)

Vinyas Singh

Hace 6 días

I guess the made up/unexplained answer of "42" we get to hear about has something to do with this universal constant of "4.669", I'm not sure though.

Xer R

Hace 6 días

You should make a podcast

O Templo de Shaka

Hace 7 días

I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.

Hein Htet

Hace 7 días

There is no chaos. Everything has a pattern at certain perspective.

Martin Da Monarch

Hace 7 días

That kinda looks like how a tree 🌳 grows lol cool

delt

Hace 7 días

Seeeeriously fascinating!!!! 😲😲

Ethan Evans

Hace 7 días

Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago

CallMeBeep

Hace 7 días

Did you upload the vid ultra-wide just for me? :D

Kelvin Francisco

Hace 7 días

This is the last time I watch any of your videos sober, 😒

Zee Y

Hace 7 días

Now someone still thinks we live in a simulation?

Rohan Dongre

Hace 7 días

What kind of math is that?? Initially you said X is no. of rabbits, then you choose X=0.4, how's that possible?? Now, if R is the rate of growth, population next year isn't X*R, but X*(1+R). Further if suggest that the rate of growth will depend on the present population, the R, for any year, will be expressed as a function of (Ps, Pp) where Ps is the saturation population assuming limited resources and Pp is the present population for that particular year. Therefore, Xn=RX(1-X) is incorrect.

Segala Nicolas

Hace 7 días

The X is the percentage of population the theoretical maximum of the population. It makes sense to choose it arbitrarily, since what we care about is the value of X when it stabilises. And it will stabilise to the same value whether we choose it to be 0.4 or 0.9 or anything between 0 and 1. And secondly, it does make sense to multiply by the growth rate, as it makes an exponential model. The math here has been established since the 1970s, there are papers on this, of course it's correct.

bereket taffesse

Hace 7 días

me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man

Pillow

Hace 7 días

so this is how the multiverse go

Pillow

Hace 7 días

multiverse

Segala Nicolas

Hace 7 días

No, this has nothing to do with that. But if you want something that feels like the multiverse, you should check out Veritasium's video on the Many Worlds theory of physics

Michael

Hace 7 días

Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.

God

Hace 7 días

THATS RIGHT!!! OH this got me so excited! :) Apply it to the cosmos and when a star releases energy to its surrounding planets. Chaos , adaptation to environment, then order but it evolves and branches out. The law of life. So many layers lol

Fractal

Hace 7 días

13:44 oh god it's the zodiac killer

Mugtba Moamed

Hace 8 días

Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.

Random X

Hace 8 días

How do you guys come up with such things.

Connor Eyer

Hace 8 días

The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp

troeteimarsch

Hace 8 días

mind blown and the day hasn't even started yet. thanks mate!

Chris Incorvati

Hace 8 días

Order begets chaos, chaos begets order.

Zygorg

Hace 8 días

You adquired a new tittle: Chaotic (Neutral)

Carlos Handojo Santosa

Hace 8 días

You just blew my mind.

Holyfield Barrett

Hace 8 días

The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason