#### Am Vor year

Dauer: 18:39

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"

## KOMMENTARE

## The Zach

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.

Vor 2 Stunden## Mahir Balushi

Thanks

Vor 5 Stunden## Daniel Edwards

Whaaaaaaaaaaatttt

Vor 6 Stunden## Brian Kleinschmidt

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

Vor 6 Stunden## Lion Deluxe

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.

Vor 9 Stunden## mt2mgames

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

Vor 10 Stunden## Marre

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

Vor 13 Stunden## Ruderaksha Karwa

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

Vor 14 Stunden## Drawing Masterclass

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

Vor 15 Stunden## Shawn Bechard

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.

Vor 16 Stunden## Nad G

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

Vor 20 Stunden## Ish Kabibble

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

Vor Tag## UhOhMeMeBiggestBoy

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

Vor Tag## Xandea Galleta

I hurt myself in confusion. :(

Vor Tag## Dodd Rougeau

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

Vor Tag## R Doody

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

Vor Tag## Leandro Placencia

19:39 10^10^100 Googolplex

Vor Tag## Leandro Placencia

10^10^100 Googolplex

Vor Tag## Rotciv Inoccic

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

Vor Tag## Netemp Witemp

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

Vor Tag## deck monkey

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".

Vor 2 Tage## Jason Brunhard

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.

Vor 2 Tage## The Rodestarr

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

Vor 2 Tage## ich

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

Vor 2 Tage## Naz Fride

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

Vor 2 Tage## Subhadeep Das

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

Vor 2 Tage## Simranjeet Singh

Your calculation is wrong

Vor 2 Tage## Ssenyonjo Jireh

Can I still answer the question

Vor 2 Tage## Ssenyonjo Jireh

Can I still answer the question

Vor 2 Tage## Chindulur Sai Kaushik

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

Vor 2 Tage## Scripted Frames

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

Vor 3 Tage## Scripted Frames

"Chaos"

Vor 3 Tage## Scripted Frames

This video proved me that I am a dumb

Vor 3 Tage## Scripted Frames

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

Vor 3 Tage## Leo Verran

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

Vor 3 Tage## Karan Jassal

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"

Vor 3 Tage## twobad

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

Vor 3 Tage## Miagi Fodder

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

Vor 3 Tage## Xing Yu

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!

Vor 3 Tage## FBI Agent

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

Vor 3 Tage## Iron work Paul

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

Vor 3 Tage## Fuzzy Ankles

holy shiet thats beautiful

Vor 3 Tage## fffrikkie 123

Life is a simulation confirmed

Vor 3 Tage## Ishita Vyavahare

what software is he using?

Vor 3 Tage## Paolo Scaramuzzino

how does it apply to the Covid-19 waves?

Vor 3 Tage## O_0

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

Vor 3 Tage## Brian Kemery

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.

Vor 4 Tage## KG Guitar

ROWAN???

Vor 4 Tage## Anthony Tran

first 10 seconds and i went dumb

Vor 4 Tage## Simon Lovelace

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

Vor 4 Tage## Juan David Barrada

Amazing!!!

Vor 4 Tage## dolf1n1

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

Vor 4 Tage## Rocket Zing

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

Vor 4 Tage## ash channan

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

Vor 4 Tage## Milkymalk

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?

Vor 4 Tage## adib z

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

Vor 4 Tage## XRay Plays

Huh

Vor 4 Tage## Phillip Plyer

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!

Vor 4 Tage## steve

I dont get it U just talk too much

Vor 4 Tage## Phineas

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

Vor 5 Tage## John Worthington

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

Vor 5 Tage## Mensa X

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

Vor 5 Tage## rendzis

In what day did god made this?😁

Vor 5 Tage## mazhar chrome

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

Vor 5 Tage## unityelt

It's like programming life

Vor 5 Tage## Slow Motion

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

Vor 5 Tage## Pula Vijaya

Is world an illusion make a video sir

Vor 6 Tage## Peacocks & Polar Bears

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

Vor 6 Tage## korteks visceralzen

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

Vor 6 Tage## Betsy Larcom

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

Vor 6 Tage## Bare Bear Hands

Chaos is natural order.

Vor 6 Tage## Eric Swenson

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...

Vor 6 Tage## Rohit Neemwal

so random numbers are not so random.

Vor 6 Tage## Rohit Neemwal

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

Vor 6 Tage## Rohit Neemwal

so , we are in simulation .

Vor 6 Tage## Steven

The mandelbrook fractal looks lika a turtle:)

Vor 6 Tage## Vinyas Singh

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.

Vor 6 Tage## Xer R

You should make a podcast

Vor 6 Tage## O Templo de Shaka

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

Vor 6 Tage## Hein Htet

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

Vor 6 Tage## Martin Da Monarch

That kinda looks like how a tree 🌳 grows lol cool

Vor 6 Tage## delt

Seeeeriously fascinating!!!! 😲😲

Vor 7 Tage## Ethan Evans

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

Vor 7 Tage## CallMeBeep

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

Vor 7 Tage## Kelvin Francisco

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

Vor 7 Tage## Zee Y

Now someone still thinks we live in a simulation?

Vor 7 Tage## Rohan Dongre

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.

Vor 7 Tage## Segala Nicolas

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.

Vor 7 Tage## bereket taffesse

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

Vor 7 Tage## Pillow

so this is how the multiverse go

Vor 7 Tage## Pillow

multiverse

Vor 7 Tage## Segala Nicolas

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

Vor 7 Tage## Michael

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

Vor 7 Tage## God

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

Vor 7 Tage## Fractal

13:44 oh god it's the zodiac killer

Vor 7 Tage## Mugtba Moamed

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

Vor 7 Tage## Random X

How do you guys come up with such things.

Vor 7 Tage## Connor Eyer

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

Vor 7 Tage## troeteimarsch

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

Vor 7 Tage## Chris Incorvati

Order begets chaos, chaos begets order.

Vor 7 Tage## Zygorg

You adquired a new tittle: Chaotic (Neutral)

Vor 7 Tage## Carlos Handojo Santosa

You just blew my mind.

Vor 8 Tage## Holyfield Barrett

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

Vor 8 Tage