## 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"

## KOMMENTARE

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

"Chaos"

This video proved me that I am a dumb

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

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

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"

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

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

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!

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

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

holy shiet thats beautiful

Life is a simulation confirmed

what software is he using?

how does it apply to the Covid-19 waves?

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

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.

ROWAN???

first 10 seconds and i went dumb

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

Amazing!!!

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

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

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

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?

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

Huh

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!

I dont get it U just talk too much

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

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

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

In what day did god made this?😁

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

It's like programming life

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

Is world an illusion make a video sir

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

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

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

Chaos is natural order.

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...

so random numbers are not so random.

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

so , we are in simulation .

The mandelbrook fractal looks lika a turtle:)

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.

You should make a podcast

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

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

That kinda looks like how a tree 🌳 grows lol cool

Seeeeriously fascinating!!!! 😲😲

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

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

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

Now someone still thinks we live in a simulation?

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

## Vor 4 Tage

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.

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

so this is how the multiverse go

## Pillow

## Vor 4 Tage

multiverse

## Segala Nicolas

## Vor 4 Tage

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

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

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

13:44 oh god it's the zodiac killer

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

How do you guys come up with such things.

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

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

Order begets chaos, chaos begets order.

You adquired a new tittle: Chaotic (Neutral)

You just blew my mind.

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

The anti-life/death equation?

rx - the population will grow exponentially rx - is a linear equation

## Segala Nicolas

## Vor 4 Tage

@ライアン but it is exponential, because x(n+1)=r*x(n) is equivalent to x(n)=r^n so it's an exponential model because it's raised to a power. Anyway, the math here is correct

## ライアン

## Vor 4 Tage

@Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies

## Релёкс84

## Vor 4 Tage

It is a linear *differential* equation, which translates to an exponential solution.

The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter

What happened to the contest after covid hit? Did the winner get to go?

The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand

The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year

I'm going to be so honest here. What the hell did I just watch and how do I feel even less about myself

Chaos is so subjective

Overpopulation debukned.

## Segala Nicolas

## Vor 4 Tage

What do you mean ? That's not the point of the video, and I'm not sure what there is to debunk about overpopulation

CERN. August 1991. I believe it was few 6th.... But, yes, it was Switzerland's CERN that quietly switched on the first research website in the aim of studying particle based physics--atom smashing! Love it.

YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9

RIGHT NOW I AM STUDYING SAME IN MY T.Y BSc

Design ..by God

I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.

When I say chaos, you say fogginbom, chaos

I didnt understand anything

When that needle happens on the chaotic part..then there will Thanos comes..

These numbers are living things. This is extraordinary.

The real Question ist: how to apply this to the Stock market?

Am i the only whos life is actually being changed by this stuff?? Its the only thing i can think about like all different types of infinity. Usually when im doing any task in my daily life ill spring into action or rather my brain does and starts think about how something can be infinite or is it infinite or can it be connected to infinity. The worst case of this is so simple but its almost hindering me, almost every two minutes in math class my brain just spits out "theres infinite amount of numbers in between ___ and ___" or "if you keep using that equation it will go for infinity" or even sometimes i try to make an infinite something like writing how many zeros after 0.0 before running out of room and having to put a 1 at the end. Tomorrow or maybe monday in class im going to use the mandelbrot equation to try and draw a small taste of a man made mandbrot set. Although I know I will be restricted by how much room I have on the page or whatever im drawing on. I almost feel restricted by reality or something. Considering everyone has ever told me that infinity is impossible to comprehend I seriously want to comprehend it or hear it or see it or just do anything that i could actually interact my sense with infinity. Of coure this will never happen considering there is no real infinity or at least not that we can "comprehend"

The only reason we call it chaos is because in order to see the chaos as a constant you would need to be in a higher dimension.

## Kim-André Johansen

## Vor 4 Tage

Yes! But maths can take us there 🙂

The correct name for a population of rabbits is Fluffle.

what is the name of the plotting tool at 3:07 ?

The sweltering ketchup fortuitously correct because kitty internationally chew within a wonderful dragonfly. fabulous, abrasive windshield

click on the video Panik : Oh god , i am so dumb, i will not be able to change the view on the world Pause the video and.. click on comment section Kalm: yhh at least....i know i am not aloooone😜

4.669 hehehe funny number.

I haven't thought about Mandelbrot sets since I was 20 and they delivered the coolest graphics on the new VGA-card. The Mandelbrot set already has something organic about it, but this takes it to a new level: the actual underpinnings of the universe. The clickbait-like title was true. Blew my mind.

This video makes me feel genius even though I don't understand any of it.

Am i the only one who sees the graph similar to the Darwin´s tree of life?

Amazing science communicator. Heads of to you sir!