## 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 đ

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"

## Komente

Now my mind has fallen into a fascinating chaos

kudos to you and your curiosity

Not even this guy knows exactly what he is saying đ€Łđ€Ł

i watched this high and i feel like my mind entered a new dimension

This video has become really relevant with covid lol (at least the R part at the beginning)

I find it odd that ever since I can remember I have been trying to figure out this pattern 2 4 8 16 32 64 128 256 512 1024 as high as I could reach. And now to be learning all of this much later in life it really makes you wonder!? Thanks for the content man I have been watching and learning with you for I think what 8 or 9 years now and you have been a constant reminder I'm not the only one kicking these ideas around. I have been poor my whole life and never had a chance to apply my brain the way I wanted to. And being in low income areas it hard to have these kind of conversations with anyone. So thanks for doing this man really you and Micheal Vsauce I only hope the best to you guys.

Finally the math that I already forgotten since high school looks interesting

So I'm on the toilet, when you push more, more flow will come out but not all at once and evenly, then eventually your muscles can't take the stress and less flow will come out. Then your muscles recharge and you go at it again maybe harder or softer... Equation works in everything

I donât know why but this whole video felt like an unskippable ad

Reverse this connection(selectablly applythe inverse function) and you have a fantastic modulus you can use to chart on an overlay the explicit proficiency to levels of implicit practicality of the teacher-student relevancy thereof.

i hope you have won some awards for your films

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

Thanks

Whaaaaaaaaaaatttt

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

This video made me obsessed. I didnât sleep last night. This morning I went to my core editor and made a Mandelbrotâs Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.

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

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

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

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

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.

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

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

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

I hurt myself in confusion. :(

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

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

19:39 10^10^100 Googolplex

10^10^100 Googolplex

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

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

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".

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.

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

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

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

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 đŻđŻđŻđŻđŻđŻ. This is mind blowing

## oh no

## 17 orĂ« mĂ« parĂ«

this has nothing to do with vegetarians??

Your calculation is wrong

Can I still answer the question

Can I still answer the question

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

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

"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 đi'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 donât 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 - ALthe 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!? đ 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?đ

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 đł grows lol cool

Seeeeriously fascinating!!!! đČđČ

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, đ

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

## 8 ditĂ« mĂ« parĂ«

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

## 8 ditĂ« mĂ« parĂ«

multiverse

## Segala Nicolas

## 8 ditĂ« mĂ« parĂ«

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