#### Am Vor 8 Monate

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

## Tater Tot

Evil 'scientists' that drugged and killed those Rabbits. Not funny at all. RIP to the Rabbits.

Vor 2 Minuten## Daan Sijbrandij

So it was never 42.... it is 4.669

Vor Stunde## Gerardo Guzman

steve harvey

Vor 9 Stunden## Ralf Baechle

Youtube is bothering me to rewatch this video for months and I finally obeyed. I'm glad I did - for a not so happy reason. The math is a more refined look at how infection numbers such as that of the covid-19 pandemic are growing.

Vor 9 Stunden## Jaden Schulz

yeah none of that made any sense sorry mate

Vor 10 Stunden## Phillip Carr Manchester Mint Crypto

I’ve a theory on this Tao

Vor 10 Stunden## Basketcase642

I have a-periodic driping... I should probably see a doctor about it

Vor 12 Stunden## GcMaf cures ANY CANCER

You sir ain't fooling me, I know you are a A.I robot 🤖

Vor 13 Stunden## j'accuse

jesus christ

Vor 13 Stunden## sascuash96

Thanks to You, I Know about this at my (x)+0+VI 💗

Vor 16 Stunden## Peter Dümpel

"That's so cool!" - The channel

Vor 16 Stunden## Giulia Emanuelli

Loved this! It is not an argument towards chaos though... quite the opposite!

Vor 17 Stunden## Markus

they should teach this in school

Vor 18 Stunden## Nyaaa UwU

I want to test heart beat map on my science teacher

Vor 18 Stunden## Relativity

Mind blowing 🤯 it tickles that inquisitive bone in my brain 🧠

Vor 20 Stunden## Jakob Reece

0:01 huh

Vor 21 Stunde## Laurent Alvaro

Pure magic...

Vor 22 Stunden## bhavya

this is my favorite veritasium video

Vor Tag## BP STREAMS

r=i p rabbits

Vor Tag## The flying Mylle

I guess my teacher watched this video, cuz he teaches like chaos.

Vor Tag## Sid Stevens

So, even in extreme chaos, symmetry still rules ?

Vor Tag## tigr312012

This looks connected to Wolfram project researches

Vor Tag## Diggity doggo

Ok I paused it before it started I’m 13 finna see if I can understand this I’ll edit if I do if I don’t then I’ll still edit 😎👴🏿 1 edit: ok im at 1:43 and i knew how the problem worked wish me luck for the rest 2 Edit: tell me if I’m wrong but I’m at 4:26 and from what I’ve gathered the reason it comes to a equilibrium is because of natural selection the dumb ones die and the smart ones get smarter this makes me think I’m smart hehe 3 edit: I got bored maybe I’ll edit this again one day prob not tho I did understanding most of it tho stopped at 6:30

Vor Tag## Ralph Dankers

This is teached at the Technical University in Eindhoven, the Netherlands, to first year Physics students, so i just got it and i remembered your video, i watched it again to help me understand it better and it worked, thanks

Vor Tag## Pace

Where do predators, human interaction, deforestation go into the equation? Since all those factors are in play.

Vor Tag## Howard Zhang

What if these constants are the key to proving that we are in a simulation?

Vor Tag## Julia Gregory

What the heck? Chaos has a pattern in nature.

Vor Tag## Julia Gregory

Wow, Our Father got trippy and slap happily beautiful with His creation! LOL, now He's just showing off!!

Vor Tag## Xyrus Mallare

Thanos: That puts a smile on my face.

Vor Tag## D V

Finger prints from God.

Vor Tag## MrPotatochips4

The rabbit fibrillation experiment is the kind of thing where there is no justification for the suffering involved.

Vor Tag## Ost san

That sponsored spot did not age well....

Vor Tag## Ange Purs

Veritasium videos are among the best YouTube has to offer. Fabulous. This one is no exception.

Vor Tag## CloudCalmaster

This is when u find out about fractals without LSD

Vor Tag## SUMIT MANDAL

This is one of the best videos of this concept and of Veritaseum, ever! Thanks Mr Derek. I hope and wish to meet you in person someday!

Vor Tag## Lieutenant Lubricant

We live in a computer.

Vor Tag## mat gof

Why why why why why why why why why why?

Vor Tag## Ben Lewis

How are visualizations made?

Vor Tag## Kenneth Rector

Hi Derek. Can you please do a video on Zeno's paradoxes on motion? I think this would fit very well into this theme of how simple equations can lead to complex things and math's relationship to nature of the universe. I realize Zeno a philosopher, but I very much enjoy the questions around whether math is fundamental structure in the world around us, i.e.- did we discover math, or is it just our invention to help describe the world we find ourselves in?'. Zeno's challenges make us look at not just the relationship between math and the world but our own relationship with math.

Vor Tag## Ekito

what's the program used at 2:47? it seems cool

Vor Tag## Kenneth Rector

I am thrilled to see the relationship of this equation to the Mandelbrot set.. I spent many hours in the late 80s on a personal computer modeling bifurcations (It was James Gleick's book Chaos where I became aware of Lorenz equations and the Mandelbrot set). I was using an 8080 processor with 64K of memory and was obsessed with finding the actual points of bifurcation by zooming in at increasing precision until I hit the limits of the machine. Never found them and eventually realized it is probably place that I could never get to but is where the true nature of the universe reveals itself. Great video!

Vor Tag## John Awakening

Just had to share this. How come I am 56 years old, reasonably well educated in science and fond of Mathematics and yet I never heard of this before. I strikes very viscerally, like a distant memory of something you Should know ... Vielen Dank!

Vor Tag## theblankuser

4.669

Vor Tag## Aaron Levy

Adjacent Number-String Relationship Phenomena or The Levy Property Of Subtraction Example 545454 - 454545 = ______ etc. etc. Use with all combinations then experiment, have fun 🌟

Vor 2 Tage## Chris Schwan

What I really love about Derek and veritasium is he always makes me want to do research. I end up going down/through a rabbit hole of information no pun intended. Absolutely amazing stuff to learn. Thank you. Humans are awesome.

Vor 2 Tage## The_VR _MD

So frikkin' cool

Vor 2 Tage## Tim A.

what software is that in the beginning? at about 4 minutes

Vor 2 Tage## Christopher Robertson

i got lost at 2

Vor 2 Tage## Albert Ochoa

Fascinating

Vor 2 Tage## Welsh Family Vlogs

4

Vor 2 Tage## Konstantin Lookeen

this is so beautiful and indcredible at the same time! ,I noticed dripping fosset music when I was a kid ,and I thought that was my imagination . and thank you for showing me that

Vor 2 Tage## JT

Too many errors in the presentation.

Vor 2 Tage## JT

@BangDroid 1) second 52. rx is a linear equation, not an "exponential" equation rx = number of rabbits . The population may be growing exponentially, but the formula is linear. What am I missing? 2) 4.30 - 4:40 "constant value". The value will not be a "constant", it will vary. Does the value approach that number or actually become that number "constant"? It is a nice presentation.

Vor 11 Stunden## BangDroid

List some, even one

Vor 15 Stunden## Steven Tarsitano

i don't typically fullscreen videos, and this aspect ratio kills me. the video is not tall enough!

Vor 2 Tage## BangDroid

I think it's an easter egg. The aspect ratio is 4.669/2

Vor 15 Stunden## Felix Scharnberg

Congratulations, a very well made video. You have explained the topic in a not too difficult manner and opened up our eyes to interconnectivity among different mathematical visualizations! Euclidian geometry is interesting enough, but mark the words of fractal and natural pattern researchers today, the fields of complexity, chaos and fractals are the future of science from here on out! It must be taught in schools if we are not to hide under a rock or bury our brains in sand from now on!!

Vor 2 Tage## Huey Edjec

Have any of you used Numerade to help with calc homework??

Vor 2 Tage## Scott P

Student in life. Good video. Tried the water dripping. It works. Thanks.

Vor 2 Tage## Akif T

https://www.youtube.com/watch?v=UC4lXtPqnpM

Vor 2 Tage## joel osuna

How come there is chaos if there is a constant

Vor 2 Tage## Mister Gunsen

This in January. If everyone understood whats taught in this video (talking about R and growth rates), people whould get, why we need to wear masks and social distance. If SARS-CoV-2's R is

Vor 2 Tage## Daniel Rud

Population doesn’t decrease, you are modeling the rate of change of the population. If P is the function of population, you are modeling dP/dt, and the solution to this differential equation is a logistic function, which is increasing and bounded by carrying capacity

Vor 2 Tage## Utku Yılmaz

That was pretty exciting. I did some computations, and saw the same pattern. However, for x(k+1) = r * x(k) * (1 - x(k)) formula, it diverges after r = 4. Also, it generates a random sequence, but its far beyond from being uniform; it's distribution has peaks in 0 and 1 and was flat-ish in the middle.

Vor 2 Tage## wh3resmycar

ok this bothered me that you used actual paper when a marker board would suffice.

Vor 2 Tage## Cody S

I feel bad for the person who won the SXSW tickets.

Vor 2 Tage## N. J.

Does this apply to humans too?

Vor 3 Tage## Delacroix Wang

不錯的視頻，我覺得可以同時介紹一下圖靈對混沌理論的貢獻

Vor 3 Tage## Daniel Williams

The population modeling formula is also used to model policy diffusion, how new policy ideas are adopted in new jurisdictions, in Political Science.

Vor 3 Tage## Giselle Cole

Why does it feel like I watched this years ago...

Vor 3 Tage## mel obrien

Equations are like magic tricks. They can look good, but at the same time they can be meaningless. This dude is picking numbers out of the air, those that suit his imaginary equations. Rabbits, me arse.

Vor 3 Tage## Keeganthenotvegan dyke

Why is this video shaped so weird? Like, even with my phone (which has a 20:9 screen) there are black bars on the top and bottom.

Vor 3 Tage## Keeganthenotvegan dyke

@BangDroid i might be missing something (maybe I'm looking at the wrong things in the stats) but it seems to me the aspect ratio is 4.716x2.

Vor 13 Stunden## BangDroid

I think it's meant to be an easter egg. The aspect ratio is 4.669/2

Vor 15 Stunden## Closeup Channel

Or the spread of viruses...

Vor 3 Tage## Gin

I don't know if I learned something and if I did I have no idea what I learned but uh, brain, video, yes, question mark

Vor 3 Tage## Phos9

Hmmmmm... Is this why the island of stability is theorized to exist?

Vor 3 Tage## blue beam

when mandelbrot set rotated it looks like it's a 5th dimensional object

Vor 3 Tage## Neena Plant

A video applying this same theory to the human population might be telling.

Vor 3 Tage## Ayberk Aydin

It's not the equation that's beautiful; it's how Benoit looked at it.

Vor 3 Tage## RedShipsofSpainAgain

6:42 "Yeah, yeah the Mandelbrot Set; everyone knows about the Mandelbrot Set. But how does that have anything to do with ---" 6:44 "Holy s**t...... I never saw that in the pattern before...."

Vor 3 Tage## Eric M

Dude has a nice house.

Vor 3 Tage## 24063457467984263567

you just explained why eugenicist gates is wrong with his "we kill billions to save the environment"

Vor 3 Tage## RIPxBlackHawk

This answers my question about hair growth

Vor 3 Tage## William Haisch

Me, after every one of his videos: Brain has melted. Insert new brain to continue. (A)bort, (R)etry, (F)ail

Vor 3 Tage## Transposed Tesseract

Coming back to this video after 8 months while actually studying Lotka-Volterra population growth models and bifurcation as part of our mechanics course, and it just feels incredible!

Vor 3 Tage## Jay D

Maybe these mysterious constants are a result of the dynamics of the collapsing wave function you have a video on? Should be a connection shouldn't there? Heck, maybe its a default value to conserve the computations of this simulation we are\are not living in.

Vor 3 Tage## Starseeker

14:40 If he said that the number of B/A was the golden ratio, AGAIN, I would have blown myself up...

Vor 3 Tage## My Name

man i love this

Vor 4 Tage## Carlos Von Doom

Get a bb rifle. Problem solved.

Vor 4 Tage## Alice D.

I came for the science - I stayed for the architecture.

Vor 4 Tage## Rosie Otis

I should have paid more attention to Mr. Blomgren, and less time drawing Whitesnake logos.

Vor 4 Tage## voovoovoodoo

Brb gonna go look for chaos theory in my piss

Vor 4 Tage## YA BOI REPTAR

woah *it didnt*

Vor 4 Tage## Dylan Walker

Great video. I must ask. After studying the madelbrot set for sometime, there are many repeated patterns in the madelbrot set; so wouldn't it be possible to predict an outcome by observing repetitiveness? I mean, there is so much repeating in nature and in the madelbrot set that it can't be ignored. Please correct me if I am wrong but I am pretty confident that repetitiveness is one major feature of chaos theory and that repetitiveness may actually give us insight into the future.

Vor 4 Tage## A Normal Platypus

ok this showed that math is actually really cool and interesting... when you understand it

Vor 4 Tage## zain m.

God Job man!

Vor 4 Tage## James Cullinan

I remember this from my lectures with Prof Alexei Pokrovskii in University College Cork.

Vor 4 Tage## Green blue

Math never gets into my mind

Vor 4 Tage## Farhat Sharif

Does anybody know what software is he using to graph?

Vor 4 Tage## blanche xxx

tsss!!

Vor 4 Tage## Tarun

R.I.P to all my 1729 brain cells :)

Vor 4 Tage## Outsider Gameing

Damn, God really was bored in quarantine

Vor 5 Tage## wj goh

Feigenbaum proves mankind's inability to affect global climate control WITHOUT a major single point event. Even geological variants can be explained by this cycle. Take time to use this theorem with the covid numbers. Nature, physics and mathematics work hand in hand. people are math illiterate, this is why they operate on emotion and buy into chaos.

Vor 5 Tage## Andrei Stanciu

I would like the name of the song at 14:03 because I couldn t find it

Vor 5 Tage