This equation will change how you see the world (the logistic map)

  • Am Vor 8 Monate

    VeritasiumVeritasium

    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"

Tater Tot
Tater Tot

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

Vor 2 Minuten
Daan Sijbrandij
Daan Sijbrandij

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

Vor Stunde
Gerardo Guzman
Gerardo Guzman

steve harvey

Vor 9 Stunden
Ralf Baechle
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
Jaden Schulz

yeah none of that made any sense sorry mate

Vor 10 Stunden
Phillip Carr Manchester Mint Crypto
Phillip Carr Manchester Mint Crypto

I’ve a theory on this Tao

Vor 10 Stunden
Basketcase642
Basketcase642

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

Vor 12 Stunden
GcMaf cures ANY CANCER
GcMaf cures ANY CANCER

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

Vor 13 Stunden
j'accuse
j'accuse

jesus christ

Vor 13 Stunden
sascuash96
sascuash96

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

Vor 16 Stunden
Peter Dümpel
Peter Dümpel

"That's so cool!" - The channel

Vor 16 Stunden
Giulia Emanuelli
Giulia Emanuelli

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

Vor 17 Stunden
Markus
Markus

they should teach this in school

Vor 18 Stunden
Nyaaa UwU
Nyaaa UwU

I want to test heart beat map on my science teacher

Vor 18 Stunden
Relativity
Relativity

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

Vor 20 Stunden
Jakob Reece
Jakob Reece

0:01 huh

Vor 21 Stunde
Laurent Alvaro
Laurent Alvaro

Pure magic...

Vor 22 Stunden
bhavya
bhavya

this is my favorite veritasium video

Vor Tag
BP STREAMS
BP STREAMS

r=i p rabbits

Vor Tag
The flying Mylle
The flying Mylle

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

Vor Tag
Sid Stevens
Sid Stevens

So, even in extreme chaos, symmetry still rules ?

Vor Tag
tigr312012
tigr312012

This looks connected to Wolfram project researches

Vor Tag
Diggity doggo
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
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
Pace

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

Vor Tag
Howard Zhang
Howard Zhang

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

Vor Tag
Julia Gregory
Julia Gregory

What the heck? Chaos has a pattern in nature.

Vor Tag
Julia Gregory
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
Xyrus Mallare

Thanos: That puts a smile on my face.

Vor Tag
D V
D V

Finger prints from God.

Vor Tag
MrPotatochips4
MrPotatochips4

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

Vor Tag
Ost san
Ost san

That sponsored spot did not age well....

Vor Tag
Ange Purs
Ange Purs

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

Vor Tag
CloudCalmaster
CloudCalmaster

This is when u find out about fractals without LSD

Vor Tag
SUMIT MANDAL
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
Lieutenant Lubricant

We live in a computer.

Vor Tag
mat gof
mat gof

Why why why why why why why why why why?

Vor Tag
Ben Lewis
Ben Lewis

How are visualizations made?

Vor Tag
Kenneth Rector
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
Ekito

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

Vor Tag
Kenneth Rector
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
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
theblankuser

4.669

Vor Tag
Aaron Levy
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
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
The_VR _MD

So frikkin' cool

Vor 2 Tage
Tim A.
Tim A.

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

Vor 2 Tage
Christopher Robertson
Christopher Robertson

i got lost at 2

Vor 2 Tage
Albert Ochoa
Albert Ochoa

Fascinating

Vor 2 Tage
Welsh Family Vlogs
Welsh Family Vlogs

4

Vor 2 Tage
Konstantin Lookeen
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
JT

Too many errors in the presentation.

Vor 2 Tage
JT
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
BangDroid

List some, even one

Vor 15 Stunden
Steven Tarsitano
Steven Tarsitano

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

Vor 2 Tage
BangDroid
BangDroid

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

Vor 15 Stunden
Felix Scharnberg
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
Huey Edjec

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

Vor 2 Tage
Scott P
Scott P

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

Vor 2 Tage
Akif T
Akif T

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

Vor 2 Tage
joel osuna
joel osuna

How come there is chaos if there is a constant

Vor 2 Tage
Mister Gunsen
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
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
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
wh3resmycar

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

Vor 2 Tage
Cody S
Cody S

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

Vor 2 Tage
N. J.
N. J.

Does this apply to humans too?

Vor 3 Tage
Delacroix Wang
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
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
Giselle Cole

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

Vor 3 Tage
mel obrien
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
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
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
BangDroid

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

Vor 15 Stunden
Closeup Channel
Closeup Channel

Or the spread of viruses...

Vor 3 Tage
Gin
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
Phos9

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

Vor 3 Tage
blue beam
blue beam

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

Vor 3 Tage
Neena Plant
Neena Plant

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

Vor 3 Tage
Ayberk Aydin
Ayberk Aydin

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

Vor 3 Tage
RedShipsofSpainAgain
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
Eric M

Dude has a nice house.

Vor 3 Tage
24063457467984263567
24063457467984263567

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

Vor 3 Tage
RIPxBlackHawk
RIPxBlackHawk

This answers my question about hair growth

Vor 3 Tage
William Haisch
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
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
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
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
My Name

man i love this

Vor 4 Tage
Carlos Von Doom
Carlos Von Doom

Get a bb rifle. Problem solved.

Vor 4 Tage
Alice D.
Alice D.

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

Vor 4 Tage
Rosie Otis
Rosie Otis

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

Vor 4 Tage
voovoovoodoo
voovoovoodoo

Brb gonna go look for chaos theory in my piss

Vor 4 Tage
YA BOI REPTAR
YA BOI REPTAR

woah *it didnt*

Vor 4 Tage
Dylan Walker
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
A Normal Platypus

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

Vor 4 Tage
zain m.
zain m.

God Job man!

Vor 4 Tage
James Cullinan
James Cullinan

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

Vor 4 Tage
Green blue
Green blue

Math never gets into my mind

Vor 4 Tage
Farhat Sharif
Farhat Sharif

Does anybody know what software is he using to graph?

Vor 4 Tage
blanche xxx
blanche xxx

tsss!!

Vor 4 Tage
Tarun
Tarun

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

Vor 4 Tage
Outsider Gameing
Outsider Gameing

Damn, God really was bored in quarantine

Vor 5 Tage
wj goh
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
Andrei Stanciu

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

Vor 5 Tage

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