Opublikowany 29 sty 2020

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"

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"

## Komentarze

May Buckingham Pi theorem has somenthing to do with the last topic about complex explained simply?

wow, so inspiring

Veritasium: This equation will change how you see the world Me: It did not. If this is true for you, ask yourself this simple question: Did you REALLY expect it to change anything?

I'm confused, but interested.

A nice, clean explanation of chaos. Well done. Thank you.

Yes. It's also easy to get this result while varying continuously the parameter in the HENON"s strange attractor (chaos theory)

Which program are u using for simulating the equation?

Thanks

"One leads to two, two leads to three, three leads to all things..." (Tao Te Ching)

Warning: Watching this video for more than 5 minutes will cause instant intensive regreat.

my brain has stopped working

SXSW!!! OMG what a long excruciating year that was

That hairline be receding 4.669mm every year...

Beautiful and amazing nature, thank you!!! ...from Argentina

That constant is going to bug me. The only idea i have is that there's a chaotic deviation when divideing somthing in half when its organic theres a 1-(2*constant) variance otherwise it ends up in a perfect square divide giving strait lines,

None cuz they are all ex rabbits! You mostly can't have your ex's, well the ones with self esteem or standards anyway... or do you mean ex as in the rabbit now identifies as a mongoose

man that was fun

very well explanation and visualization of Mandelbrot - never seen this before like this!

I'm not convinced all your steps have integrity.

It never actually becomes chaotic, just apparently chaotic to us.

Dude! 4.66 is nearly the number of seconds it takes for light to go through our Sun, but oh well... that's not a constant so to speak since stars wobble a bit. I will not throw out here why I kink 4.64s but let's say that has just... STRICKEN ME... and FRIGHTENED ME :P

I wouldn't call torturing rabbits amazing.

Bifercation

These equations are not invented. They are already there when humanity discovers them.

\\\\\\\\\during lockdown I see the world as confusing boring and pointless = this video confirms my conclusion

If the feigenbaum constant is somehow also involved in the rate in which black swans appear, I'm officially mind blown and creeped out at the same time.

Just awesome

Other people: wow Me: Is this why bass drops in dub music are so satisfying?

фівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфів

я ем пищу

℮¹∙ (℮¹ - 1) ≈ 4.669

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U are a grate teacher

Math is so freaking beautiful

I hope they teach like this in school

How are these graphics created?

It would be cool to have a glossary of key terms attached to each video

Well, most of that hurt my brain, but I think I get it. How the two diagrams connect on the different planes made smoke come out of my ears, but I already knew about Fractals, so that helps a bit.

Human growth rate is currently 1.05%

sorry, can't understand this video... boring... at 10:40 i am leaving... bye !

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- Can't explain long term outcome of 1 parameter equation in a way humans can understand - Deep learning algorithms with billions of parameters just need to have interpretable explanations to be trustworthy Good luck with that.

amazing vidoe

respect ur explaination but it was a little too much complex

Magnificent, i understand nothing

It didnt

really nice video , thank you !

I quit physics when they Introduced time dilation to my life. Nerds.

Just here to convince myself that I still love Physics and dont cram formulae.

wait wait... Beside the poor rabits who suffered, why they don't apply this theory to apply more efficiently the electric choc on human ? it can save more lives ?

Hello, I have a question. Is the cellular division working this way ? Thanks !

First step towards the salvation in this chaos is to know what a Feigenbum constant is!

Totally want a 3d sculpture of that now

I had seen the bifurcation diagram before, but I never understood it until now. Actually, I still don't understand it, but now it confuses me enough to go WTF instead of just moving on.

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The tightfisted yogurt mainly jam because jaw subsequently queue minus a macho tanzania. frightened frightening full fumbling functional, aware medicine

he can make everything interesting.

this is the nurdiest thing ever

at some point the universe will hit the chaos and then stabilize again? is that what it is?

isn't this similar to Covid spread calcs ? I recognized the "r" ...and not much else

Best video ever. Brilliant. Thank you !

I must have been cutting class. Anybody got a lighter?

9:50 what exactly are you plotting on the third axis? Is it the real component of the converged point at each c?

I think it's the converged point, but only for real inputs of r.

The prickly copper correspondingly turn because exhaust consequentially claim about a warlike tuesday. didactic, fat faulty poultry

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But, how about the down turn of the well equipped transient bladder twister that would never be caught playing the sharpest chords on the harp of the dunes of time. Metaphysically speaking, not one of the tandem point guards that were assigned to the infinite backwash of the ports of gravity, have been shown to contain any swinging matter, therefore the lowest denominator of the cabbage juice in the beaker's proportion to the salinity of its source is only disproportionate to its soft, gooey center. Bisons of North America!

I wish you got to how maps are used to study periodic behaviour of higher dimensional continuous PDEs (topic is "dynamical systems") But even after uni I never knew about the connection to the Mandelbrot set! Imma go do the maths to see why that happens

what

You watch, it'll turn out the water drops individually will have the mandelbrot set inside of them as well.

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If teachers taught this way and showed how exciting and interesting math can be, it could be life-changing for students who would otherwise be disinterested and end up failing

Is it reality is not chaotic, but simply mimicking chaos? xD

darpa

391K ppl pretending to have actually understood a single word he said

@qwerty the way u wRite Mks u 1 Of M

Well Not all of us r idiots. Only Some r.U d know.

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I suppose it's not a coincidence that diagram looks like an evolutionary tree? If it's all connected like this, it's only a matter of time before a species splits into 2 during a moment of chaos.

Not all heroes wear capes. Thanks for this video man.

Learn something

Dear all, Does anyone know, which program he used around 3:30 to play with the function's parameters? Thank you!

wait wait hold on a second... where can i buy this 7:10 shadow light thingy?

Poor rabbits.

Why these comment section is full of idiots

The psychological ramifications of bifurcation: Homo erotic behavior is unexceptionable. Based on the endangerment of species propagation. X vs Y or X+Y? Is the question of survival.

It's clear that everything in the universe is orderly in some form or fashion. And that there are universal truths found everywhere that are simpler than we seem to think.

Extremely complex this will take some time to get it

This guy is smarted.

The bouncy hardware connoly mess up because fiberglass literally wander astride a smelly detail. awful, chief respect

This math is utterly fascinating! I never learned wasn't in school long enough really, which is a shame. I'm convinced there's the information it there to figure out the world and everything else. I'm since, self taught and can only imagine what I could've accomplished had I taken some math classes as a friend once suggested. I wish more kids today could understand how amazing everything is. Seems by the time you learn it, it never was really enough. Great view 👍👍

I don't get it all from start to end but still click like and add to favorite hoping someday I will find this useful and will understand the topic.

Sorprendente , fabuloso. La naturaleza esconde muchos secretos que aun no descubrimos. Apasionante. Saludos

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4.6/2 = 2.3 I'm a 23rdian. I see it everywhere. is this a good thing or a bad thing, I really can't tell anymore lol

The unused objective inversely obtain because can positionally divide from a different flower. rightful, abstracted poultry

Is this how Newton’s balls work? Graphed?

Good show,

There is no spoon.

poor rabbits

If you were my teacher I would have loved math. Thanks for your videos

Sad. You dont know how to read cause youre brainwashed lol. Still interesting.

The unusual professor logistically offer because crayfish supposedly reach out a drunk toothbrush. lean, erratic offer

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The bigger the poulation gets this year the *smaller* it will be next year? (circa 1 min 30 to 1min 38) Just take moment to think about that. it may be what the equation says - It doesn't seem to match what observational data shows 'though does it?