Veritasium - 2020-01-29
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: https://www.fasthosts.co.uk/veritasium Code for interactives is available below... Animations, coding, interactives in this video by Jonny Hyman 🙌 Try the code yourself: https://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). https://doi.org/10.1038/261459a0 Robert Shaw, The Dripping Faucet as a Model Chaotic System https://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). https://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. http://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: https://epidemicsound.com "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4" https://ve42.co/Artlist "Busy World" "Children of Mystery"
When you turned the Mandelbrot on it’s side to show the bifurcation, I’ll be honest, it blew my mind.
It was quite beautiful to see the real number line graphically perpendicular to the complex numbers
Can someone post videos of Mandelbrot fractal zooms from and angle??? Ive only ever seen STRAIGHT ON ZOOMS.
Can we get a super awesome angle zoom with directional changes!?!?
It blew my mind as well. I've written programs for the Mandelbrot set many times and never paid attention to the actual values that the members of the set stabilized on. I'm going to have to play with that!
if only he had put the axis
Yup
"I'm so excited about chaos" -man one month into 2020
@Sku11zthere u did it
@Sku11z cant u see his name consists the word "priest"
2020 well this didn't age well
@Starry Epidemic25 so what. He wanted to know, watchu gonna do
Sounds like heresy to me... the Inquisition will get in touch shortly.
"Its the simplest equation you can make"
well alrighty then
Haha yep… and I just realized I am even dumber than my original assessment.
Do you speak English!
Saw sus whe. N he said it lol
0=0
the
The 3D Mandelbrot looks like a bunch of pringles... maybe I’m just hungry
my understanding is that you find Mandelbrot in bunch of pringles. Or in your hunger. Or in my fascination and understanding of the topic or text i wrote.
wow, I didn't notice that before, but you are right, it does look like pringles XD
yeah math is cooler when you are high
Fun Fract: Mathematicians have designated the Pringles stacks for the period 7 bulbs as Honey BBQ flavor.
I'M NOT THE ONLY ONE!!!
So basically like when the bass drops, the tempo keeps doubling until it just goes into complete madness.
@GetMoGaming frequency = 1 / period in systems that have a frequency and a period. If the frequency doubles the period halves; if the period doubles the frequency halves. That's the situation for oscillations in linear systems. In non-linear systems all sorts of strange things can happen, which is why the word 'chaos' is used in the extreme case..Chaotic systems exhibit extreme sensitivity to initial conditions. Start two such systems, made as identical as measurement will allow, running at the same time and the tiniest difference between them rapidly causes them to get wildly out of sync. Numerical simulations get out of sync with themselves, unless infinite precision arithmetic is used, for which you'd need an infinite computer.
But, hey, it's nearly 40 years since I worked and published in this area and I'd now have trouble dredging up explanations of Smale Horseshoes and other goodies off the top of my head (to mix metaphors).
@GetMoGaming You've probably plucked a string which needed changing, though; I know I sure have! lohl...
Consider plain, unwrapped guitar strings, whether nylon or steel or a cobalt alloy. There will be microscopic imperfect distributions of mass, and inclusion of imperfections. The anchors at the nut and bridge are irregular at a microscopic level. Plucking a new, high-quality string on a high-quality guitar will create a sine wave, unless you zoom in -- WAY in -- to see the effects of the imperfections. Of course, there are imperfections in the measuring equipment which show up under magnification.....
Buddy, this blew my frickin mind
Timbre and registration have nothing to do with constancy in tempo . Beat only changes if players change it . Pitches go up and down anyways all he time . Obviously you're not a musician & that's ok . But You've never heard real music like Boulez 2nd Sonata !
Good point, rightly pointed out.
“A common man marvels at uncommon things. A wise man marvels at the commonplace”
@jason prevo I didn’t craft that quote, it’s by Confucius lol
@ahmed almerza guess it can't be lame then?
@ahmed almerza So what? You are misusing that quote. And where is your proof confucius ever said that?
@jason prevo Wise person sees uncommon things in the commonplace
Woah ! Well said.
I wish math was taught this way when I was a kid. We did a lot of one thing at a time (sausage stuffing, as we call it in Sweden :), but never got the explanations of their relations and that you can express something in many different ways with graphs, trigonometry etc. Granted, I chose the humanities side of studies later on; but if my teacher showed that an equation can be found within the Mandelbrot set or how you can represent it in many different ways, I think it would have created a lot more interest. This was a couple of decades ago, but still I wish my teachers had just scratched the surface of what lies beneath the "repeat this type of equation until your eyes bleed".
Time to go out and shout at kids about how things were better yesteryear and that we only had tape recorders to store data on and 8-bit consoles. And, of course, that we walked 8 km either way to school, uphill in both directions with snow all year 'round.
math teacher usually sucks at their major
You're also expecting the teachers to understand this subject and teach it. Unfortunately most teachers just regurgitate what's in the "teachers manual"
@Arthur Nall I have a couple of friends who are teachers, and the level of education they have to reach to be "certified" is way above what they teach. I guess it's a question of enjoying your work. You are definitly on to something though; the difference between an Office space-type and Dead poets society teacher is quite broad :) Also, at least locally, the work of education is relatively low paying. I'm probably naive in thinking it should be a kind of important thing no matter if the school is private or public. Money, money, money.
But now it's time to go out and tell the kids of today how we used to play with twigs and cones; and we had so much fun! They don't know how good they have it today... mumbles about the price of milk
The real truth that they don't tell you is that 99% of math in school is building up to one thing ... and that is Calculus. It's this that is important above all and gives you 99.9% of the things you have in the world. That's the main connection/secret that is missing.
I wish the same. I wish I had these videos when I was younger.
Me: So everything was just the Feigenbaum constant?
Veritasium: Always has been
"It is the first method for Generating Random Number in Computers"
Me : "Ah yes, the Ancestor of Gacha system"
Once the video reaches a certain rate of complexity, our brain starts to understand only periodic parts of it. Until it's all chaos and you throw your phone away.
At a rate of 4.669
😂
At this point I’m scared this might actually show up in a graph if someone were to experiment
work for larry david. seriously.
on end he was talking about chaos ,so somehow you understood ;p
When I was setting a router I realized that the logistic diagram is related to the velocity of download and upload of internet, and for low velocities you can how it start to separete into two states and when you reach a few gigas per second of velocity it is caos
Id be really intrigued to see the this chaotic nature of the Figon constant in music structure. It reminds me of the recent discovery of a quaternion system in natural octaves, which reveals a periodic pattern of fundamental constants found in nature. Really cool stuff!🤓😊
Uh huh uh huh... Yes.. Yes I see it
ah yes, this formula is a perfect description of what my level of motivation is. Just let the time be representing by minutes instead of years.
Every single video I watch I end up yelling "no wayyyy" or "that's crazy"
Thank you for making these and teaching so brilliantly well
Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.
@Amit Rana you bring shame to your famery!! Shame on yuu!
Crazy image looks like a mammogram
@Reach 3D Printers I've been trying to do this for 3 months but I'm dumb 1:19 space over time
@h b So is trimming your hair or beard.
@Sammy Williams Yeah, its beyond me.... though bob wood above mentions the video actually is in a way, as the viewer orbits, you could consider the set being giving a variable that rotates it on its axis, and so the set rotating is a permutation.... though I was kinda thinking about one that grows... though, that might just have the effect of enlarging it, making it feel like the viewer is zooming in.
Im not that skilled in maths, Im more of a visual arts guy.
Veritasium: looks hears fosset dripping my god, this is utter chaos
I’m convinced this is the best channel on YouTube. Absolute gold. Keep it up!
VSauce 1-3 be like >:(
I'm reading through James Gleick's: chaos, and this really helps me understand the more convoluted aspects.
Btw I completely recommend it too. It's written like a philosophical detective novel at some parts and I never expected to be so enthralled by old crazy German men. I stan Mandelbrot, his deva nature, and his dimension hopping yarn ball.
I'm convinced my schooling was all in preparation for this moment, watching this and eating Jack in the Box
Why does the Mandelbrot set look like a Crab? Could there be a relation between carcinisation and the Mandelbrot set?
Everything returns to crab
Even Geometry
@Ahmad Rino abandon humanity, grow to crab
crab people
🦀Mandelbrot is gone🦀
Interesting video! The only thing I really understood and remembered is that they designed a true random number generator. Which in itself is pretty amazing
I have been watching selections from your gallery one after the other and I have to say this has been a wonderfully confusing form of enlightenment that in the end was digestible. I struggle to think of how much any of it lends itself to practical application but that shouldn't suggest it isn't valuable outside the context of being both a beautiful example of applied theory and genuinely fascinating on it's own merit.
As a simple example, Mandelbrot was studying noise in communication lines when he created his equation. Phone lines are clearer because of this. Fractals are used in your cell phone antenna. We are just beginning to understand the potential of this math applied.
Watching this after reading Taleb's "The Black Swan" reeeeeeallly hits the spot with the Mandelbrot set.
"Oh cool, the Mandelbrot-Set. I have seen that before."
turns Mandelbrot-Set in 3D
"What the ...?! That's illegal!"
If you have a 6DoF VR headset, you can go visit the fractal explorer world in VR-Chat. Lets you fly through a shifting mandelbrot fractal as if you're really there.
that's where the aliens from Vega embedded their instructions for a machine that can take us to other worlds
yeah.....
I had the same reaction
I still don't know what an almond bread has to do with maths.
Interesting, thanks. One thing is the assumption that x (which has to be between 0 and 1 to get the formula converging) is a percentage of the maximum. Which maximum?
I, a Neanderthal, showing this to my Neanderthal friend:
“Isn’t that crazy”
“Yeah—I mean, wow.”
“Yeah”
“Math is...Crazy”
“Wow”
“Yea”
@Doc. Manhattan i just clicked on show answers to see if someone actually wrote this and here we go
@Doc. Manhattan Ikr, but popular culture portrays them as dimwitted which is inaccurate
@choggerboom considering mathematical intelligence in modern humans has been linked with Neanderthal DNA, probably. yknow, when they weren't busy with the whole surviving an ice age thing.
yèh
wòw
I read netherland friends and was so confused
Letting Feigenbaum be Feigenbaum for a moment: this is an incredible house with spectacular views!
This is the most significant video by Veritasium. A strong connection between the logistic map, chaos and fractals. Many deep implications. Beautiful!
It's like discovering some of the software God used to write the Universe.
I think it is
@GreatBriton ur a great person, idk
@GreatBriton omg I wish I was as articulate as you because you described what I’ve been telling people for years but like waayyy better lol. I used to get scared during those pausing of knowing what the person would say because I would think what if I sayed something that I didn’t expect to happen. However, every time after the realization of these events that I could possibly change how they went. It would just be me trying to change it but I knew exactly everything still and nothing really changed. People say this is deja vu but I think deja vu is different from this experience. Deja vu is more of a familiar kind of vibe. What you described it more of a clairvoyant type thing. Knowing every single thing that is going to happen Down to the tea is not like deja vu.
@GreatBriton oh so you actually thought you could change it! In my experience when I would try to change whatever was happening. I would just end up saying everything I thought would change it but I still knew I was going to do that in the end.
@Max LohI’m commented to you and Great Britoin. Don’t you see that contradiction is already apart of our universe and may be apart of all things because it seems that randomness is more common than initially thought. I like that you say disprove and prove because that is true. I think that since randomness and contradictions are natural in the universe then that’s probably what state our consciousness is in. Always deciding not deciding or neither. So I guess I agree with what you were saying more Max.
"i'd rather watch the kitchen tap drip" makes a bit more sense now🤣
Finally, he steps out of the "Cone of Silence" to expose Chaos....
My God this was a good video! Honestly, everything you make turns to absolute gold. Loving the channel lately! 🔥📚❤️🤩
It´s one of those videos i would literally like to put it in a frame to hang it on a wall in my living room! It shows the true beauty of our world!
I am a mathematician, and I do study phenomena associated with the Feigenbaum constant. You did justice to the topic! Excellent video!
It's like discovering some of the software God used to write the Universe.
@Leif the faster you go, the harder the brakes, in effect. old UK duffer here, hopefully not confusing you further :)
@Christian Mathison shut up m9ron
@Leif because that term will always evaluate within the range of zero to one. So. As x gets close to one the (1-x) term approaches zero. As x approaches zero the (1-x) term approaches one. It is what changes the equation from a simple exponential growth equation into a logistic equation.
@Brad scott
That's how I see it
I learned about this in my high school biology class.
You were lucky to have a teacher to teach it and even luckier if you understood it!
Fantastic video, your ability to clearly explain something that I think looks like utter madness astounds me. Though I do feel like a bit of a smooth brain when you talk about that being a "simple equation" and I'm sitting here as a 33 year old man who can barely do most simple multiplications without a calculator lmao.
I studied these mathematical sets in the eighties. Also the Hénon attractor and other chaotic and fractal maps.
Poincaré maps of double pendulum is also very interesting.
The Mandelbrot set looks scary to me. All fractals look scary. I have the feeling to fall and drown in it's complex landscape.
At the first bifurcation, the graph looks like the pressure-temperature plotting of entropy as in a Moliere diagram!
"How did I get to be 37 years old without hearing about the Feigenbaum constant", thank you for lowering that bound to at least a 24 year old. Your videos always leave me inspired!
Seriously I’m 43. Heard the name. But never learned about this. Great stuff.
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I'm 66. I only just heard of it!
Watchin it from seminiferous tubule
Escape to the Hollow Earth
https://www.youtube.com/watch?v=C1XzncjIj2s
i want the bifurcating Mandelbrot as one of those laser etched glass cubes
I've been playing with fractals since Fractint first came out almost 30 years ago... I have never seen the Mandelbrot Set flipped up like that. Amazing demonstration.
Love this! I happen to be friends with one of the scientists who did the salamander work (Crevier) and he was just as excited as you were explaining how it linked to this equation.
"chaos theory"
ahh the chaos again
doing its misdeeds even before the holy imperium
Math is heresy
The emperor protects
Amazing. It must be interesting to monitor this on Bose-Einstein condensate
perfectly explained, i was able to score an A in my kindergarten exam
I have goosebumps when you start to explain from faucte's point of view.
Thanks for this! Just read the Chaos book and this helped me understand some things
The Mandelbrot Set in 3D is probably one of the coolest things I've ever seen
About 15 years back I wrote a script in C++ which when interfaced with Autocad built the Mandelbrot in 3-d. I had to build an extremely powerful water cooled PC (much like they use for Bitcoin mining now - or at least they did a few years back).. I managed to take it to 37 Billion iterations, I was 3 Billion off the world record at the time, but my CPU overheated and melted down through the floor into the apartment below. But hey, the girl who lived below just happened to be a hottie and she's now my wife... so I guess the Mandelbrot DID change my life !!
Thanks for the suggestion. 😳
@Jonny Rocket wow!!!u are awesome man😯😯😯😯
@erteple it... Basically is lol
The big part looks like the peach emoji 🍑
The difference between order and chaos is our scale of comprehension. Larger scales require more time for us to wrap our minds around the complicated order.
Austen Alexander - 2020-02-01
Me: struggles with elementary algebra
Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram
Me: go on
ZayTaz - 2021-08-01
I'm going to learn elementary algebra this year in my school, i know expressions should make things easier but for me it looks more complicated -_-
ウサコフスキーキリル - 2021-08-01
@Nick Reed Our school had math branch to algebra and geometry in 5th grade
Dhonnano - 2021-08-06
Lol
Jack Schmit - 2021-08-07
Me: watches this and nods
Also me: how much is 15% tip on a 20 dollar bar tab?
tommytigerpants - 2021-08-10
Whyyyyy am I like this!?