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 🙌
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.
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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.
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I think this graph also represents the evolution of human intelligence. 👉Think 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 didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s 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 😯😯😯😯😯😯. This is mind blowing
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 😅
"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 😂i'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 don’t 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 - MNred 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!? 😜 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?😁
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 🌳 grows lol cool
Seeeeriously fascinating!!!! 😲😲
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, 😒
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.
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
multiverse
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
Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.
THATS RIGHT!!! OH this got me so excited! :) Apply it to the cosmos and when a star releases energy to its surrounding planets. Chaos , adaptation to environment, then order but it evolves and branches out. The law of life. So many layers lol
13:44 oh god it's the zodiac killer
Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.
How do you guys come up with such things.
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mind blown and the day hasn't even started yet. thanks mate!
Order begets chaos, chaos begets order.
You adquired a new tittle: Chaotic (Neutral)
You just blew my mind.
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