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

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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/ShawRober...

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:01... . 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"

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28 Oca 2020

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YORUMLAR 25 972
Daniel Smania
Daniel Smania Yıl önce
I am a mathematician, and I do study phenomena associated with the Feigenbaum constant. You did justice to the topic! Excellent video!
Hidde
This concept is actually taught in engineering. Particularly in Control Engineering. It's taught because it gives a lot of intuition in nonlinear differential equations. These differential equations occur quite often in nature and in engineering problems when you have to model the dynamics of a system!
janki prasad soni
Me: That was fascinating and mind blowing.
jemert96
rotates the Mandelbrot plot
Sara Ashley
I love that you mentioned that things like this should be taught to students. I completely agree!! Topics like this are why I started to be so interested in mathematics.
Wackeydelly
The reason that the bifurcation still happens when you change xn(1-xn) to sin(xn) is because that technically is your initial condition. The rate (r) is really what is important because this is just a fancy exponential function written in recursive form. The only condition on the initial condition is that it needs to cross the x axis at least twice (polynomial or trig function). Try doing Xn+1= r(xn^2-.01)
BelgianBush Rc
BelgianBush Rc Yıl önce
I am intelligent enough to find this interesting but not quite smart enough to fully understand... Great video!
Karl Davis
I love how this converges to the VALUE of the Mandlebrot set at each point. I've often seen the drawing of where the set has valid values, but never thought about the values it holds in those areas.
Dale Leighton
I was taught about chaos theory in high school at Qld Australia. I am very grateful to have had the teacher that I did for both our Extension Math classes AND our Physics classes. Thank you Ian Spence. 👍
Hrishikesh Rai
I’ve been studying mathematics all my life in school. Now in college, I’m doing a triple majors degree and one of the majors is math.
Nathan Isaac
I love this channel, he explains stuff in a way that I can actually follow. I never would have understood anything like this were this to be taught in a classroom setting.
Matt
Hey there! Huge, huge fan of your videos. I've learned more from you than any teacher taught me in school, so thank you for that! Anyway, I was just wondering if you or someone on your crew still has the 3D renders for the Mandelbrot set you guys did. Or even just some high res images... And if so if you'd be willing to share them with me (specifically the one from the top of the "needle" where you can see those secondary variations in 3D) because I'd like to avoid having to deal with graphing renders myself and I've got an idea for a project I'd really like to try.
Warren Chinn
Warren Chinn Yıl önce
Magnificent. I am a 53 year old professional entomologist and this is utterly pertinent to invertebrate population biology. You state you are 37 years old in this presentation and I feel very humbled. Thank you for restoring my confidence in a world that seems bent on science denial, superficiality and facebook banality. Please keep up these exceptional presentations of important and complex concepts in nature, top marks !
Steve RGR
You seriously blew my mind with this! I have never heard of it so far, yet when you told me the first thing jumping to my mind was the wave pendulum experiment. Isn’t that also an example of the sudden reorganisation after a period of chaos?
Philip Crotts
Loved James Gleick’s books and Chaos is a great read. My favorite Math course in college was on fractals and chaos, learning about the Lorentz attractor, the Mandelbrot and Julia sets, and this equation about the period doubling bifurcation to chaos. Learning about fractal dimensions. Thanks so much for making your videos and keeping my love of mathematics going. Makes me want to look into chaos with all the other parabolic equations and check out feigenbaum’s constant.
Shot Logic
between James Gleick's "Chaos" and Stephen Hawking's "A Brief History of Time" I've taken on a whole new perspective and appreciation for the ways in which the universe does its thing and the mathematics that we use to describe said thing. They're honestly pretty easy books to understand, Gleick and Hawking really did write their work in everyday-vernacular.
Bruce Lawrence
So well done. A difficult subject made lucid with a great script and perfect visuals. Kudos.
Tcloud
I think if you increase the frequency of a sine wave enough you get something like this pattern too which is pretty crazy as well.
Tanvi Sharma
Tanvi Sharma Yıl önce
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.
Lyle Wells
Great videos! Great channel! I just discovered it and watched about 10 in a row. It is uncommon for me to revisit channels this much ever. Let alone view back to back. I rarely find anything with subject matter I find interesting and a narrator/host that doesn't bore me or get on my nerves. Very interesting with some information on almost every episode I was completely ignorant of. Which is nice and also rare. Especially the first 4-5 I watched which were all on mathematics. The incomplete episode Newton and this were my first 3 and I was hooked. I came back to comment here as this one stands out as one of the best for sure.
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