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

Animations, coding, interactives in this video by Jonny Hyman 🙌

References:
James Gleick, Chaos
Steven Strogatz, Nonlinear Dynamics and Chaos

Robert Shaw, The Dripping Faucet as a Model Chaotic System

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

Xujun Ye, Kenshi Sakai. A new modified resource budget model for nonlinear dynamics in citrus production. Chaos, Solitons and Fractals 87 (2016) 51–60

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:

[AustenAlexander]

Me: struggles with elementary algebra
Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram
Me: go on

[tanvisharma]

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.

[brucefoote]

Your 3 dimensional animation of the rotating Mandelbrot Set graph conveys so very much information and complexity. Amazing!

[joekelley]

I've had courses in Algebra, Calculus and Trigonometry, but never really had these concepts connected to actual real-world phenomena, so it always felt very... mechanical, very transactional. If they incorporated these concepts into the teaching, I believe it would make it much more relatable during the process.

[ColorwaveCraftsCo]

The Mandelbrot Set in 3D is probably one of the coolest things I've ever seen

[Chord_]

"I'm so excited about chaos" -man one month into 2020

[zanityedpo]

When I was young, I always paid attention to my leaky faucets. I would mess with the flow since we were already wasting water, and I noticed this happening. Warms my heart to see it explained 💜

[falcxne]

For anyone wanting to study the math of this, I recommend Steven Strogatz - Nonlinear Dynamics and Chaos. That was the textbook I used in undergrad.

[entropy_]

Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.

[BAgodmode]

When you turned the Mandelbrot on it’s side to show the bifurcation, I’ll be honest, it blew my mind.

[maegodragon]

Only got to 5 mins and 18secs and already getting Heart Flutter! This video animations, graphing bifurcations, and the questions you pose prior to clear explanation is absolutely AWESOME! Thanks for the Thrills!

[BanditMatt]

Currently writing a report on chaotic behaviours and bifurcations, remembered this video existed and im so grateful now

[DanielSmania]

I am a mathematician, and I do study phenomena associated with the Feigenbaum constant. You did justice to the topic! Excellent video!

[feynstein]

Numberphile: Makes video about the Feigenbaum constant
Veritasium: Makes video about the Feigenbaum constant but includes the z-axis

[Sagitarria]

You really did a good job with this one. This is something that’s been fascinating to me for a long time, and there was even a point a few years ago when I was trying to explain to my mathematical friends, the connections between the logistic map and the Mandelbrot set and they didn’t believe me! This stuff seems so fundamental, but it doesn’t seem like it’s tot as a unifying principle when it could be. It’s just nice to see somebody acknowledge all of these different pieces of the puzzle so thank you and thank you for making some thing I can .2.

[Peace]

Thank you for making some fundamental mysteries of math/nature at least approachable if not fully understandable to the general public. Great job!

[youmaybebusy]

"Oh cool, the Mandelbrot-Set. I have seen that before."
*turns Mandelbrot-Set in 3D*
"What the ...?! That's illegal!"

[garfieldturismo]

Everyone here were gangsta till he turned the Mandelbrot-set 3D

[ainzulgone]

Who's here in 2024 after the 37 video and noticed he said 37 as a random example 😅

[jaianupamvarun]

I truly am humbled by the way you present such a complicated topic in such a simple way that even i who isn't a fan of mathematics got interested immediately 😃❤️💕