Chaos Theory: the language of (in)stability

The field of study of chaos has its roots in differential equations and dynamical systems, the very language that is used to describe how any physical system evolves in the real world. This video aims to tell the story of chaos step by step, from simple non-chaotic systems, to different types of attractors, to fractal spaces and the language of unpredictability.
Timestamps:
00:00 - Intro
02:17 - Dynamical Systems
04:11 - Attractors
06:28 - Lorenz Attractor: Strange
08:54 - Lorenz Attractor: Chaotic
Music by:
Karl Casey @ White Bat Audio
• 80s Horror Cinematic T...
• Cyberpunk Dark Synthwa...
/ @whitebataudio
LAKEY INSPIRED
/ lakeyinspired
/ @lakeyinspired
Phil Lober
/ @musicofphil
• Phil Lober - Igneous
References
Chaos: The Mathematics Behind the Butterfly Effect - James Manning
www.colby.edu/mathstats/wp-co...
YFX1520 Nonlinear Dynamics Lecture 9 - Dmitri Kartofelev
www.ioc.ee/~dima/YFX1520/Lect...
Attractors: Nonstrange to Chaotic - Robert L. V. Taylor
evoq-eval.siam.org/Portals/0/P...

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Me too

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I fainted.

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As a graduate student in Mathematics with speciality in (infinite dimensional) dynamical systems and differential equations, I must admit this has to be one of the most beautiful videos on the internet about this topic!

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I google the topic with filetype:pdf at the end

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@@Gonkee so research papers mainly?

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@@SYBIOTE Research papers are sometimes very dense. However, you can find many tutorials and introductions online. For instance, he nicely summarized a part of what you would get in a course in nonlinear analysis.

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where does the 6 come from? I would have expected 13x3*45

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This video explained this concept so well. Thanks a lot man :)

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How did you animate the slope field at 2:08? My guess is manim but I'd be curious to see if there are other options.

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Chaos theory is very interesting

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Such a beautiful explanation !!

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What software do you use to make these BEAUTIFUL animations?

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He could be using manim, the software developed by 3blue1brown: github.com/3b1b/manim

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In his video about epidemiology - kzbin.info/www/bejne/rqTQh2mFnpaebdE He answered someone - "I'm writing my own graphics library with Java as I make these videos, which uses LWJGL and NanoVG." Edit: Thanks @LimitedWard, I was actually searching for this!

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It isn't difficult. For the dual Lorenz animation around 8:00 I wrote a program and you can get it free here: www.fractal-animation.net/progz/filez.html .

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nice summary of Chaos. Thank you

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