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 https://www.youtube.com/watch?v=Gao-DHIyj0Q&ab_channel=WhiteBatAudio https://www.youtube.com/watch?v=2gsn1HrDtdI&ab_channel=WhiteBatAudio https://www.youtube.com/channel/UC_6hQy4elsyHhCOskZo0U5g LAKEY INSPIRED https://soundcloud.com/lakeyinspired https://www.youtube.com/channel/UCOmy8wuTpC95lefU5d1dt2Q Phil Lober https://www.youtube.com/@MusicOfPhil https://www.youtube.com/watch?v=vj_tauJsURI&ab_channel=PhilLober References Chaos: The Mathematics Behind the Butterfly Effect - James Manning https://www.colby.edu/mathstats/wp-content/uploads/sites/81/2017/08/2017-Manning-Thesis.pdf YFX1520 Nonlinear Dynamics Lecture 9 - Dmitri Kartofelev https://www.ioc.ee/~dima/YFX1520/LectureNotes_9.pdf Attractors: Nonstrange to Chaotic - Robert L. V. Taylor http://evoq-eval.siam.org/Portals/0/Publications/SIURO/Vol4/Attractors_Nonstrange_to_Chaotic.pdf?ver=2018-04-06-103239-977