 or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable - two different initial conditions that are very close together can end up arbitrarily far apart.
Music from https://epidemicsound.com "The Longest Rest" "A Sound Foundation" "Seaweed")
Captions provided by CCTubes – Captioning the Internet! Chaos theory means deterministic systems can be unpredictable. Thanks to LastPass for sponsoring this video. Click here to start using LastPass: https://ve42.co/VeLP
Animations by Prof. Robert Ghrist: https://ve42.co/Ghrist
Want to know more about chaos theory and non-linear dynamical systems? Check out: https://ve42.co/chaos-math
Butterfly footage courtesy of Phil Torres and The Jungle Diaries: https://ve42.co/monarch
Solar system, 3-body and printout animations by Jonny Hyman
Some animations made with Universe Sandbox: https://universesandbox.com/
Special thanks to Prof. Mason Porter at UCLA who I interviewed for this video.
I have long wanted to make a video about chaos, ever since reading James Gleick’s fantastic book, Chaos. I hope this video gives an idea of phase space – a picture of dynamical systems in which each point completely represents the state of the system. For a pendulum, phase space is only 2-dimensional and you can get orbits (in the case of an undamped pendulum) or an inward spiral (in the case of a pendulum with friction). For the Lorenz equations we need three dimensions to show the phase space. The attractor you find for these equations is said to be strange and chaotic because there is no loop, only infinite curves that never intersect. This explains why the motion is so unpredictable – two different initial conditions that are very close together can end up arbitrarily far apart.
Music from https://epidemicsound.com “The Longest Rest” “A Sound Foundation” “Seaweed”
