Wow. I haven't seen this channel before - definitely sub-worthy stuff. I really loved the music and the creative use of sound throughout. It's sort of psychedelic in a way.
Wow. I haven't seen this channel before - definitely sub-worthy stuff. I really loved the music and the creative use of sound throughout. It's sort of psychedelic in a way.
Amazing video! For those wanting to dip their toes into this type of math, the most approachable books I ever read on the subject was Nonlinear dynamics and chaos, by Strogatz. Can be read for the...
Amazing video! For those wanting to dip their toes into this type of math, the most approachable books I ever read on the subject was Nonlinear dynamics and chaos, by Strogatz. Can be read for the intuition alone, but working the problems will help if you have the requisite maths. His section on chaos is towards the end.
For anyone coming to the comments first looking for some kind of synopsis whiel out-and-about: This youtuber takes the angles and starting velocities of double pendulums (a pendulum with a second...
For anyone coming to the comments first looking for some kind of synopsis whiel out-and-about:
This youtuber takes the angles and starting velocities of double pendulums (a pendulum with a second pendulum hanging off the bottom) while they dangle around and he plots the data. The main visual contrast is shown between the double pendulums that retrace their paths vs. pendulums that don't. This is represented on a very large-scale plot that looks sort of fractal and trippy. They navigate around these data visualizations pointing out unique swinging patterns.
It's all accompanied by some fun synth-y audio tones that are also derived from the swinging patterns. It's a remarkably well done video and I highly recommend watching it when you can listen to it.
Really interesting video! The musician part of me noticed something in his sonification of the angle-tracing data (at 4:35): The "islands of stability" that he points out all form the consonant...
Really interesting video! The musician part of me noticed something in his sonification of the angle-tracing data (at 4:35): The "islands of stability" that he points out all form the consonant musical interval of a perfect twelfth, which in corresponds to a 1:3 ratio between the lower and higher notes' frequencies. I wonder what the mathematical reason for that is? Maybe some relation between the three nodes of the pendulum? Maybe it's π? 1:3 and 1:π are pretty close. If anyone smarter than me knows the reason I'd be very curious to find out!
Top comment on the video from 3blue1brown:
High praise coming from another great channel.
Wow. I haven't seen this channel before - definitely sub-worthy stuff. I really loved the music and the creative use of sound throughout. It's sort of psychedelic in a way.
Amazing video! For those wanting to dip their toes into this type of math, the most approachable books I ever read on the subject was Nonlinear dynamics and chaos, by Strogatz. Can be read for the intuition alone, but working the problems will help if you have the requisite maths. His section on chaos is towards the end.
For anyone coming to the comments first looking for some kind of synopsis whiel out-and-about:
This youtuber takes the angles and starting velocities of double pendulums (a pendulum with a second pendulum hanging off the bottom) while they dangle around and he plots the data. The main visual contrast is shown between the double pendulums that retrace their paths vs. pendulums that don't. This is represented on a very large-scale plot that looks sort of fractal and trippy. They navigate around these data visualizations pointing out unique swinging patterns.
It's all accompanied by some fun synth-y audio tones that are also derived from the swinging patterns. It's a remarkably well done video and I highly recommend watching it when you can listen to it.
I was skeptical going into this one, but he marvelously illustrates his point. These are some really awesome visualizations!
Such a great channel. I loved their previous video on lambda calculus and this one was completely new to me.
Really interesting video! The musician part of me noticed something in his sonification of the angle-tracing data (at 4:35): The "islands of stability" that he points out all form the consonant musical interval of a perfect twelfth, which in corresponds to a 1:3 ratio between the lower and higher notes' frequencies. I wonder what the mathematical reason for that is? Maybe some relation between the three nodes of the pendulum? Maybe it's π? 1:3 and 1:π are pretty close. If anyone smarter than me knows the reason I'd be very curious to find out!
I also got this video recommended by youtube yesterday, really cool.