Discrete convolutions, from probability, to image processing and FFTs.
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Other videos I referenced
Live lecture on image convolutions for the MIT Julia lab
https://youtu.be/8rrHTtUzyZA
Lecture on Discrete Fourier Transforms
https://youtu.be/g8RkArhtCc4
Reducible video on FFTs
https://youtu.be/h7apO7q16V0
Veritasium video on FFTs
https://youtu.be/nmgFG7PUHfo
These animations are largely made using a custom python library, manim. See the FAQ comments here:
https://www.3blue1brown.com/faq#manim
https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
https://github.com/3b1b/videos/
Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
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https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
Timestamps
0:00 - Where do convolutions show up?
2:07 - Add two random variables
6:28 - A simple example
7:25 - Moving averages
8:32 - Image processing
13:42 - Measuring runtime
14:40 - Polynomial multiplication
18:10 - The fast algorithm
21:22 - Concluding thoughts
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