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Title:From Newton’s method to Newton’s fractal (which Newton knew nothing about)
Duration:26:06
Viewed:0
Published:12-10-2021
Source:Youtube

Who knew root-finding could be so complicated? Next part: https://youtu.be/LqbZpur38nw Special thanks to the following supporters: 3b1b.co/lessons/newtons-fractal#thanks An equally valuable form of support is to simply share the videos. ------------------ Interactive for this video: www.3blue1brown.com/lessons/newtons-fractal On fractal dimension: https://youtu.be/gB9n2gHsHN4 Mathologer on the cubic formula: https://youtu.be/N-KXStupwsc Some articles on Newton's Fractal, and its cousins: www.chiark.greenend.org.uk/~sgtatham/newton/ blbadger.github.io/polynomial-roots.html Some of the videos from this year's Summer of Math Exposition are fairly relevant to the topics covered here. Take a look at these ones, The Beauty of Bézier Curves https://youtu.be/aVwxzDHniEw The insolubility of the quintic: https://youtu.be/BSHv9Elk1MU The math behind rasterizing fonts: https://youtu.be/LaYPoMPRSlk Viewer-made interactive: codepen.io/mherreshoff/full/RwZPazd --- These animations are largely made using a custom python library, manim. See the FAQ comments here: www.3blue1brown.com/faq#manim github.com/3b1b/manim github.com/ManimCommunity/manim/ You can find code for specific videos and projects here: github.com/3b1b/videos/ Music by Vincent Rubinetti. www.vincentrubinetti.com/ Download the music on Bandcamp: vincerubinetti.bandcamp.com/album/the-music-of-3bl… Stream the music on Spotify: open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ Timestamps: 0:00 - Intro 0:48 - Roots of polynomials 5:55 - Newton’s method 11:16 - The fractal 17:56 - The boundary property 23:13 - Closing thoughts ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe Various social media stuffs: Website: www.3blue1brown.com/ Twitter: twitter.com/3blue1brown Reddit: www.reddit.com/r/3blue1brown Instagram: www.instagram.com/3blue1brown_animations/ Patreon: patreon.com/3blue1brown Facebook: www.facebook.com/3blue1brown

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