Who knew root-finding could be so complicated? Next part: https://www.youtube.com/watch?v=LqbZpur38nw Special thanks to the following supporters: https://3b1b.co/lessons/newtons-fractal#thanks An equally valuable form of support is to simply share the videos. Thanks to these viewers for their contributions to translations German: Luatic Hebrew: Omer Tuchfeld Portuguese: luiz12apn ------------------ Interactive for this video: https://www.3blue1brown.com/lessons/newtons-fractal On fractal dimension: https://www.youtube.com/watch?v=gB9n2gHsHN4 Mathologer on the cubic formula: https://www.youtube.com/watch?v=N-KXStupwsc Some articles on Newton's Fractal, and its cousins: https://www.chiark.greenend.org.uk/~sgtatham/newton/ https://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://www.youtube.com/watch?v=aVwxzDHniEw The insolubility of the quintic: https://www.youtube.com/watch?v=BSHv9Elk1MU The math behind rasterizing fonts: https://www.youtube.com/watch?v=LaYPoMPRSlk Viewer-made interactive: https://codepen.io/mherreshoff/full/RwZPazd --- 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/ Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://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: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com/ Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown