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Newton’s fractal (which Newton knew nothing about)

Who knew root-finding could be so complicated? Next part:    • Beyond the Mandelbrot set, an intro t...   Special thanks to the following supporters: https://3b1b.co/lessons/newtons-fract... 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/n... On fractal dimension:    • Fractals are typically not self-similar   Mathologer on the cubic formula:    • 500 years of NOT teaching THE CUBIC F...   Some articles on Newton's Fractal, and its cousins: https://www.chiark.greenend.org.uk/~s... https://blbadger.github.io/polynomial... 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    • The Beauty of Bézier Curves   The insolubility of the quintic:    • Why There's 'No' Quintic Formula (pro...   The math behind rasterizing fonts:    • The Math Behind Font Rasterization | ...   Viewer-made interactive: https://codepen.io/mherreshoff/full/R... --- 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/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw... ------------------ 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:   / 3blue1brown   Reddit:   / 3blue1brown   Instagram:   / 3blue1brown_animations   Patreon:   / 3blue1brown   Facebook:   / 3blue1brown