From Newton’s method to Newton’s fractal (which Newton knew nothing about)

Who knew root-finding could be so complicated? Next part: Special thanks to the following supporters: #thanks An equally valuable form of support is to simply share the videos. ------------------ Interactive for this video: On fractal dimension: Mathologer on the cubic formula: Some articles on Newton’s Fractal, and its cousins: ~sgtatham/newton/ 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 insolubility of the quintic: The math behind rasterizing fonts: Viewer-made interactive: --- These animations are largely made using a custom python library, manim. See the FAQ comments here: #manim You can find code for specific videos and projects here: Music by Vincent Rubinetti. Download the music on Bandcamp: Stream the music on Spotify: ------------------ 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: Various social media stuffs: Website: Twitter: Reddit: Instagram: Patreon: Facebook: