Newton's Fractal (which Newton knew nothing about)

Who knew root-finding could be so complicated?
Early view of the next part: https://www.patreon.com/posts/57323044
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Special thanks to the following supports: https://3b1b.co/lessons/newtons-fractal#thanks

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Interactive for this video:
https://www.3blue1brown.com/lessons/newtons-fractal

On fractal dimension:
https://youtu.be/gB9n2gHsHN4

Mathologer on the cubic formula:
https://youtu.be/N-KXStupwsc

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

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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

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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
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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

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