Newton's Fractal (which Newton knew nothing about)

2021-10-12

[public] 286K views, 91.1K likes, 65.0 dislikes audio only

4K

Who knew root-finding could be so complicated?

Next part: /youtube/video/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:

/youtube/video/gB9n2gHsHN4

Mathologer on the cubic formula:

/youtube/video/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://youtu.be/aVwxzDHniEw

The insolubility of the quintic:

https://youtu.be/BSHv9Elk1MU

The math behind rasterizing fonts:

https://youtu.be/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