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

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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...

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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/a...

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

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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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