Newton’s Fractal (which Newton knew nothing about)

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:

Mathologer on the cubic formula:

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:

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:

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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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