Who knew root-finding could be so complicated?
Early view of the next part: https://www.patreon.com/posts/57323044
An equally valuable form of support is to simply share the videos.
Special thanks to the following supports: https://3b1b.co/lessons/newtons-fractal#thanks
Interactive for this video:
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:
You can find code for specific videos and projects here:
Music by Vincent Rubinetti.
Download the music on Bandcamp:
Stream the music on Spotify:
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
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