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:
An equally valuable form of support is to simply share the videos.

Special thanks to the following supports:


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:

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