Who knew root-finding could be so complicated?
Next part: • Beyond the Mandelbrot ...
Special thanks to the following supporters: 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:
www.3blue1brown.com/lessons/n...
On fractal dimension:
• Fractals are typically...
Mathologer on the cubic formula:
• 500 years of NOT teach...
Some articles on Newton's Fractal, and its cousins:
www.chiark.greenend.org.uk/~s...
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 C...
The insolubility of the quintic:
• Why There's 'No' Quint...
The math behind rasterizing fonts:
• The Math Behind Font R...
Viewer-made interactive:
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:
www.3blue1brown.com/faq#manim
github.com/3b1b/manim
github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
github.com/3b1b/videos/
Music by Vincent Rubinetti.
www.vincentrubinetti.com/
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
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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