Рет қаралды 1,425,662
An intro to holomorphic dynamics, the study of iterated complex functions.
Video on Newton's fractal: • From Newton’s method t...
Special thanks to these supporters: 3b1b.co/lessons/holomorphic-d...
Extra special thanks to Sergey Shemyakov, of Aix-Marseille University, for helpful conversations and for introducing me to this phenomenon.
Introduction to Fatou sets and Julia sets, including a discussion of Montel's theorem and its consequences:
www.math.stonybrook.edu/~scott...
Numberphile with Ben Sparks on the Mandelbrot set:
• What's so special abou...
Ben explains how he made the Geogebra files on his channel here:
• Julia Sets and Orbits ... (part 1)
• Mandelbrot Orbits and ... (part 2)
Excellent article on Acko.net, from the basics of building up complex numbers to Julia sets.
acko.net/blog/how-to-fold-a-j...
Bit of a side note, but if you want an exceedingly beautiful rendering of the quaternion-version of Julia fractals, take a look at this Inigo Quilez video:
• "Geodes" - 3D Julia se...
I first saw Fatou's theorem in this article:
projecteuclid.org/journals/co...
Moduli spaces of Newton maps:
arxiv.org/pdf/1512.05098.pdf
On Montel's theorem:
people.ucsc.edu/~fmonard/Sp17...
On Newton's Fractal:
core.ac.uk/download/pdf/16338...
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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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
3:02 - Rational functions
4:15 - The Mandelbrot set
8:12 - Fixed points and stability
12:51 - Cycles
16:25 - Hidden Mandelbrot
21:17 - Fatou sets and Julia sets
26:24 - Final thoughts
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