Channel: 3Blue1Brown

Category: Education

Tags: mathematics3 blue 1 brown3 brown 1 blue3b1bthree blue one brown3brown1bluethree brown one blue

Description: An intro to holomorphic dynamics, the study of iterated complex functions. Video on Newton's fractal: youtu.be/-RdOwhmqP5s Special thanks to these supporters: 3b1b.co/lessons/holomorphic-dynamics#thanks 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: math.stonybrook.edu/~scott/Papers/India/Fatou-Julia.pdf Numberphile with Ben Sparks on the Mandelbrot set: youtu.be/FFftmWSzgmk Ben explains how he made the Geogebra files on his channel here: youtu.be/ICqj7nJbiRI (part 1) youtu.be/3BXoNOahFJk (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-julia-fractal 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: youtube.com/watch?v=rQ2bnU4dkso I first saw Fatou's theorem in this article: projecteuclid.org/journals/communications-in-mathematical-physics/volume-91/issue-2/On-the-iteration-of-a-rational-function--computer-experiments/cmp/1103940533.pdf Moduli spaces of Newton maps: arxiv.org/pdf/1512.05098.pdf On Montel's theorem: people.ucsc.edu/~fmonard/Sp17_Math207/lecture11.pdf On Newton's Fractal: core.ac.uk/download/pdf/1633889.pdf ------------------ These animations are largely made using a custom python library, manim. See the FAQ comments here: 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. vincentrubinetti.com Download the music on Bandcamp: vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 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 ------------------ 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: 3b1b.co/subscribe Various social media stuffs: Website: 3blue1brown.com Twitter: twitter.com/3blue1brown Reddit: reddit.com/r/3blue1brown Instagram: instagram.com/3blue1brown_animations Patreon: patreon.com/3blue1brown Facebook: facebook.com/3blue1brown