An intro to holomorphic dynamics, the study of iterated complex functions. Video on Newton's fractal: Special thanks to these supporters: #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: ~scott/Papers/India/ Numberphile with Ben Sparks on the Mandelbrot set: Ben explains how he made the Geogebra files on his channel here: (part 1) (part 2) Excellent article on , from the basics of building up complex numbers to Julia sets. 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: I first saw Fatou's theorem in this article: Moduli spaces of Newton maps: On Montel's theorem: ~fmonard/Sp17_Math207/ On Newton's Fractal: Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ These animations are largely made using a custom python library, manim. See the FAQ comments here: #manim You can find code for specific videos and projects here: Music by Vincent Rubinetti. Download the music on Bandcamp: Stream the music on Spotify: ------------------ 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: Various social media stuffs: Website: Twitter: Reddit: Instagram: Patreon: Facebook: