An intro to holomorphic dynamics, the study of iterated complex functions.
Video on Newton's fractal: https://youtu.be/-RdOwhmqP5s
Special thanks to these supporters: https://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.

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Introduction to Fatou sets and Julia sets, including a discussion of Montel's theorem and its consequences:
http://www.math.stonybrook.edu/~scott/Papers/India/Fatou-Julia.pdf

Numberphile with Ben Sparks on the Mandelbrot set:
https://youtu.be/FFftmWSzgmk

Excellent article on Acko.net, from the basics of building up complex numbers to Julia sets.
https://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:
https://www.youtube.com/watch?v=rQ2bnU4dkso

I first saw Fatou's theorem in this article:…