More than being an intro to Julia fractals, I think this post is a great introduction to complex numbers and functions of the complex plane[1]. The way this is

More than being an intro to Julia fractals, I think this post is a great introduction to complex numbers and functions of the complex plane[1]. The way this is presented is very similar to how most math-folk I know picture these concepts in their head. This is probably one of the toughest things for beginners, who don't understand that (most) math-folk think in pictures like this and not in symbols. For example, starting at around Slide 29 in the first visualization, the author actually paints a picture of a branch cut[2] without using that term. Likewise, starting at around Slide 12 of the last visualization, the author hints at the special relationship between complex numbers and differentiation in the complex plane. The jargon-y stuff involved here are holomorphic functions[3], the Cauchy-Riemann equations[4], and the very surprising-but-central theorem of complex analysis: Cauchy's integral theorem[5]. [1]: Functions from ℂ to ℂ are "hard" to reason about because there are 4 dimensions involved, at least if you're picturing ℂ as a 2-dimensional plane. [2]: https://en.wikipedia.org/wiki/Branch_point#Branch_cuts [3]: https://en.wikipedia.org/wiki/Holomorphic_function [4]: https://en.wikipedia.org/wiki/Cauchy-Riemann_equations [5]: https://en.wikipedia.org/wiki/Cauchy%27s_integral_theorem