# A Thrice-a-Day Complex Analysis Infusion

Sometimes I like to sit back and take in math via pictures only. The newest addition to my math picture blog stable is kettenreihen.wordpress.com where three times a day, a beautiful picture appears.

Credit: Thomas Baruchel

These are graphs of complex-valued functions based on continued fractions. White points are where the function takes on real values, black are imaginary, and the other points are colored according to angle. On the blog’s “about” page, Baruchel explains the notation, which is not the most common continued fraction notation.

It’s fun to look at a graph and try to figure out why it looks the way it does: why are there purely real or imaginary values in particular places, why a graph has horizontal or vertical symmetry, and so on. These are not straightforward functions, so I must admit I don’t always get anywhere, but it’s fun to think about anyway. If I were teaching complex analysis, I would probably try to work this blog into my class somehow, if only to gawk at pretty things with my students.

I’ve been trying to decide which kinds of graphs are prettiest. “Flowers” are nice.

Credit: Thomas Baruchel

But so are hearts.

Credit: Thomas Baruchel

Graphs that evoke mathematical symbols are always on trend.

Credit: Thomas Baruchel

Simple ones are nice.

Credit: Thomas Baruchel

And so are the wild, busy ones.

Credit: Thomas Baruchel

Luckily you don’t have to choose. Just add the blog to your feed, put your feet up, and relax with some gorgeous mathematical illustrations.

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### 2 Responses to A Thrice-a-Day Complex Analysis Infusion

1. Nalin Pithwa says:

thanks. Such pictures are sheer joy to the heart and head. Thanks to you for sharing, and to the author/creator.

2. visualia says:

Wow!! These plots are very interesting. I’d like to know the method used for such image generation.

Here is a list of notebooks that explain how to generate different colored complex functions (click on each link and read the corresponding notebook; to download it click on the upper right downward arrow) https://github.com/empet/Math/blob/master/README.md