For my February 2017 diary, go here.

Diary — March 2017

John Baez

March 11, 2017

When light kisses darkness

This is one of many beautiful images on Thomas Baruchel's blog. They depict functions on the complex plane. Some are exquisitely baroque. This one is delightfully simple: a circle of light intersecting a larger circle of darkness. Its intense contrast reminds me of a solar eclipse.

The function here, like most on the blog, is supposedly defined by a continued fraction:

$$ \frac{z \exp(2\pi i / 3)}{z + \frac{z \exp(4\pi i / 3)}{z/2 + \frac{z \exp(6\pi i / 3)}{z/3 + \cdots}}} $$

He says that "white parts on the picture are real values; black parts are imaginary ones." That doesn't fully explain how the numbers get turned into shades of gray. It would be nice to know the exact recipe. A more obvious choice would be to use the color wheel to describe the phase of a complex number and brightness or intensity to describe its absolute value. But the simplicity of a grayscale image pays off in a kind of classic beauty.

Here's the image on Baruchel's blog:

It's number 146 of a long series. He has threatened to produce three a day — and so far he seems to be keeping up!

For my April 2017 diary, go here.

© 2017 John Baez