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!