Some years ago I was making some decorations for my wall. I was arranging everything on that wall in a fibonacci spiral and making droplets emanating from the center where there was a pyramid with an eye at the top, a commonly used symbol for God. I think I was making my picture of creation. As part of this I wanted to make a yin-yang.

How does one make a yin-yang that looks good? If you are me, you certainly don’t do it free hand. I figured out that to make a yin-yang you divide a circle in two, and then make half as big circles over the boundry. Click through this illustration to see what I mean:

When I made one of those, naturally I wondered what it would look like if each of those smaller circles were in turn a yin-yang.

I started with paper and scissors and did that over and over again, i.e. I made the smaller circles into yin-yangs, but also in those I made the even smaller circles yin-yangs, and so on:

I found it interesting and fun but it’s a slow process to explore with paper and scissors, so I wrote some code to look at what different things could be changed and what it’d look like. The most interesting thing I found was that by turning the yin-yang on each level some degrees relative to the previous level, I got something that looked really nice. Try this interactive demo I made when playing with it:

When I turned the yin yang about 45 degrees on each iteration of the recursion, and had a recursion depth of 4 or 5, I found something I recognised as the wave from the japanese painting: The Great Wave off Kanagawa.

By coloring each iteration to match that paiting I found a logo I really like.

I haven’t managed to find anyone else making recursive yin yangs like this so it feels personal and like a nice mix of math and spirituality.

For me, from a structural point of view, it symbolizes how the world is made from opposing forces and polarities in nested interdependent levels.

Aesthetically it brings me a sense of flow and water, which is how I try to relate to the world. You can’t step into the same river twice and all that.