Does this picture represent anything mathematically?

Question

This image here shows a beautiful fractal-like image. Does this map some sort of function, each number corresponding to a section/colour? Or is this just pretty art? Thanks!

Answer 1

This image represents the progression of the first $10,000$ digits of $\pi$, and was produced by Cristian Ilies Vasile using the software Circos (or so a Google search tells me).

To elaborate on this, since $\pi$ begins $3.14159\ldots$, you would begin to form this image by first adding an edge/arc from $3$ to $1$, then $1$ to $4$, then $4$ to $1$, and so on.

You can see this image as related to the question of if $\pi$ is a normal number, which is still unknown. Roughly speaking, a number is normal if it's digit progressions of all lengths are 'random,' in the sense that all finite digit progressions of a given length occur with equal frequency. For this image, that would mean that there are a roughly equal number of edges leading from any one node to any other node (and also from any node to itself, but I don't see those edges drawn).

Answer 2

The method used to generate this image using the digits of $\pi$ is described here.

I disagree with your characterization of the image as "fractal-like".