Numerology is bogus, but art based on numbers has a beautiful random quality.
Cristian Ilies Vasile had the idea of representing the digits of π as links that connected segments associated with successive digits. The image is composed of links (segment:position) 3:0 → 1:1 → 4:2 → 1:3 → 5:4 …
I added to Cristian's representation by showing the transition probabilities for each digit across bins of 10 digits. For a given digit segment, d, the inner bubble plot shows the number of times a digit i was found immediately before d. The outer bubble plot shows the number of times i followed d.
The transition probabilities for each 10 digit bin for the first 2,000 digits of π, φ and e are shown in the image below. The large bubble on the 9 segment for π is due to the unusual "999999" sequence at decimal place 762, which occurs significantly earlier than expected.
Below are more images by Cristian Ilies Vasile, where dots are used to represent the adjacency between digits. Each digit 0-9 is represented by a colored segment. Dots assigned to a segment represent digits that follow the digit represented by the segment. The position of the dot is roughly the position within the number that the digit appears.
For example, for π the dot coordinates for the first 7 digits are The image is composed of dots using third coordinates (segment:position:label) 3:0:1 >>> 1:1:4 >>> 4:2:1 >>> 1:3:5 >>> 5:4:9 ....
segment position label digit3 0 1 digit1 1 4 digit4 2 1 digit1 3 5 digit5 4 9 digit9 5 2 digit2 6 6
When the digits of π, e and φ are aligned, positions at which the three numbers have the same digit yield the accidental similarity number (ASN). Below is a dot plot of the transition of the ASN.
It's fitting to use Circos to visualize the digits of π. After all, what is more round than Circos?
Choose symbols that overlap without ambiguity and communicate relationships in data.
Using Strunk's Elements of Style as an example of writing guidelines, I look how these can be translated to creating figures.
When we create figures, we must communicate and design. In my talk I discuss some of the rules that turn graphical improvisation into a structured and reproducible process.