For some time I have been thinking about creating minimalist typographical art based on the digits of π. Yesterday was π day (March 14), a fitting reason to try a few experiments. If a day late.
For each digit in π, i, define its i-ness based on how close i is to its n neighbours, arithmetically.
For each neighbour (e.g. 8), compute the relative difference between i and the neighbour (e.g. 8-4=+4). The average of these differences is the i-ness.
Thanks to Lance Bailey for suggesting how to measure 4ness.
Let's look at an example. Consider the sequence "31415". The 4 neighbours of the 4 are 3, 1, 1 and 5. The relative distances are -1, -3, -1 and 1. The average is -1.5 and the standard deviation is 1.7. In the 4ness of π poster, the average is mapped onto a color and the standard deviation onto size.
Based on the color you can tell how far away from 4 the neighbours are. Brown 4s have smaller neighbours and blue/green 4s have larger ones, on average.
Based on size you can tell how the neighbours are distributed. Large 4s have neighbours that are similar and small 4s have neighbours that are different.
The type face of the main digits is Gotham. Index annotation is set in The Sans Mono Condensed Light and the neighbour and statistics annotations in Inconsolata.
Compare the iness of π to that of the other famous transcendental number, e, and the mysterious but attractive Golden Ratio, φ.
I assure you — π has a lot of 4s. Why, in the first 19,528 digits there are 2,000 of them! That's a lot.
How do the digits of π, φ and e compare when lined up?
The numbers overlap in 21 places in the first 2,070 digits, at least once for each 0-9. The most overlaps are seen in the number 7, at positions (1-indexed) 100, 1,595, 1,706 and 1,743.
The exact number of times π, φ and e overlap in the first 2,070 digits is
digit overlaps positions 0 . 828 1 ... 396 500 1,385 2 ... 825 1,283 1,292 3 . 2,021 4 .. 596 1,906 5 .. 841 941 6 . 2,061 7 .... 100 1,595 1,706 1,743 8 . 607 9 ... 13 170 694
The type is Neutraface Slab Display Medium.
As soon as I made this overlap, the next natural direction was to create the quantitity called Accidental Similarity Number.
The accidental similarity number is derived from two or more numbers at positions where the numbers have the same digit. In the poster below, is the 9,996 digit ASN from the first 1,000,000 digits of π, φ, and e.
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.