Protein fix: Martin Krzywinski, a well known pi artist, here lets the first 768 decimal digits of pi behave like the string of amino acids in a protein. In other words, he arbitrarily lets the prime digits (2,3,5 and 7) be black dots. The remaining dots each are colour-coded. A computer algorithm then ‘folds’ the string in such a way to maximize the number of adjacent black dots. He said: “The colour scheme is inspired by the Bauhaus movement. By smoothly deforming the lattice that holds the path into a circle and adjusting the sizes of digit circles, we can get something that starts to look like a globe, with clusters of prime digits being the land and composite digits forming a broken shoreline.” He explains his method in fantastic detail on his website, but even if you don’t understand it entirely, it still looks cool.

Martin - who works in bioinformatics and data visualization - has made lots of art based on pi, and some can be bought as posters. The reason why pi makes interesting art is because the digits that appear in the decimal expansion obey no understandable order. (And the reason why it is Pi Day today is because it’s March 14, or 3/14). In this image, Martin colour-coded the digits from 0 to 9 and spiralled the digits of pi out from the centre for 13,688 decimal places.

The first person to visualize the random nature of pi’s decimal digits was the Victorian mathematician John Venn. In The Logic of Chance (1888), he suggested that the digits 0 to 7 represent eight compass directions, and he followed the path tracked by these digits in pi. He misses out the initial 3, and starts 14159. Venn’s image was the first “random walk”, an idea now used frequently in probability and statistics. (The illustration is taken from my book, Alex's Adventures in Numberland)

Francisco Aragón and his colleages converted pi into base 4, meaning that it is written using only the digits 0, 1, 2 and 3, and with these digits representing north, south, east and west, tracked a random walk of pi for 100 billion digits. Their site is here and a paper on their work is here. It looks like a puff of magic smoke.

Here’s a close-up of Aragón’s 100 billion random walk.

If that’s a bit overwhelming, here is a random walk that uses only the first 10 billion base 4 digits of pi. Image: Franciso Aragón et al/CARMA, Newcastle University, Australia

This random walk is just the first 10,000 digits of pi. Cristian Vasile used the base ten digits, and let each number represent ten directions, each separated by 36 degrees. Rather than linking each digit, the path hops between dots.

In this work, Vasile converted pi into base 16. The sixteen segments around the circle represent the 16 digits of this base. He then traced pi for 3600 digits, going from segment to segment based on the value of the digit. A fuller explanation is here and Vasile’s art can be bought here.

In this “bubble heap” image Vasile stacked coloured dots around the segments based on the digit sequence of pi. A fuller explanation is here and Vasile’s art can be bought here.

Francisco Aragón and his collaborators coloured a million squares based on the base four dits of pi. Each square - going from left to right, and then top to bottom - is coloured red (0), green (1), cyan (2) and purple (3).

And here’s a close up. Image: Franciso Aragón et al/CARMA, Newcastle University, Australia