While John Venn is best-known for the Venn Diagram, Alex Bellos mentions Venn’s other invention in his quite-good book “Here’s Looking at Euclid” (page 231). Venn was the first to create a “random walk” or “drunk walk”. Using the decimal expansion of pi, each digit is seen as a cardinal direction. I’ve updated Venn’s experiment slightly (his ignored the numbers 8 and 9) – each number from 0-9 rotates the direction of movement by a factor of 36º and takes a step 20 pixels forward.

The above image is the first 1120 decimal places of pi, starting at the gray dot. Created using Processing.

I’m really glad to see this and I would like to learn more. I did something independent that produces a very similar result to Venn’s method, only it is functional and not merely graphical. I created a set of rules for expanding non-decreasing sequences of real numbers into the plane effectively functionalizing such sequences for analysis.

Once I realized that irrational numbers could be converted into sequences by treating each digit as the delta between successive numbers in a sequence, and then expanded into the plane via my function rules, I conceived basically the same idea where we can construct a random zig-zag walk out of the digits of pi, but again the difference is that it is a functional random walk in the plane.

It’s still in the conceptual phase though, so I haven’t had time to produce a graph of the Pi walk under my function. Would you be interested in learning about my function, and maybe attempting to plotting my version of the Pi-walk?

@Watson – that sounds very cool! Post a link to an image or post when you’re done.

Thanks Jeff ok I will do so! It may take me till after New Years, but I won’t forget. Seasons Greetings!