Visualising the p-adic integers

Goal:

Let p be a prime number. The p-adic numbers are an analog of the real numbers, in the sense that every p-adic number can be represented by an (infinite) p-adic expansion (instead of the decimal expansion); the p-adic integers are those p-adic numbers "without denominator". However, there are major differences between the p-adics and the reals; for instance, the p-adic are "totally disconnected".

The goal is to visualise the p-adics in a graph. There is a quite well known way to do this, and the graph will look like a fractal, but many of the properties of the p-adics can be seen in this graph. The visualisation should be automated.

Interested students could moreover try to think of ways to visualise other features of the p-adics or to visualise the p-adics in different ways.

Participants: Brian Courtehoute, Pablo Guzman, Antoine Ronk.

Supervisors: Gabor Wiese, Panagiotis Tsaknias

Difficulty level: Experimental Mathematics 1.

Results: Project report
7-adic integers

FSCT -- University of Luxembourg