## 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