**Goal:**

Consider a n x n grid of sites. Each site is either blocked or open. Initially open sites are empty. A full site is an open site that can be connected to an open site in the top row via a chain of neighboring (left, right, up, down) open sites. If there is a full site in the bottom row, then we say that the system percolates (see picture below). If sites are independently set to be open with vacancy probability p, what is the probability that the system percolates? It turns out that there is a value of p above which the system percolates almost always. This threshold value of p can be estimated via Monte Carlo simulation. One can study further related concepts like bond percolation and passage time.

**Supervisor:**
George Kerchev

**Difficulty level:**
Introductory

**Tools:**
Any programming language