Bootstrap percolation on a graph is a simple to describe yet hard to analyze process on a graph. It begins with some initial configuration (open or closed) on the vertices. At each subsequent step a vertex may change from closed to open if enough of its neighbors are already open. For a random initial configuration where each vertex is open independently with probability p, how does the probability that eventually every vertex will be open change as p varies?

The large neighborhood size of the Hamming torus leads to a distinctly different flavor than previous results on the grid and hypercube. We will focus on Hamming tori with high dimension, giving a detailed description of the long term behavior of the process.