Largest Minimal Percolating Sets in Hypercubes under 2-Bootstrap Percolation

Consider the following process, known as r-bootstrap percolation, on a graph G. Designate some initial infected set A and infect any vertex with at least r infected neighbors, continuing until no new vertices can be infected. We say A percolates if it eventually infects the entire graph. We say A is a minimal percolating set if A percolates, but no proper subset percolates. We compute the size of a largest minimal percolating set for r = 2 in the n-dimensional hypercube.