About
Bootstrap percolation: start with a random set of active cells. At each step, an inactive cell becomes active if it has at least k active neighbors (out of 4). The cascade continues until no more activations are possible. For k=2, there exists a sharp threshold density p_c above which percolation (full activation) occurs with high probability. For k=3 or 4, the threshold is higher and the transition is sharper — a discontinuous phase transition.