  Bootstrap percolation is a type of cellular automaton on graphs, introduced
as a simple model of the dynamics of ferromagnetism. Vertices in a graph can be
in one of two states: `healthy' or `infected' and from an initial configuration
of states, healthy vertices become infected by local rules. While the usual
bootstrap processes are monotone in the sets of infected vertices, in this
paper, a modification is examined in which infected vertices can return to a
healthy state. Vertices are initially infected independently at random and the
central question is whether all vertices eventually become infected. The model
examined here is such a process on a square grid for which healthy vertices
with at least two infected neighbours become infected and infected vertices
with no infected neighbours become healthy. Sharp thresholds are given for the
critical probability of initial infections for all vertices eventually to
become infected.
