  A commonly used model for fault-tolerant computation is that of cellular
automata. The essential difficulty of fault-tolerant computation is present in
the special case of simply remembering a bit in the presence of faults, and
that is the case we treat in this paper. The conceptually simplest mechanism
for correcting errors in a cellular automaton is to determine the next state of
a cell by taking a majority vote among its neighbors (including the cell
itself, if necessary to break ties). We are interested in which regular
two-dimensional tessellations can tolerate faults using this mechanism, when
the fault rate is sufficiently low. We consider both the traditional transient
fault model (where faults occur independently in time and space) and a recently
introduced combined fault model which also includes manufacturing faults (which
occur independently in space, but which affect cells for all time). We
completely classify regular two-dimensional tessellations as to whether they
can tolerate combined transient and manufacturing faults, transient faults but
not manufacturing faults, or not even transient faults.
