  Thermal noise in a cellular automaton refers to a random perturbation to its
function which eventually leads this automaton to an equilibrium state
controlled by a temperature parameter. We study the 1-dimensional majority-3
cellular automaton under this model of noise. Without noise, each cell in this
automaton decides its next state by majority voting among itself and its left
and right neighbour cells. Transfer matrix analysis shows that the automaton
always reaches a state in which every cell is in one of its two states with
probability 1/2 and thus cannot remember even one bit of information. Numerical
experiments, however, support the possibility of reliable computation for a
long but finite time.
