  Motivated by questions in biology and distributed computing, we investigate
the behaviour of particular cellular automata, modelled as one-dimensional
arrays of identical finite automata. We investigate what sort of
self-stabilising cooperative behaviour these can induce in terms of waves of
cellular state changes along a filament of cells. We discover what the minimum
requirements are, in terms of numbers of states and the range of communication
between automata, to observe this for individual filaments. We also discover
that populations of growing filaments may have useful features that the
individual filament does not have, and we give the results of numerical
simulations.
