Wave propagation in filamental cellular automata

Motivated by questions in biology and distributed computing, the authors investigate the behaviour of particular cellular automata, modelled as one-dimensional arrays of identical finite automata. They investigate what kinds of self-stabilising cooperative behaviour may be induced in terms of waves of cellular state changes along a filament of cells. The authors report the minimum requirements, in terms of numbers of states and the range of communication between automata, for this behaviour to be observed in individual filaments. They also discover that populations of growing filaments may have useful features not possessed by individual filaments, and they report the results of numerical simulations.