We consider a two-dimensional cellular automaton whose rule consists of two subrules. The first, applied synchronously, is a local rule inspired from the 'game of life', with a larger neighbourhood. The second, applied sequentially, describes the motion of a fraction m of individuals. Such rules appear to be useful for modelling complex systems in ecology, such as natural populations of animals, in which the motion of the individuals is believed to play an important role. If the motion is long-range, the density of individuals exhibits a sequence of period-doubling bifurcations and behaves chaotically when m is large enough. If the motion is short-range (i.e. restricted to first neighbours), patterns become inhomogeneous. Spatial correlations decay with a finite correlation length xi of the order of square root m. We observe the formation of domains, of mean width xi , with a chaotic behaviour of the local density of individuals, but the collective behaviour is stationary (the global density tends to a fixed value when the lattice size is much larger than xi * xi ).