The deconfinement transition of (3+1)-dimensional pure SU(N) lattice gauge theory can be directly related to the magnetic transition of an effective 3-dimensional spin system, which is invariant under the center group Z(N). In this picture, the spins of the system correspond to the local Polyakov loops of the underlying gauge theory. A particular feature of many spin systems is the percolation of suitably defined clusters. It is thus natural to investigate, if such spin-like behaviour can be observed directly in a gauge theory. Indeed, lattice studies of pure SU(2) and pure SU(3) gauge theories confirmed that there is a connection between the deconfinement transition of gauge theories, and the onset of percolation for the center degrees of freedom.Pure SU(4) lattice gauge theory could behave differently, because here 1/N = 1/4 = 0.25, remains below the percolation threshold, p 0.3116, for random site percolation on a 3-dimensional simple cubic lattice.In this work, we try to learn about the nature of the deconfinement transition of (3+1)-dimensional pure SU(4) lattice gauge theory, by investigating the possibility of relating the latter tothe geometric phase transition of a 3-dimensional effective spin model, which is signaled by the spontaneous breaking of the underlying Z(4) symmetry, and the presence of percolating SU(4) center clusters.To this end, we define a simple cluster construction, and study a selected set of cluster properties related to the size as well as to the structure of the center clusters. Our analysis shows that the percolation picture of the deconfinement transition holds true for lattices with small temporal extent, but loses validityas we go to finer lattices. Furthermore, we find that the cluster definition we use does not allow for a sensible continuum limit.