My aim was to show how individual-oriented (or artificial life) models may provide an integrative background for the development of theories about dominance by including effects of spatial structure. Dominance interactions are thought to serve two different, contrasting functions: acquisition of high rank and reduction of aggression. The model I present consists of a homogeneous virtual world inhabited by artificial agents whose actions are restricted to grouping and dominance interactions in which the effects of winning and losing are self-reinforcing. The two functions are implemented as strategies to initiate dominance interactions and the intensity of aggression and dominance perception (direct or memory based) are varied experimentally. Behaviour is studied by recording the same behavioural units as in real animals. Ranks appear to differentiate more clearly at high than at low intensity of aggression and also more in the case of direct than of memory-based rank perception. Strong differentiation of rank produces a cascade of unexpected effects that differ depending on which function is implemented: for instance, a decline in aggression, spatial centrality of dominants and a correlation between rank and aggression. Insight into the origination of these self-organized patterns leads to new hypotheses for the study of the social behaviour of real animals.