  A mutualism is an interaction where the involved species benefit from each
other. We study a two-dimensional hexagonal three-state cellular automaton
model of a two-species mutualistic system. The simple model is characterized by
four parameters of propagation and survival dependencies between the species.
We map the parametric set onto the basic types of space-time structures emerged
in the mutualistic population dynamic. The structures discovered include
propagating quasi-one dimensional patterns, very slowly growing clusters, still
and oscillatory stationary localizations. Although we hardly find such
idealized patterns in nature, due to increased complexity of interaction
phenomena, we recognize our findings as basic spatial patterns of mutualistic
systems, which can be used as baseline to build up more complex models.
