Semantic maps have offered linguists an appealing and empirically rooted methodology for describing recurrent structural patterns in language development and the multifunctionality of grammatical categories. Although some researchers argue that semantic maps are universal and given, others provide evidence that there are no fixed or universal maps. This paper takes the position that semantic maps are a useful way to visualize the grammatical evolution of a language (particularly the evolution of semantic structuring) but that this grammatical evolution is a consequence of distributed processes whereby language users shape and reshape their language. So it is a challenge to find out what these processes are and whether they indeed generate the kind of semantic maps observed for human languages. This work takes a design stance towards the question of the emergence of linguistic structure and investigates how grammar can be formed in populations of autonomous artificial ?agents? that play language games with each other about situations they perceive through a sensori-motor embodiment. The experiments reported here investigate whether semantic maps for case markers could emerge through grammaticalization processes without the need for a universal conceptual space.