This paper describes a model of the emergence and the universal structural tendencies of vowel systems. Both are considered as the result of self-organisation in a population of language users. The language users try to imitate each other and to learn each other's vowel systems as well as possible under constraints of production and perception, while at the same time maximising the number of available speech sounds. It is shown through computer simulations that coherent and natural sound systems can indeed emerge in populations of artificial agents. It is also shown that the mechanism that is responsible for the emergence of sound systems can be used for learning existing sound systems as well. Finally, it is argued that the simulation of agents that can only produce isolated vowels is not enough. More complex utterances are needed for other interesting universals of sound systems and for explaining realistic sound change.