In recent years there has been much debate concerning the human language faculty and the presence of a recursive mechanism in our mental grammar. In a similar vein, syntactic recursion (e.g. centre-embedded clauses: [the rat [the dog chased] died]) makes it theoretically possible to infinitely embed clauses within clauses. This work offers experimental evidence relevant to these issues. Firstly, through transmission and communication an initially random language becomes more structured and more easily learnable in an idealised version of cultural evolution known as iterated learning. Secondly, it is shown that the languages generated in this manner can be characterised by a recursive grammar rule and potentially exhibit some centre-embedded structure. In line with previous results in computational linguistics, these findings suggest that cultural evolution could have been influential in the evolution of recursive syntax.