Chacon transformations: Combinatorics, geometric structure, link with systems of complexity 2n+1

We show that Chacon's map is a system of complexity (2n - 1); we describe the associated graph of words, and use it to give a primitive form of the substitution, and a geometric representation of the transformation, as an exduction of a triadic rotation; then we compute the complexity of some more general systems, substitutive or not, which are the simplest known weakly mixing systems.