Rhythmic generation of infinite trees and languages

This work introduces the idea of breadth-first generation of infinite trees and languages. It is orthogonal to usual descriptions by classical objects such as automata and grammars which refer more naturally to a depth-first approach. This idea is brought into play with periodic inputs, a case that comes from the study of rational base number systems which correspond to specific inputs derived from Christoffel words. Conversely, we characterise languages generated in that way as representations of integers in such number systems with non-canonical alphabets of digits.