Starting from a dynamical system (Ω, G), with G a generic topo-
logical group, we present an algorithm that generates families of patterns in
the Euclidean space, on which G acts by rigid shifts. We call such patterns
dynamically generated. When identical resonators are placed on the positions
indicated by such patterns, their dynamics can be analyzed using Bellissard’s
C-algebraic formalism. In this talk I will present examples obtained by the
methods described above, together with explicit computations of the associated
algebras of observables. Laboratory examples involving coupled mechanical res-
onators will be also discussed. As we shall see, their dynamics share many
similarities with that of 2-dimensional electrons in a magnetic field.