pattern.

A great success in the topic of point patterns is the possibility to handle a pattern $\Lambda _0$ of $\mathbb{R}^d$ by considering the *dynamical system* associated to it. It consists of a space $\mathbb{X}_{\Lambda_0}$ called the *hull* of $\Lambda_0$, which is formed of all other point patterns locally looking as $\Lambda_0$ and endowed with a suitable compact topology, together with an action of the space $\mathbb{R}^d$ by homeomorphisms. Natural properties of a pattern which are of geometric, combinatoric and/or statistical nature are then displayed by topological, dynamical and/or ergodic features on this dynamical system. This is particularly true for long range order on point patterns, where the counterpart seems to rely on the existence of *eigenfunctions* for the associated dynamical system. For instance, within the class of substitutive point patterns the *Meyer property*, which is a strong form of internal order [@Mo], is equivalent to the existence of a non-trivial eigenfunction for the associated dynamical system [@LeeSo]. This type of statement also exists outside the realm of substitution patterns [@KeSa]. Another example concerns the subclass of *regular model sets*, which can be viewed as the most ordered aperiodic patterns, where the property to be a regular model set is 