If these proposals and suggestions can be considered to be adequate responses to Weyl’s tile problem, recently another fine example of a no-go approach (and accompanying theorem) is to be found in Fritz (2013). Start out with an abstract formulation of a periodic graph, i.e., a set of vertices and a set of edges. For practical purposes, the periodicity can be thought of as a crystalline structure. This means that we have a basic finite unit that can cover the whole of the graph through iterated copies of that basic unit. Take as an example a two-dimensional structure. The vertices can be labeled or “weighted” by two numbers \((i, j)\). A trajectory \((f_{n})_{n\in N}\) is a sequence of weights of vertices, such that the vertices carrying \(f_{n}\) and \(f_{n+1}\) are connected by an edge. Next we define the (macroscopic) velocity of such a trajectory as