When μ is fixed, a decrease of R corresponds to a change (increase) in the generation number. In the figure 7b where μ=2, we see clearly that for R<μ the torus are of type 3 and that for R>μ, the torus are of type 2. Therefore, increasing the value of R for a given value of μ permits to pass from layers of type 3 with two sheets to layers of type 2. The limit between these two kinds of layers is R=μ as represented in Figure 7b, in which μ=2 for varying values of R (R=1, R=2 and R=3). In fact, when one moves in the plane of the Apollonius tiling from the biggest circles towards the smaller circles, the layers of type 2 become of types 3 with two sheets. These two tendencies are summarized in Figure 8a,b when one moves in the two directions indicated by the arrows.