When R is fixed, the generation number is fixed because all the radii of circles belonging to a same generation are identical. In the figure 7a where R=2, we see clearly that when μ<R the torii are of type 2, and that when μ>R the torii are of type 3. Therefore, increasing the value of μ for a given value of R permits to pass from layers of type 2 to layers of type 3 with two sheets. The limit between these two kind of layers is μ=R as represented in Figure 7a, in which R=2 for different varying values of μ (μ=1, μ=2 and μ=3). In fact, when one moves in a vertical plane perpendicular to the Apollonius tiling, the layers of type 2 become of type 3 with two sheets (for increasing values of μ).