(2005) Mahmoodi Baram, Reza; Herrmann, Hans (Prof. Dr.)
In this thesis we developed an algorithm for constructing three dimensional self-similar space-filling packings of spheres. Among the constructed configurations is the classical three dimensional Apollonian packing which was the only previously-known configuration. The difference between the calculated fractal dimensions indicates the topological difference between these configurations.
Among the obtained packings there is one for which only two colors are necessary for coloring the spheres such that no two spheres having the same color touch each other. This is equivalent to saying that the packing consists of only even loops of touching spheres. In two dimensions this is the necessary and sufficient condition for a packing to act like a bearing. In three dimensions, however, it is not obvious that this is the case, since the particles have more rotational degrees of freedom. We showed that having only even loops is the necessary and sufficient condition for a packing to act like a bearing in three dimensions as well. We have given an explicit expression for the angular velocity of every sphere of the entire packing, in terms of the angular velocity of an arbitrarilily chosen sphere, and a factor $c\geq 0$.
