Identifying space with a superconducting cosmic dust, the structure of
the 'world crystal' is built. Particles moving on open geodesics are
assimilated with the 'electron gas' in a lattice, and those moving on
closed geodesics with nodes of the same lattice. By considering that t
his kind of structure may be achieved by pinning on a background gravi
tomagnetic field, the properties of such fields are studied. From this
analysis and computing the background energy we are lead to a Cantori
an-fractal structure of space-time, which allows one to interpret the
gravitational interaction in terms of a mechanism similar to the compo
site fermions mechanism.