  The distribution of the deformations of elementary cells is studied in an
abstract lattice constructed from the existence of the empty set. One
combination rule determining oriented sequences with continuity of set-distance
function in such spaces provides a particular kind of spacetime-like structure
that favors the aggregation of such deformations into fractal forms standing
for massive objects. A correlative dilatation of space appears outside the
aggregates. At the large scale, this dilatation results in an apparent
expansion, while at the submicroscopic scale the families of fractal
deformations give raise to families of particle-like structure. The theory
predicts the existence of classes of spin, charges, and magnetic properties,
while quantum properties associated to mass have previously been shown to
determine the inert mass and the gravitational effects. When applied to our
observable spacetime, the model would provide the justifications for the
existence of the creation of mass in a specified kind of "void", and the
fractal properties of the embedding lattice extend the phenomenon to formal
justifications of Big-Bang-like events without need for any supply of an
extemporaneous energy.
