This paper addresses the open problem of assembling multi-levelled
hierarchical
structure. It presents a model of an
infinitely-levelled, self-assembling dynamical hierarchy that arises
from the interaction of geometric primary elements with a fixed
complexity. A formal description of the presented hierarchy is
derived. This quantifies the relative compression achieved by
describing the system in terms of components of different
organization. The relationship between properties of representations
and those of physical objects is then discussed to support the view
that at each level in the hierarchy presented, the components
exhibit emergent
properties not possessed by those
at the levels below. It is concluded that these new properties are
trivial and that such infinitely-levelled structures may be
constructed easily. However, since the definition of the problem in
the literature admits such trivial possibilities, more specific
definitions are required.