Self-Assembling Dynamical Hierarchies

This paper addresses the open problem of assembling multilevelled hierarchical structure. It presents a model of an infinitely-levelled, self-assembling dynamical hierarchy which 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, further discussion is required to ensure “interesting” emergent properties are clearly distinguished from those that are not.