Dorin, Alan, and Jon McCormack. “Self-assembling dynamical hierarchies.” Artificial Life 8 (2003): 423-428.
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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.