Generation of Higher Order Emergent Structures

In the study of complex systems---in particular self-organizing systems---the notions of emergence and higher order structures come up. A framework for studying them was given in [1,2] where the notion of a hyperstructures occur both in an intuitive and a formal sense. But in formalizations of these systems it has turned out to be quite difficult to produce higher order emergence from first principles. The first problem is of course to agree on what a higher order structure is. It is known that second order structures occur relatively easy, the problem is to know how to proceed to third order without external interference. The goal of this paper is to discuss these problems in the light of the discrete field automata formulated in [19] and [12]. Then we shall try to extract some of the formal principles involved in the generation of higher order (hyper-) structures and relate it to dynamical systems.