Rasmussen, S., C. L. Barrett, and M. W. Olesen. Dynamical hierarchies-A summary. No. LA-UR-96-660; CONF-960284-1-Summ. Los Alamos National Lab., NM (United States), 1996.
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This paper summarizes some of the problems associated with the generation of higher order emergent structures in formal dynamical systems. In biological systems, higher order hyperstructures occur both in an intuitive and a formal sense: monomers, polymers, membranes, organelles, cells, tissues, organs, etc. constitute an observable hierarchy, apparently generated by the underlying biomolecular process. However, in models and simulations of these systems, it has turned out to be quite difficult to produce higher order emergent structures from first principles. The first problem is to agree on what a higher order structure is. An emergent structure can be defined through an introduction of an observational function. If a property can be observed in the dynamics, but not at the level of the fundamental first order interacting structures, we define it to be emergent. It is well known that second order structures occur relatively easy in simulation, so the problem is how to proceed to third and higher order without external interference. A third order structure is defined through the interaction of second order structures forming a new observable not found at the lower levels.