Self-Reproduction of Dynamical Hierarchies in Chemical Systems

In biological systems higher order hyperstructures seem to occur both in an intuitive and a formal sense. Starting at a molecular level of description we have: molecules, polymers, supramolecular structures, organelles, cells, tissues, organs, etc. but in models and simulations of these systems it has turned out to be difficult to produce higher order emergent structures from first principles. We demonstrate how monomers (first order structures) compose polymers (second order structures) which in turn can assemble into ordered, micellar (third order) structures, which in turn can self-reproduce as they catalyse the formation of additionaly amphiphilic molecules. Processes of this particular kind have probably been important for the origins of life. Our molecular system is defined on a 2-D lattice and the dynamics is modeled as a discrete automaton. In this system all interactions (electromagnetic forces) are decomposed and communicated via propagating information particles. Each lattice site has an associated data structure where molecules are represented by inforamtion particles and their associated force fields (excluded volumes, kinetic energies, bond forces, attractive and repulsive forces) are decomposed and propagated as information particles as well. The propagation and interaction rules are derived from Newton's Laws. Based on this self-assembly and self-reproduction example it is possible to extract some of the principles involved in the generation of higher order (hyper-) structures and relate them to dynamical systems. An Ansatz for generating higher order structures in formal dynamical systems is given.