# Self-Reproduction of Dynamical Hierarchies in Chemical Systems

Bernd Mayer

University of
Vienna, Austria, USA

http://asterix.msp.univie.ac.at/local-link
Steen Rasmussen

Los Alamos
National Laboratory and Santa Fe Institute, USA

### Abstract

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 additional 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 information 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.