  This paper applies Algorithmic Information Theory to simple examples of
replication processes to illustrate how replicating structures can generate and
maintain order in a non equilibrium system. Variation in replicating structures
enhances the system's ability to maintain homeostasis in a changing environment
by allowing it to evolve to a more restricted region of its state space.
Stability is further enhanced when replicating systems develop dependencies, by
sharing information or resources. Such systems co-evolve, becoming more
independent of the external environment. Nested systems have a hierarchy of
dependency but have low algorithmic entropy as they are in principle simpler to
describe algorithmically. Nesting of replicating systems offsets the need for
increased variety by allowing the structures to increase in organizational
complexity with little increase in algorithmic entropy. Chaitin's d-diameter
complexity provides a measure of the level of order in nested replicating
systems.
