State aggregation and population dynamics in linear systems
posted 8/16/04
Jonathan E. Rowe}
School of Computer Science
University of Birmingham
Birmingham B15 2TT
Great Britain
J.E.Rowe@cs.bham.ac.uk
Michael D. Vose}
Computer Science Department
University of Tennessee
Knoxville, TN 37996
USA
vose@cs.utk.edu
Alden H. Wright
Computer Science Dept.
Univ. of Montana
Missoula, MT 59812
USA
wright@cs.umt.edu
(406) 243-4790
This paper has been accepted for publication in the journal
Artificial Life. The version posted here may differ slighly
from the final published version. An date for publication has not
been set.
Abstract
We consider complex systems that are comprised of many interacting elements,
evolving under some dynamics. We are interested in characterising the ways
in which these elements may be grouped into higher-level, macroscopic states
in a way which is compatible with those dynamics. Such groupings may then be
thought of as naturally emergent properties of the system. We formalise this
idea, and, in the case that the dynamics are linear, prove necessary and sufficient
conditions for this to happen. In cases where there is an underlying symmetry
amongst the components of the system, group theory may be used to provide a strong
sufficient condition. These observations are illustrated with three artificial life
examples.