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

Michael D. Vose}
Computer Science Department 
University of Tennessee 
Knoxville, TN 37996 

Alden H. Wright
Computer Science Dept.
Univ. of Montana
Missoula, MT 59812
(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.


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