Predicting Emergence from Cell’s Structure - Systematic Design for Emergence in Cellular Nonlinear Networks - page 109

7

Predicting Emergence from Cell's Structure

7.1 Introduction

In Chaps. 4 and 5 several measures for emergence were introduced and as seen in
Chap. 6 they can be integrated in an intelligent sieving process to select among a
huge number of possible cells only those leading to CA dynamics that is meaning-
ful for certain desired tasks. Still, evaluating the measures of emergence needs
extensive running of the CA system for each member of the family, giving thus
important limitations in terms of computing time. While the CA is mainly deter-
mined only by the cell structure (assuming that all cells are identical) and by the
interconnection between cells (also assumed to be regular and simple) it would be
reasonable to investigate the possibility to predict the CA behaviors solely based
on the structure of the cell. That will dramatically reduce the computation time

eliminating the need to simulate the entire CA.

The main questions around which this chapter is build are the following:

- Is there any possibility to predict the CA behavior without simulating the

cellular model?
- Are there any relationships between the cells' structure as described by its
binary gene and the observed behaviors of the underlying CA?
- Can we establish a mapping between the gene space and a hypothetical
“behavior space”, which may be eventually described by the set of com-
plexity measures ( U , Trans , Var , Clus )?
In the case of continuous-time Reaction-Diffusion cellular systems, the theory
of local activity [7] was already successfully employed to detect regions of com-
plexity called “edge of chaos” in the cell parameter space by simply examining the
cell [9, 10, 11]. However, in those cases it was not possible to predict precisely if a
cell with parameters within the “edge of chaos” region will give emergent behav-

iors. The reason stands in the existence of some additional parameters related to the
coupling between cells, the diffusion coefficients. These parameters was not inclu-
ded in the local activity theory and therefore they should be experimentally ad-
justed to obtain emergent behaviors.

Within this chapter we will investigate the case of discrete binary time cellular
automata and we will assume the same connectivity (simply defined by the