Predicting Emergence from Cell’s Structure - Systematic Design for Emergence in Cellular Nonlinear Networks - page 110

neighborhood topology) among all cells. Therefore there is no connectivity

parameter and the behavior should be entirely determined by the cells' structure

and its neighborhood.

7.2 Relationships Between CA Behavior and the Boolean
Description of the Cell

Let us focus on the following question: Are there any relationships between the
cells' structure as described by its binary gene and the observed behaviors of the
underlying CA?

Fig. 7.1. A parametrization of the 2s5 family with respect to the U measure of emergence.
A particular cell is depicted with a gray color ranging from white for “passive” ( U < 1) to
black for “highly unstable” ( U >> 1) and its corresponding pixel is located in the 32×32
tableau according to its binary ID. Note the regularity of the distribution, indicating that a
connection between cells' structure and behavior may be established

In order to grasp an answer to this question let us consider a matrix representa-
tion for all 1,024 Boolean cells from the “2s5” family, as seen in Fig. 7.1. In the
next we will call such a representation a parametrization P as defined in other
works [74]. Note that in other related works [7] a similar concept was introduced
under the name “decoding card”.
A parametrization matrix P is defined as a visually convenient form of represent-
ing an entire family of cells where each matrix element is uniquely associated to

P , j

a member of the CA family. The value of

P , is associated with a behavioral quality
e.g. one of the previously defined measures of emergence or with a fuzzy member-

j