Exponents of Growth - Systematic Design for Emergence in Cellular Nonlinear Networks - page 84

5.3 Distribution of Exponents of Growth Among Families
of Genes
It would be interesting to see how emergent properties measured by the exponent of
growth U are distributed among an entire family of genes. Histograms may give
such a synthetic view, as seen in Fig. 5.13, where two families of semi-totalistic
cells are considered (the “2s5” and the “2s9”). Note the similarities between the
two distributions. A large fraction of genes is related to “fast growing” emergent
phenomena (with U around 49). Interesting emergent behaviors are located within
the range 0<U<20 (detailed in the figure). Within this range, there is a large num-
ber of genes “on the edge” (i.e. with U = 1) and also a large number of genes with
U = 15 (explosive behaviors but with half of the “speed of light”). The most inter-
esting genes are among those located in the range 1<U<15.
Fig. 5.13. A set of histograms depicting the distribution of the exponent of growth “ U ”
among two families (“2s5” and “2s9”) of semi-totalistic cells on a 2D grid topology
What are the possibilities to increase the fraction of interesting behaviors in the
“unstable near edge” class? As seen from Fig. 5.13, for semi-totalistic cells, add-
ing more inputs (as in the case of “2s9” compared to “2s5” families) the fraction
of genes within the “interesting” region grows. If there is no semi-totalistic restric-
tion at all (universal cells), an even higher increase of that fraction is observed, as
seen in Fig. 5.14 where the the “2a4” family was considered (with a four input cell
on a 2D grid topology and a neighborhood formed by the North, South, West and
East cells).