Exponents of Growth - Systematic Design for Emergence in Cellular Nonlinear Networks - page 85

Fig. 5.14. A set of histograms depicting the distribution of the exponent of growth “U” for
the “2a4” family of universal cells (all possible Boolean functions with four inputs) distributed
on a 2D grid topology

Table 5.1 lists the distribution of genes among the “2s5” family and the corre-
sponding percentages of their membership to the behavioral categories introduced
previously:

Table 5.1. Distribution of genes among the behavioral categories defined in Sect. 5.1

Category (a) Passive (b) Stable

near edge

(c) Edge (d) Unstable

near edge

(e) “Nested”
near edge

(f) Un-
stable

Number
of genes:

43 149 321 10 4 497

% 4.20 14.55 31.35 0.98 0.39 48.54

Only a small fraction of the entire set of genes represent highly complex
emergent cellular systems. Table 5.2 lists 10 genes from each category (in case of
category “e” they are only 4). Among all 10 genes in the “interesting” class d),
gene 49 was found to have interesting properties making possible to build excit-
able temporal membranes with some interesting applications in signal recognition,

as detailed in Sect. 8.3 (Fig. 8.9).

Table 5.2. A list of 10 genes from each behavioral category

Category (a) (b) (c) (d) (e) (f)

ID U ID U ID U ID U ID U ID U

107
128
136
144
152
256
264
272
280
862

0
0
0
0
0
0
0
0
0
0

104
108
111
112
115
116
119
120
123
124

0.46
0.60
0.64
0.13
0.11
0.67
0.34
0.47
0.25
0.67

131
134
135
138
139
142
143
146
147
150

1
1
1
1
1
1
1
1
1
1

41
49
69
81
101
375
463
471
487
503

4.98
1.36
2.98
1.18
1.85
2.08
1.18
1.40
1.29
1.29

330
341
682
693

4
5
5
4

418
419
421
422
423
425
426
427
429
430

44.04
15.28
46.49
44.04
6.02
46.49
44.04
15.28
46.44
44.04