Exponents of Growth - Systematic Design for Emergence in Cellular Nonlinear Networks - page 88

Fig. 5.16. An effect of the “small-worlds” model: Until the fraction of random connections
f reaches a bifurcation value (here 0.02) the behavior is of the “edge” type, i.e. drawing
squares around the main clusters. Beyond the bifurcation value, the behavior becomes an
“unstable” or explosive one
system will evolve towards the easy to detect state with “all cells black”. A similar
effect is described in Fig. 5.17 for gene ID = 801 (also belonging to the “edge”
category for the pure cellular model).
We may assign a social meaning to the emergent phenomena depicted in
Fig. 5.17. When f grows beyond a certain value (here 0.1) the “isolated civiliza-
tions” represented in the initial state by the three isolated spatial clusters will col-
lapse into a unique global “civilization” as a result of an increasing fraction of the
distant communications
Note that for the simulations shown in the first two rows in Fig. 5.17, the evo-
lution is of an “edge” type, with some dynamic clusters evolving around the initial
state spatial clusters but eventually stabilizing their boundaries after several hun-
dreds of iterations. Although long-distance communication exists it does not yet
have a dramatic effect on altering the boundaries constructed in the first iterations.