Exponents of Growth - Systematic Design for Emergence in Cellular Nonlinear Networks - page 79

Note also that after the first iteration the active square in the middle becomes a
negate of the initial, a process which continues with period 2, but which can be
taken in consideration by the program evaluating the size of the cluster. It is easy
to prove that such evolutions always happen for odd values of the cell ID.
Let us consider a more detailed evolution of a random pattern using this gene
(ID = 471) in Fig. 5.6:

Fig. 5.6. Slow evolution towards a self-making (stable) pattern for gene ID = 471

In the above case a stable pattern (cluster) emerges after sufficient iterations
(about 330), much like a living being develops its “far from equilibrium” stable
state from an embryo.

d U , nested). This is another example of unstable near the edge of chaos
behaviors in which “nested patterns” (as referred in [55]) occur. It is characterized
by a relatively fast growth until a group of 4 or 5 initial state clusters (identical
with the original one) emerge. Usually there is a power of 2 number of iteration be-
tween states of the CA characterized by the presence of several “clones” of the ini-
tial state spatial cluster. Such phenomena were characterized by Fredkin in [82] as
trivial examples of self-reproduction (see Fig. 5.7).

(e) (

4 d 5