Emergence, Locating and Measuring It - Systematic Design for Emergence in Cellular Nonlinear Networks - page 48

Now let's use the program ca_sim.m or any other convenient simulator presented
in the previous chapter to simulate the entire family of 1,024 CAs corresponding
to the label 1s5 . In order to do so, simply type the following line in the Matlab
console:

>> for ID=1:1024; [x0]=ca_sim('mid101','1s5',150,ID,1,1,0); axis image; waitforbuttonpress; end

The CA evolution is shown as a spatio-temporal figure with 150 iterations on
the vertical axis, while the states of all 101 cells composing the cellular automata
are displayed horizontally. The initial state contains all “black” cells except some
11 cells in the middle assigned with random states (and probability ½).
Let now consider different CA behaviors from each of the classes mentioned
above. First let's start with examples belonging to Class I, as displayed in Fig. 4.1.
Although they all fit Wolfram's definition (the CA converges towards an equilib-
rium with all cells in the same state), at a closer look they exhibit different com-
plexities and even emergence.

(a) (b) (c)

(d) (e)

Fig. 4.1. Different behaviors of CAs belonging to Wolfram's Class I