Cellular and Natural Computing Models and Software Simulation - Systematic Design for Emergence in Cellular Nonlinear Networks - page 37

than lower complexity classes ( m =1) display “low frequency” features, i.e. less

transitions from 0 to 1, while highest complexity cells ( m ) display “high fre-
quency” features (many transitions from 0 to 1 and viceversa). The most numer-
ous are the functions with an intermediate degree of structural complexity. These
functions exhibit a wide-spectrum of frequencies (assuming that a certain spectral
transform is applied to the binary strings representing the functions). It is interest-
ing to note that there is a relation between the nature of the emergent phenomena
in the global array and the local structural complexity of the cells.

3.5 Modeling and Simulation of Semitotalistic Cellular
Automata

In the following we will expose the concepts of emergence and some practical
tools for locating emergence using cellular automata based on semitotalistic cells.
The piecewise-linear representation discussed above represents not only a conven-
ient solution for the hardware implementation of such systems but also a solution
for building fast simulators using the interpreter language atlab. hile defining
the cell as a table will require a call to the table for each particular cell location
(thus requiring many slow atlab accesses

to the table function, the nonlinear

(piecewise-linear) description in (3.) gives directly a vectorial atlab function

which computes the outputs for all cells internally in the precompiled atlab
functions. Of course, for a C/C+ or other compiler-based language implementa-
tion of the cellular system is more convenient to consider the table-definition of
the cell. The atlab program for implementin

g the semitotalistic cellular automata

is presented next:

function [x0]=semit_ca(name,steps,ID,dig,eps,vis,f);
% name - character string conatining the initial state
% steps - number of discrete time steps used in simulation
% ID - the decimal representation of the ID
% dig - =1 implements Boolean cells; =0 implements continuous state cells
% eps - a perturbation value to investigate emergence
% in the case of continuous state cells (normally 0)
% vis - =1 succesive steps of simulation are visualized; =0 not visualized
% f>0 fraction of randomized links (for the Small-World model)
% f=0 the simple cellular model
%------------------------------------------------------------------
% x0 - the 2D array of cells in the end
%------------------------------------------------------------------
% Load the set of parameters (b,t0,t1,..) for the given ID
load rezult; a=Btab(ID+1); ntr=Ntrtab(ID+1); mm=ntr-1; tr=Ttab(ID+1,:);
% Mutate tr with eps
tr(1)=tr(1)+eps;
% Compute the z offset in (8)