Information Technology Reference
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3.3.3 Simulation of Standard Cellular Neural Networks
As we already discussed, simulating the CNN reduces to the particular case of
simulating a coupled GCA for only one discrete time step. The GCA_C_CELL is
activated and it will simulate the CNN. Its parameters and even novel CNN mod-
els can be easily simulated by properly re-editing the GCA_C_CELL.M file.
3.4 Nonlinear Representation of Cells
In the next we will consider GCAs with uncoupled Boolean cells (i.e. having only
two possible states). Such GCAs correspond to cellular automata (CA) with two
states per cell. Even in this simple case, considering a nine cell neighborhood,
there is a huge number of
9
2
512
of possible cells. Searching for emergent
behaviors in such a huge cell space is impossible. Arguments extensively pre-
sented in Chap. 4 indicates the need to restrict the cell model so that the search
space can be reduced to a much reasonable number of cells.
The
semitotalistic cell
is such a convenient model. In a semitotalistic cell the
output depends only on two numbers:
D
which represents the contribution (sum-
mation) of all neighboring cells (except the central cell). Assuming that cell out-
puts belong to the
^
2
2
set it follows immediately that
^
1
and therefore
0
D
0
,..,
n
^
it has only
n
discrete values. The second number
E
can take only two dis-
crete values and represents the contribution of the central cell. It follows that for a
cell with
n
inputs there are only 2
n
possible combinations of inputs, each corre-
sponding to an output chosen among two values. Therefore there are only
0
2
n
2
semitotalistic cells with
n
inputs. For typical neighborhood sizes
n
the result is a
tractable number of possible cells
.
For instance in the case of a 5-cell neighbor-
hood there are only 1,024 possible cells to investigate while in the case of 9-cells
neighborhood there are 262,144 possible semitotalistic cells. Let us first consider
the case of a 5-neighborhood cell.
Each cell output
y
,
1
within the cellular system grid can have either 0 or 1 value
and it corresponds to a black or a white pixel respectively in an image to be processed.
The image is applied as an initial state
i
j
^
i
,
j
i
,
j
, where the indexes
point
Y
(
0
y
(
0
1
to the row and the column, and the subscript “1” identify the central cell in a
neighborhood (as in Fig. 3.1). Using cells defined by gene
G
the automaton is run for
1
T
1
iterations, then the gene may be changed into
G
2
and run another
T
2
iterations and
so on.
The sequence
>
@
3
will define an overall processing
function, i.e. a “program”. Note that unlike in the case of traditional computing
systems where programs are defined by algorithms, here we need to search for
those emergent genes
G
,
T
,
G
,
T
,...
G
m
T
,
1
1
1
2
m
G
,..
1
and associate the underlying processing with certain
useful information processing functions. The above is the subject of “designing for
G
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