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of
,
1
parameters. n example is 63* belonging also to the case
m=
1
(linearly separable) which leads to the useful emergent function of
edge detection
.
Other families of cells can be obtained as well by replacing
s
b
t
,...
t
m
5
>
@
with
and taking various
D
y
t
y
t
y
t
y
t
D
¦
a
1
y
y
1
a
2
3
4
5
i
i
i
i
i
2
binary values for
>
@
others than
>
@
(i.e. inverting some of
A
a
,
a
,
a
,
a
A
0
2
3
4
5
the neighboring inputs). For instance one may take
>
@
A
.
sing the above transformations it follows that there are possible 32 different
families of 1,024 functions each. ll these
1
families have the same common set of
s
,
b
,
t
,...
t
parameters.
1
m
3.4.3 Structured Universes of Cells
Figure 3.4 depicts the whole set of 1,024 functions from the basic family of
semitotalistic functions with five inputs grouped into complexity (
m
) classes. Note
than lower complexity classes (
m
=1) display “low frequency” features, i.e. less
Fig. 3.4.
The structured universe of semitotalistic oolean functions. ost of the 1,024
functions are in the categories
m
4
and
m
5
. Only 38 of them are linearly separable
(
m
1
) and only two functions have the highest possible level of complexity
m
8
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