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FIGURE 39. First and second order neighbors in
a body centered cubic lattice (two dimensional
“cube”).
On the other hand, the input information on a sensory organ with
N
binary
receptors is
HN
IN
=
.
A sensory network is properly matched to its structure if
(119)
HH
IN
=
,
F
or, in other words, if its input information corresponds to its computation
capacity stored in its structure. We have with eqs. (116), (117), (119):
2
=
Ó
2
2
4
k
square lattice
hexagonal lattice
N
(
)
3
kk
+
1
The following table relates the size of the sensory organ that is properly
matched to its computing network which utilizes
k
th order neighbors, con-
stituting a receptor field of
n
elements:
Nk
s
k
h
n
s
=
n
h
10
2
1.29
1.07
6.65
10
4
1.82
1.68
13.2
10
5
2.04
1.91
16.7
10
6
2.24
2.12
20.0
10
7
2.41
2.31
23.2
10
8
2.58
2.52
26.5
This table indicates that in an eye of, say, 10
6
receptor elements a receptor
field of more than 20 elements is very unlikely to occur.
In conclusion it may be pointed out that the evolution of abstracting
network structures as a consequence of interactions with an environment
gives rise to new concepts of “memory” which do not require the faithful
recording of data. In fact, it can be shown that a theory of memory that is
based on mechanisms that store events is not only uneconomical bordering
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