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each potential site in both the bit-string and 2D universes. If the space is really
separated into tolerant and intolerant zones, then we expect to find a distribution
in which a large number of the cells receive little or no field, and the remainder
receive high field. Figures 5 and 6 illustrate the result for both shape-spaces.
The histograms obtained show very similar distributions — in both cases show
a power-law distribution (e.g
y
=
x
−a
) is observed. For the 2D shape-space, as
expected, a large number of sites receive no field whatsoever. The remainder
receive a spread of field-values, indicating their reactivity. Thus, the different
shape-spaces appear to
both
support the notion that tolerant and non-tolerant
regions should be observed in the shape space. Yet we have just shown in the
previous section that this is not the case! In the next section, we offer an expla-
nation for this effect.
5
Complementarity Is not the Same as Similarity
An explanation for the inability of the networks obtained in bit-string shape
space can be gleaned by first considering the behaviour of a network in 2D shape-
space with an anity function based on
similarity
. Consider figure 7 which shows
a snapshot of a network obtained after 10000 iterations of a network in which
cells
a
and
b
stimulate each other if
b
lies within a recognition region centered
on
a
. Contrast this picture with the snap-shot of the network obtained with a
complementary anity function shown in figure 1. There is now no separation
of the physical space into distinct zones; rather we see a “Jackson Pollock” like
distribution of cells throughout the shape-space. Figure 8 illustrates the field
now received by hypothetical cells placed at each potential site in the network,
and those sites at which the total stimulation received is greater than 10,000.
The field is now much more homogeneous across the network, caused by the
Fig. 7.
Snapshot of a network obtained after 10000 iterations of a network in 2D shape-
space with a similarity anity function
