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Fig. 5. The regular 30-cluster found for I = 30. It has the shape of a 6-dimensional
hypercube projected into the plane. Figure produced using yEd [18].
All of these patterns can be explained considering modules with more than
two determinant bits. As explained above, the dimension d M of the module is
just the number of determinant bits. Many results for the 2-cluster pattern also
hold for the patterns of higher complexity. Given a module dimension d M the
number of groups, and their (relative) sizes can be calculated and arranged as
in Pascal's triangle, cf. Table 2.
Table 2. Pattern modules in G (2)
12
observed patterns in G (2)
12
|S i |/ 2 d−d M
d M
with i ∈{ 1 ,...,d M +1 }
0
1
1
1
1
2
1
21
-cl ster
3
13 3
1
24-cluster
4
1
4
641
-cl ster
5
1 5 0 05 1
6
1
6
15
20
15
6
1
30-cluster
The third column shows examples of patterns that are really observed in
simulations on G (2)
12 and that can be explained by means of the pattern modules of
the respective dimension. The bold numbers indicate groups which are occupied
in these example patterns. For instance, the 2-cluster pattern described above
has three groups: one occupied group, a group of potential hubs, which is twice
as large, and a group of stable holes.
The possible links between vertices of different groups are -of course- con-
strained by the mismatch rule.
 
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