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FIGURE 6. Symbolization of a finite state
machine by a computational tile. Input
region white; output region black.
tion,” . The operations performed by the
i
th tile shall be those of a finite
state machine, but different letters, rather than subscripts, will be used to
distinguish the two characteristic functions. Subscripts shall refer to tiles.
yf
=
(
xz
,
)
i
i
i
i
=
(
)
(48)
zgxz
,
i
i
i
i
Figure 7/I sketches the eight possible ways (four each for the parallel and
the antiparallel case) in which two tiles can be connected. This results in
three classes of elementary tesselations whose structures are suggested in
Fig. 7/II. Cases I/1 and I/3, and I/2 and I/4 are equivalent in the parallel
case, and are represented in II/1 (“chain”) and II/2 (“stack”) respectively.
In the antiparallel case the two configurations I/1 and I/3 are ineffective,
for outputs cannot act on outputs, nor inputs on inputs; cases I/2 and I/4
produce two autonomous elementary tesselations
A
= [
a
+
,
a
-
}, distinct only
by the sense of rotation in which the signals are processed.
Iterations of the same concatenations result in tesselations with the fol-
lowing functional properties (for
n
iterations):
1.
Stack
n
Â
1
(
)
nT
:
y
=
f
x
,
z
(49)
i
i
i
2.
Chain
(
(
**
)
*
)
(
()
()
)
Tyf
n
:
=
f
f
...
xz
n
*
,
n
*
...
zzz
(50)
nn
-
1
n
-
2
n
-
2
n
-
1
n
3.
A
= {a
+
,a
-
}
aa
aa
+-
aa
aa
++
˛
=
˛
π
0
0
-+
--
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