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FIGURE 7. Elementary tesselations.
(i)
Stack
nA
n
(51)
(ii)
Chain
A
n
(52)
Introducing a fourth elementary tesselation by connecting horizontally
T
Æ
A
Æ T, or
TAT
, we have
4.
TAT
(i)
Stack
n
(
TA
n
T
)
(53)
(ii)
Chain
(
TAT
)
n
(54)
Figure 8 suggests further compositions of elementary tesselations. All of
these contain autonomous elements, for it is the presence of at least two
such elements as, e.g., in (
TAT
)
2
, which constitute a finite function machine.
If none of these elements happens to be “dead”—i.e., are locked into a
single state static equilibrium—they will by their interaction force each
other from one dynamic equilibrium into another one. In other words,
under certain circumstances they will turn each other from one trivial finite
function machine into another one, but this is exactly the criterion for being
a nontrivial finite function machine.
It should be pointed out that this concept of formal mathematical enti-
ties interacting with each other is not new. John von Neumann (1966) devel-
oped this concept for self-reproducing “automata” which have many
properties in common with our tiles. Lars Löfgren (1962) expanded this
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